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Contents

FDA models

FUNCTIONAL DATA ANALYSIS

Functional model

• Plot the metrics
• Outlier detection
• Functions for fitting the functional regression model

MODELS for Heart Rate

• HR ~ alt + noise
• HR ~ alt + noise + Sex (const basis for sex)
• HR ~ alt + noise + Sex (B spline for sex)
• HR ~ alt + noise + temp (Empatica)
• HR ~ alt + noise + temp (Entrant)
• HR ~ alt + n + t + acc
• HR ~ alt + n + t + speed
• HR ~ alt + n + t + steps
• HR ~ alt + body_temp
• HR ~ alt + noise + body_temp
• HR ~ alt + noise + PM25
• HR ~ alt + temp + PM25
• HR ~ alt + noise + PM1
• HR ~ alt + temp + PM1
• HR ~ alt + n + acc + body_temp
• HR ~ air pressure + noise
• HR ~ air pressure + noise + air temp
• HR ~ alt + n + acc + Sex
• HR ~ alt + speed + Sex
• HR ~ alt + steps + Sex
• HR ~ alt + n + acc
• HR ~ alt + n + speed
• HR ~ alt + n + steps
• HR ~ alt + n + acc + PM25
• HR ~ alt + n + speed + PM25
• HR ~ alt + n + steps + PM25
• HR ~ alt + n + acc + PM1
• HR ~ alt + n + speed + PM1
• HR ~ alt + n + steps + PM1
• HR ~ alt + n + body_temp + PM25
• HR ~ alt + n + body_temp + PM1
• HR ~ alt + speed + PM25
• HR ~ alt + speed + PM1
• Model comparison

MODELS for EDA

• EDA ~ alt + noise
• EDA ~ alt + noise + Sex (B spline for sex)
• EDA ~ alt + noise + temp (Empatica)
• EDA ~ alt + noise + temp (Entrant)
• EDA ~ alt + n + t + acc
• EDA ~ alt + n + t + speed
• EDA ~ alt + n + t + steps
• EDA ~ alt + body_temp
• EDA ~ alt + noise + body_temp
• EDA ~ alt + noise + PM25
• EDA ~ alt + temp + PM25
• EDA ~ alt + noise + PM1
• EDA ~ alt + temp + PM1
• EDA ~ air pressure + noise
• EDA ~ air pressure + noise + air temp
• EDA ~ alt + n + acc
• EDA ~ alt + n + speed
• EDA ~ alt + n + steps
• EDA ~ alt + n + acc + PM25
• EDA ~ alt + n + speed + PM25
• EDA ~ alt + n + steps + PM25
• EDA ~ alt + n + acc + PM1
• EDA ~ alt + n + speed + PM1
• EDA ~ alt + n + steps + PM1
• EDA ~ alt + n + body_temp + PM25
• EDA ~ alt + n + body_temp + PM1
• EDA ~ noise + temp + body temp
• EDA ~ alt + noise + temp + body temp
• Model comparison

FUNCTIONAL DATA ANALYSIS

In the previous code, we preproccessed the data so they are now in the right form for functional data analysis. Because the recordings seem to have some common shape in most metrics, we want tu use tools of FDA to study relationships in data.

The procedure of the analysis is as follows:

1. load the data,
2. transform them into variable that can be used for FDA,
3. smooth the measurements,
4. plot smoothed curves and
5. apply some advanced analysis (functional linear model, functional ANOVA, etc.).

Load libraries: Load important libraries which we need for further analysis. We use suppressPackageStartupMessages() function to suppress messages and warnings.

# libraries
library(ggplot2) |> suppressPackageStartupMessages() |> suppressWarnings()
library(dplyr) |> suppressPackageStartupMessages() |> suppressWarnings()
library(tidyr) |> suppressPackageStartupMessages() |> suppressWarnings()
library(openxlsx) |> suppressPackageStartupMessages() |> suppressWarnings()
library(lubridate) |> suppressPackageStartupMessages() |> suppressWarnings()
library(viridis) |> suppressPackageStartupMessages() |> suppressWarnings()
library(fda.usc) |> suppressPackageStartupMessages() |> suppressWarnings()
library(fda) |> suppressPackageStartupMessages() |> suppressWarnings()
library(patchwork) |> suppressPackageStartupMessages() |> suppressWarnings()
library(fdapace) |> suppressPackageStartupMessages() |> suppressWarnings()
library(GET) |> suppressPackageStartupMessages() |> suppressWarnings()

# options for graphics
options(repr.plot.width = 20, repr.plot.height = 10, repr.plot.res = 300)

Change working directory: Change the current working directory if needed. New directory should contain the same folders as City_measurements_preprocessed folder.

setwd('Z:/GAMU-STRECITY/04_Codes/FDA')

Load important files: To be able to execute the code below, we need some important files (they contain information about times and segments).

## data frame of time points with date format
df_times_date <- read.xlsx("Z:/GAMU-STRECITY/04_Codes/FDA/auxiliary data/time_points.xlsx")
## data frame of time points without date format
df_times <- read.csv('Z:/GAMU-STRECITY/04_Codes/FDA/auxiliary data/time_points.csv', row.names = NULL)[, 2:5]
## data frame of time segments
seg_tp_load <- read.xlsx("Z:/GAMU-STRECITY/04_Codes/FDA/auxiliary data/time_points_segments.xlsx")
# change characters to dttm format
for(j in 2:dim(seg_tp_load)[2]) {
    seg_tp_load[, j] <- seg_tp_load[, j] |> as.POSIXct()
}
seg_tp <- seg_tp_load
## data frame of registered times
Times_of_segments <- read.csv('recordings/registration/Times_of_segments.csv')[, c(2, 3)] |> 
        mutate(time = as.POSIXct(time))

participant_info <- read.xlsx("Z:/GAMU-STRECITY/04_Codes/FDA/auxiliary data/participant_info.xlsx")

Center the EDA curves: In the preprocessing step, we center the Heart Rate curves to remove individual differences in mean heart rate (by subtracting each subject’s mean heart rate from the entire curve so that all HR curves are centered at zero). The same approach can be applied to EDA curves. To enable this, set the parameter center_EDA_curves = TRUE; otherwise, use center_EDA_curves = FALSE.

center_EDA_curves <- TRUE

Note: In the section Air pressure data below, we introduce and describe in details important steps in the process of converting discrete measurements to functional type of data. We have to load the data, select appropriate participants, smooth the data (transform, choose optimal smoothing parameter $\lambda$, smooth the curves), plot them and optionally calculate and plot the derivatives of curves.

In the next section, we define a function that does the described process above automatically. Then, we can apply the smoothing to other metrics and finally work with the functional data (define models, etc.).

Functional model

Finally, we can fit the functional linear model. Generally, we have two options for modelling the dependence of two functional objects $-$ concurrent model and fully functional regression model.

1. Concurrent model: this model relates the value of outcome $y$ in time $t$ (i.e. $y_i(t)$) to the value of covariates $z_j$ at the same time $t$ (i.e. $z_{ij}(t)$). Therefore, the model can me described as $$y_i(t) = \beta_0(t) + \sum_{j=1}^K\beta_j(t) z_{ij}(t) + \varepsilon_i(t) \tag{1}$$ for $K$ covariates.
2. Fully functional regression model: we can generalize the previous model by taking $K\rightarrow \infty$. Then, we have parameter $\beta_1(t, s)$, which defines the dependence of $y_i(t)$ on covariate $z_i(s)$ at each time $t$. The model is decribed as $$y_i(t) = \beta_0(t) + \int_{\Omega_t}\beta_1(t, s) z_{i}(s)\text d s + \varepsilon_i(t) \tag{2},$$ where ${\Omega_t} = \{s|s<t\}$ for historical linear model and ${\Omega_t} = \{s\ \text{unconstrained}\}$ for full integration regression.

We will use the model $(1)$.

Convert to one fd object: First, we have to define appropriate data objects. Because different curves are defined by the different number of observed points, but by the same basis, we should be able to merge the curves into one fd object. We have to do this for outcome and also for covariates. Therefore, we define function convert_to_fd() that will do this for input BSmooth object, which is an output of data_to_function() function.

convert_to_fd <- function(BSmooth) {
    # first, we create data frame, in columns are the coefficients of B-spline basis
    merged_coefs <- BSmooth[[1]]$fd$coef
    for (i in 2:length(BSmooth)) {
        merged_coefs <- cbind(merged_coefs, BSmooth[[i]]$fd$coef)
    }
    # add names to columns
    colnames(merged_coefs) <- names(BSmooth)
    # now, create fd object
    merged_fd <- fd(coef = merged_coefs, basisobj = BSmooth[[1]]$fd$basis)
    
    return(merged_fd)
}

# options for graphics
options(repr.plot.width = 20, repr.plot.height = 10, repr.plot.res = 100)

Now, we load the files from smooth_data folder.

files_load <- list.files('recordings/smooth_data')
files_load

1. 'Acceleration_smooth_norder1.RData'
2. 'Acceleration_smooth_pos.RData'
3. 'Air_pressure_smooth.RData'
4. 'Altitude_smooth.RData'
5. 'EDA_smooth.RData'
6. 'Entrant_AIR_TEMP_2_smooth.RData'
7. 'Entrant_BODY_TEMP_3_smooth.RData'
8. 'GEO_altitude_smooth.RData'
9. 'GEO_cadence_smooth.RData'
10. 'GEO_HR_smooth.RData'
11. 'Heart_rate_smooth.RData'
12. 'Noise_smooth.RData'
13. 'Pollution_PM1_smooth.RData'
14. 'Pollution_PM10_smooth.RData'
15. 'Pollution_PM25_smooth.RData'
16. 'Speed_smooth.RData'
17. 'Speed_smooth_norder1.RData'
18. 'Steps_smooth_norder1.RData'
19. 'Steps_smooth_norder4.RData'
20. 'Temperature_smooth.RData'

files_load <- files_load[!files_load %in% c(
    'Acceleration_smooth_nopos.RData', 'Acceleration_smooth_pos.RData', 
    'GEO_cadence_smooth.RData', 'Pollution_PM10_smooth.RData',
    'Steps_smooth_norder4.RData', 'Speed_smooth.RData'
    )]
for(i in files_load) {load(paste0('recordings/smooth_data/', i), verbose = TRUE)}

Loading objects:
  BSmooth_accel
Loading objects:
  BSmooth_air_pressure
Loading objects:
  BSmooth_altitude
Loading objects:
  BSmooth_EDA
Loading objects:
  BSmooth_air_temp
Loading objects:
  BSmooth_body_temp
Loading objects:
  BSmooth_GEO_altitude
Loading objects:
  BSmooth_GEO_HR
Loading objects:
  BSmooth_HR
Loading objects:
  BSmooth_noise
Loading objects:
  BSmooth_pollution1
Loading objects:
  BSmooth_pollution25
Loading objects:
  BSmooth_Speed
Loading objects:
  BSmooth_Steps
Loading objects:
  BSmooth_temp

Function for plotting the functional observations.

plot_fd <- function(fd_obj, ylab = 'Value', xlab = 'Time') {
    # add to graphs vertical lines indicating segments
    important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
    
    rangeval <- fd_obj$basis$rangeval
    time_vec <- seq(rangeval[1], rangeval[2], by = 1)
    
    # data frame with evaluated curves
    df_plot_smooth <- eval.fd(fd_obj, evalarg = time_vec) |> 
        as.data.frame() |> 
        pivot_longer(cols = everything(), names_to = "ID", cols_vary = 'slowest') |>
        mutate(time = rep(time_vec, length(unique(ID))),
               ID = substr(ID, 4, 7))
    
    df_plot_smooth |> ggplot(aes(x = time, y = value, colour = ID)) + 
        geom_line(linewidth = 1) + 
        # facet_wrap(~ID, nrow = 2) +
        geom_vline(xintercept = important_times, linewidth = 0.6, col = 'grey', linetype = 'dashed') +  
        theme_bw() + 
        theme(panel.grid.major.x = element_blank(),
              panel.grid.minor = element_blank(),
              axis.text.x = element_text(angle = 90, vjust = 0.5, hjust = 1)) +
        scale_x_continuous(breaks = important_times,
                           labels = Times_of_segments$Time_point) +
        scale_color_viridis(discrete = TRUE, option = "B") +
        labs(x = xlab, y = ylab)
}

Models

Now, we want to model heart rate and EDA on covariates. Therefore, we create fd objects for each metric. Plot the result.

# convert metrics to fd objects
HR_fd <- convert_to_fd(BSmooth_HR)
EDA_fd <- convert_to_fd(BSmooth_EDA)

altitude_fd <- convert_to_fd(BSmooth_altitude)
airpressure_fd <- convert_to_fd(BSmooth_air_pressure)
noise_fd <- convert_to_fd(BSmooth_noise)
speed_fd <- convert_to_fd(BSmooth_Speed)
steps_fd <- convert_to_fd(BSmooth_Steps)
acceleration_fd <- convert_to_fd(BSmooth_accel)
temperature_fd <- convert_to_fd(BSmooth_temp)

air_temperature_ENT_fd <- convert_to_fd(BSmooth_air_temp)
body_temperature_ENT_fd <- convert_to_fd(BSmooth_body_temp)
altitude_GEO_fd <- convert_to_fd(BSmooth_GEO_altitude)
HR_GEO_fd <- convert_to_fd(BSmooth_GEO_HR)
pollution1_fd <- convert_to_fd(BSmooth_pollution1)
pollution25_fd <- convert_to_fd(BSmooth_pollution25)

fd_objects <- ls()[grepl('_fd', ls())]
fd_objects <- fd_objects[!fd_objects %in% c('convert_to_fd', 'merged_fd', 'plot_fd')]
fd_objects

1. 'acceleration_fd'
2. 'air_temperature_ENT_fd'
3. 'airpressure_fd'
4. 'altitude_fd'
5. 'altitude_GEO_fd'
6. 'body_temperature_ENT_fd'
7. 'EDA_fd'
8. 'HR_fd'
9. 'HR_GEO_fd'
10. 'noise_fd'
11. 'pollution1_fd'
12. 'pollution25_fd'
13. 'speed_fd'
14. 'steps_fd'
15. 'temperature_fd'

There are vertical differences between curves for heart rate and also EDA (if center_EDA_curves = TRUE). We want to get rid of it (the model should then include also some dummy variable for identifying the participants or better use mixed model). Fot that we subtract the mean value of heart rate for each participant.

# compute and subtract the mean HR for each curve so they will be aligned
rangeval <- HR_fd[1]$basis$rangeval 
tt <- seq(rangeval[1], rangeval[2], length = 101)

pom <- HR_fd$coefs
EHR <- c()
for (i in 1:length(colnames(HR_fd$coefs))) {
    EHR <- c(EHR, mean(eval.fd(HR_fd[i], tt)))
    pom[, i] <- (HR_fd[i] - mean(eval.fd(HR_fd[i], tt)))$coefs[, 1] |> c() 
}

HR_fd$coefs <- pom

The same for Heart rate from GEO data.

# compute and subtract the mean HR for each curve so they will be aligned
rangeval_GEO <- HR_GEO_fd[1]$basis$rangeval 
tt_GEO <- seq(rangeval_GEO[1], rangeval_GEO[2], length = 101)

pom_GEO <- HR_GEO_fd$coefs
EHR_GEO <- c()
for (i in 1:length(colnames(HR_GEO_fd$coefs))) {
    EHR_GEO <- c(EHR_GEO, mean(eval.fd(HR_GEO_fd[i], tt_GEO)))
    pom_GEO[, i] <- (HR_GEO_fd[i] - mean(eval.fd(HR_GEO_fd[i], tt_GEO)))$coefs[, 1] |> c() 
}

HR_GEO_fd$coefs <- pom_GEO

The same for EDA curves (if center_EDA_curves = TRUE).

# compute and subtract the mean EDA for each curve so they will be aligned
if (center_EDA_curves) {
    rangeval_EDA <- EDA_fd[1]$basis$rangeval 
    tt_EDA <- seq(rangeval_EDA[1], rangeval_EDA[2], length = 101)
    
    pom_EDA <- EDA_fd$coefs
    EEDA <- c()
    for (i in 1:length(colnames(EDA_fd$coefs))) {
        EEDA <- c(EEDA, mean(eval.fd(EDA_fd[i], tt_EDA)))
        pom_EDA[, i] <- (EDA_fd[i] - mean(eval.fd(EDA_fd[i], tt_EDA)))$coefs[, 1] |> c() 
    }
    
    EDA_fd$coefs <- pom_EDA
}

Plot the metrics

# plot the metrics
par(mfrow = c(1, 2))
plot_fd(HR_fd, ylab = 'HR_fd')
plot_fd(EDA_fd, ylab = 'EDA_fd')
plot_fd(altitude_fd, ylab = 'altitude_fd')
plot_fd(airpressure_fd, ylab = 'airpressure_fd')
plot_fd(noise_fd, ylab = 'noise_fd')
plot_fd(speed_fd, ylab = 'speed_fd')
plot_fd(steps_fd, ylab = 'steps_fd')
plot_fd(acceleration_fd, ylab = 'acceleration_fd')
plot_fd(temperature_fd, ylab = 'temperature_fd')
plot_fd(air_temperature_ENT_fd, ylab = 'air_temperature_ENT_fd')
plot_fd(body_temperature_ENT_fd, ylab = 'body_temperature_ENT_fd')
plot_fd(altitude_GEO_fd, ylab = 'altitude_GEO_fd')
plot_fd(HR_GEO_fd, ylab = 'HR_GEO_fd')
plot_fd(pollution1_fd, ylab = 'pollution1_fd')
plot_fd(pollution25_fd, ylab = 'pollution25_fd')

Outlier detection

In functional linear model, we are also interested in model diagnostics. Now, we check, whether there are outliers in our data. We check all the functional covariates. Two functions are used:

• functional_boxplot() from fdaoutlier package ... returns indices of possible outliers
• fBoxplot() from GET package ... creates functional boxplot

library(fdaoutlier)

rangeval <- HR_fd$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = 1001) 

options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 150)

Warning message:
"package 'fdaoutlier' was built under R version 4.4.1"

Heart Rate

data_out <- eval.fd(HR_fd, evalarg = tt)
rownames(data_out) <- tt
# fdaoutlier package
colnames(data_out)[functional_boxplot(t(data_out), depth_method = "mbd")$outliers]
# GET package
data_out <- curve_set(obs = data_out, r = tt)
plot(fBoxplot(data_out, coverage=0.5, type="area", factor=1.5)) + theme_bw()

1. 'ID_1864'
2. 'ID_3304'
3. 'ID_5321'
4. 'ID_5951'
5. 'ID_6812'

Altitude

data_out <- eval.fd(altitude_fd, evalarg = tt)
rownames(data_out) <- tt
# fdaoutlier package
colnames(data_out)[functional_boxplot(t(data_out), depth_method = "mbd")$outliers]
# GET package
data_out <- curve_set(obs = data_out, r = tt)
plot(fBoxplot(data_out, coverage=0.5, type="area", factor=1.5)) + theme_bw()

1. 'ID_1604'
2. 'ID_1864'
3. 'ID_2476'
4. 'ID_2837'
5. 'ID_8805'

Noise

data_out <- eval.fd(noise_fd, evalarg = tt)
rownames(data_out) <- tt
# fdaoutlier package
colnames(data_out)[functional_boxplot(t(data_out), depth_method = "mbd")$outliers]
# GET package
data_out <- curve_set(obs = data_out, r = tt)
plot(fBoxplot(data_out, coverage=0.5, type="area", factor=1.5)) + theme_bw()

EDA

data_out <- eval.fd(EDA_fd, evalarg = tt)
rownames(data_out) <- tt
# fdaoutlier package
colnames(data_out)[functional_boxplot(t(data_out), depth_method = "mbd")$outliers]
# GET package
data_out <- curve_set(obs = data_out, r = tt)
plot(fBoxplot(data_out, coverage=0.5, type="area", factor=1.5)) + theme_bw()

1. 'ID_1487'
2. 'ID_1538'
3. 'ID_1864'
4. 'ID_2476'
5. 'ID_3266'
6. 'ID_3304'
7. 'ID_3626'
8. 'ID_4874'
9. 'ID_5321'
10. 'ID_6811'
11. 'ID_6812'
12. 'ID_7238'
13. 'ID_8252'
14. 'ID_8791'

Temperature

data_out <- eval.fd(temperature_fd, evalarg = tt)
rownames(data_out) <- tt
# fdaoutlier package
colnames(data_out)[functional_boxplot(t(data_out), depth_method = "mbd")$outliers]
# GET package
data_out <- curve_set(obs = data_out, r = tt)
plot(fBoxplot(data_out, coverage=0.5, type="area", factor=1.5)) + theme_bw()

'ID_3082'

Acceleration

data_out <- eval.fd(acceleration_fd, evalarg = tt)
rownames(data_out) <- tt
# fdaoutlier package
colnames(data_out)[functional_boxplot(t(data_out), depth_method = "mbd")$outliers]
# GET package
data_out <- curve_set(obs = data_out, r = tt)
plot(fBoxplot(data_out, coverage=0.5, type="area", factor=1.5)) + theme_bw()

1. 'ID_1538'
2. 'ID_1864'
3. 'ID_2837'
4. 'ID_5196'
5. 'ID_5321'
6. 'ID_5951'
7. 'ID_6811'
8. 'ID_8791'

Steps

data_out <- eval.fd(steps_fd, evalarg = tt)
rownames(data_out) <- tt
# fdaoutlier package
colnames(data_out)[functional_boxplot(t(data_out), depth_method = "mbd")$outliers]
# GET package
data_out <- curve_set(obs = data_out, r = tt)
plot(fBoxplot(data_out, coverage=0.5, type="area", factor=1.5)) + theme_bw()

1. 'ID_1487'
2. 'ID_1626'
3. 'ID_1864'
4. 'ID_5196'
5. 'ID_5951'
6. 'ID_6812'
7. 'ID_8403'
8. 'ID_8805'
9. 'ID_8991'

Speed

data_out <- eval.fd(speed_fd, evalarg = tt)
rownames(data_out) <- tt
# fdaoutlier package
colnames(data_out)[functional_boxplot(t(data_out), depth_method = "mbd")$outliers]
# GET package
data_out <- curve_set(obs = data_out, r = tt)
plot(fBoxplot(data_out, coverage=0.5, type="area", factor=1.5)) + theme_bw()

1. 'ID_1487'
2. 'ID_1626'
3. 'ID_1746'
4. 'ID_1864'
5. 'ID_2362'
6. 'ID_2404'
7. 'ID_2476'
8. 'ID_3082'
9. 'ID_5321'
10. 'ID_6071'
11. 'ID_6211'
12. 'ID_7004'
13. 'ID_8805'
14. 'ID_8991'

Air pressure

data_out <- eval.fd(airpressure_fd, evalarg = tt)
rownames(data_out) <- tt
# fdaoutlier package
colnames(data_out)[functional_boxplot(t(data_out), depth_method = "mbd")$outliers]
# GET package
data_out <- curve_set(obs = data_out, r = tt)
plot(fBoxplot(data_out, coverage=0.5, type="area", factor=1.5)) + theme_bw()

1. 'ID_3134'
2. 'ID_3626'
3. 'ID_8403'

Air temperature ENTRANT

data_out <- eval.fd(air_temperature_ENT_fd, evalarg = tt)
rownames(data_out) <- tt
# fdaoutlier package
colnames(data_out)[functional_boxplot(t(data_out), depth_method = "mbd")$outliers]
# GET package
data_out <- curve_set(obs = data_out, r = tt)
plot(fBoxplot(data_out, coverage=0.5, type="area", factor=1.5)) + theme_bw()

Body temperature ENTRANT

data_out <- eval.fd(body_temperature_ENT_fd, evalarg = tt)
rownames(data_out) <- tt
# fdaoutlier package
colnames(data_out)[functional_boxplot(t(data_out), depth_method = "mbd")$outliers]
# GET package
data_out <- curve_set(obs = data_out, r = tt)
plot(fBoxplot(data_out, coverage=0.5, type="area", factor=1.5)) + theme_bw()

1. 'ID_1626'
2. 'ID_5794'

Altitude GEO

data_out <- eval.fd(altitude_GEO_fd, evalarg = tt)
rownames(data_out) <- tt
# fdaoutlier package
colnames(data_out)[functional_boxplot(t(data_out), depth_method = "mbd")$outliers]
# GET package
data_out <- curve_set(obs = data_out, r = tt)
plot(fBoxplot(data_out, coverage=0.5, type="area", factor=1.5)) + theme_bw()

1. 'ID_2476'
2. 'ID_5561'
3. 'ID_7004'
4. 'ID_8805'

Heart rate GEO

data_out <- eval.fd(HR_GEO_fd, evalarg = tt)
rownames(data_out) <- tt
# fdaoutlier package
colnames(data_out)[functional_boxplot(t(data_out), depth_method = "mbd")$outliers]
# GET package
data_out <- curve_set(obs = data_out, r = tt)
plot(fBoxplot(data_out, coverage=0.5, type="area", factor=1.5)) + theme_bw()

1. 'ID_3304'
2. 'ID_5321'
3. 'ID_5951'
4. 'ID_6811'
5. 'ID_8805'
6. 'ID_8991'

Pollution 1

data_out <- eval.fd(pollution1_fd, evalarg = tt)
rownames(data_out) <- tt
# fdaoutlier package
colnames(data_out)[functional_boxplot(t(data_out), depth_method = "mbd")$outliers]
# GET package
data_out <- curve_set(obs = data_out, r = tt)
plot(fBoxplot(data_out, coverage=0.5, type="area", factor=1.5)) + theme_bw()

1. 'ID_1538'
2. 'ID_2293'
3. 'ID_3082'
4. 'ID_5794'
5. 'ID_8252'

Pollution 25

data_out <- eval.fd(pollution25_fd, evalarg = tt)
rownames(data_out) <- tt
# fdaoutlier package
colnames(data_out)[functional_boxplot(t(data_out), depth_method = "mbd")$outliers]
# GET package
data_out <- curve_set(obs = data_out, r = tt)
plot(fBoxplot(data_out, coverage=0.5, type="area", factor=1.5)) + theme_bw()

1. 'ID_1538'
2. 'ID_2293'
3. 'ID_3082'
4. 'ID_5794'
5. 'ID_8252'

Majority of outliers is no problem for us, but for some variables (EDA, Noise, HR), we should be careful about them.

• Heart rate - some outliers detected, but no need to extract them from analysis,
• Altitude - some outliers detected, but no need to extract them from analysis,
• Noise - one and no outlier detected, no problem,
• EDA - some outliers detected, potentially we can omit them in the analysis,
• Temperature - one outlier , but different by the two methods,
• Acceleration - many outliers, no problem,
• Steps - similar situation,
• Speed - similar situation,
• Air pressure - three curves have lower values then the rest, maybe center them,
• Air temp entrant - no outlier,
• Body temp entrant - one outlier (5794),
• Geo altitude - seems OK,
• Geo HR - seems OK,
• Pollution 1 - some outliers, maybe ID 1538 to omit,
• Pollution 25 - similar situation.

# We omit the ID 3626 for centered case
if (center_EDA_curves) {
    EEDA <- EEDA[!colnames(EDA_fd$coefs) %in% c("ID_3626")]
    EDA_fd <- EDA_fd[!colnames(EDA_fd$coefs) %in% c("ID_3626")]
}

Functions for fitting the functional regression model

This functions fit the functional regression model with specified outcome and covariates, calculates the $R^2$ and permutation $F$-test, constructs the pointwise confidence intervals for regression parameters using bootstrap principle and plot and save all the results.

Unfortunately, the function fRegress() from fda package requires to define outcome and covariates in the global environment. Therefore, we have to extract the fRegress() from the global function for fitting the model and calculating all the metrics. We have created different functions:

• model_fRegress_1() is used to prepare the outcome and covariates for fitting the functional model. It also return the betafdPar object.
• model_fRegress_2() is used after the fitting the functional regression model. We have to input the fitted model and other variables, then the function plot the results and calculate functional $R^2$ and permutation $F$-test.
• bootstrap_CI() is used after calculating the bootstrapped parametric functions. It plots the pointwise bootstrap confidence intervals for all parametric functions. The basic bootstrap CI's are considered instead of percentile bootstrap intervals.
• plot_GET() function plots the output of GET package, which constructs the global envelope test. The plot is complemented by the parametric function $\widehat\beta_j(t)$ estimated by functional model along with its pointwise CI's calculated using bootstrap procedure.

########################################################################################
## First function for regression before fitting the functional model
########################################################################################

model_fRegress_1 <- function(outcome, covariates, basis_params, path_plot, factors = NA) {
    #=========================================
    # create folder for graphs
    if(!substr(path_plot, 9, nchar(path_plot)) %in% list.files('figures/')) {
        dir.create(path_plot)
    }
    ncovariates <- length(covariates)
    # defining formula of the model
    formula <- paste0('outcome ~ ')
    for(cov in names(covariates)[-ncovariates]) {formula <- paste0(formula, cov, '+')}
    formula <- paste0(formula, names(covariates)[ncovariates])
    if(!is.na(factors[1])) {for(nam in names(factors)) {formula <- paste0(formula, '+', nam)}}
    formula <- as.formula(formula)
    # Define IDs that are in both fd objects. 
    common_IDs <- list(colnames(outcome$coefs))
    for (i in 1:ncovariates) {
        common_IDs <- c(common_IDs, list(colnames(covariates[[i]]$coefs)))
    }
    common_IDs <- Reduce(intersect, 
                         common_IDs)
    if(!is.na(factors[1])) {common_IDs <- common_IDs[common_IDs %in% paste0('ID_', participant_info$ID)]}

    message(paste0("Final number of observations = ", length(common_IDs), "."))
    # select IDs that are common
    outcome <- outcome[common_IDs]
    for (cov in names(covariates)) {
        covariates[[cov]] <- covariates[[cov]][common_IDs]
    }
    #=========================================
    # betaFdpar for beta0
    betafdPar <- list(fdPar(fd(rep(0, basis_params$beta_0$nbetabasis), 
                               create.bspline.basis(rangeval = outcome$basis$rangeval, 
                                                    nbasis = basis_params$beta_0$nbetabasis,
                                                    norder = basis_params$beta_0$norder)), 
                            lambda = basis_params$beta_0$lambda))
    # betaFdpar for other beta functions
    for (i in 1:ncovariates) {
        betafdPar_j <- list(fdPar(fd(rep(0, basis_params[[i+1]]$nbetabasis), 
                                   create.bspline.basis(rangeval = covariates[[i]]$basis$rangeval,
                                                        nbasis = basis_params[[i+1]]$nbetabasis, 
                                                        norder = basis_params[[i+1]]$norder)), 
                                lambda = basis_params[[i+1]]$lambda))
        betafdPar <- c(betafdPar, betafdPar_j)
    }
    if(!is.na(factors[1])){
        for (i in 1:length(factors)) {
            if(!names(factors)[i] %in% names(basis_params)) {
                betafdPar_j <- list(fdPar(fd(0, create.constant.basis(rangeval = outcome$basis$rangeval))))
            } else {
                betafdPar_j <- list(fdPar(fd(rep(0, basis_params[[i+1+ncovariates]]$nbetabasis), 
                                   create.bspline.basis(rangeval = outcome$basis$rangeval,
                                                        nbasis = basis_params[[i+1+ncovariates]]$nbetabasis, 
                                                        norder = basis_params[[i+1+ncovariates]]$norder)), 
                                          lambda = basis_params[[i+1+ncovariates]]$lambda))
            }
        betafdPar <- c(betafdPar, betafdPar_j)
    }}
    return(list(outcome = outcome, 
                covariates = covariates, 
                betafdPar = betafdPar, 
                formula = formula,
                common_IDs = common_IDs))
}

########################################################################################
## Second function for regression after fitting the functional model
########################################################################################

model_fRegress_2 <- function(model_concurrent, outcome, covariates, basis_params, 
                           path_plot, nperm = 200, factors = NA, HR = TRUE, lenght_tt = 1001) {
    #=========================================
    ncovariates <- length(covariates)
    # defining formula of the model
    formula <- paste0('outcome ~ ')
    for(cov in names(covariates)[-ncovariates]) {formula <- paste0(formula, cov, '+')}
    formula <- paste0(formula, names(covariates)[ncovariates])
    if(!is.na(factors[1])) {for(nam in names(factors)) {formula <- paste0(formula, '+', nam)}}
    formula <- as.formula(formula)
    # Define IDs that are in both fd objects. 
    common_IDs <- list(colnames(outcome$coefs))
    for (i in 1:ncovariates) {
        common_IDs <- c(common_IDs, list(colnames(covariates[[i]]$coefs)))
    }
    common_IDs <- Reduce(intersect, 
                         common_IDs)
    # select IDs that are common
    outcome <- outcome[common_IDs]
    for (cov in names(covariates)) {assign(cov, covariates[[cov]][common_IDs])}
    
    yhatfd  <- model_concurrent$yhatfdobj  # Fitted smooths. 
    rangeval <- outcome$basis$rangeval
    tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) # time vector
    #=========================================
    message('Plotting the fitted curves  ...')
    df_est <- eval.fd(yhatfd, tt) |> 
        as.data.frame() |> 
        pivot_longer(cols = contains('reps'), values_to = 'est', 
                     names_to = 'rep', cols_vary = 'slowest') 
    df_obs <- eval.fd(outcome, tt) |> 
        as.data.frame() |> 
        pivot_longer(cols = contains('ID'), values_to = 'obs', 
                     names_to = 'ID', cols_vary = 'slowest') |>
        mutate(ID = factor(ID))
    df_plot <- cbind(df_est, df_obs) |> 
        mutate(time = rep(tt, length(common_IDs)))
    if(HR) {
        df_plot <- df_plot |> mutate(
            est = est + rep(EHR[colnames(HR_fd$coefs) %in% common_IDs], each = length(tt)),
            obs = obs + rep(EHR[colnames(HR_fd$coefs) %in% common_IDs], each = length(tt))
        )
    }
    if(center_EDA_curves) {
        df_plot <- df_plot |> mutate(
            est = est + rep(EEDA[colnames(EDA_fd$coefs) %in% common_IDs], each = length(tt)),
            obs = obs + rep(EEDA[colnames(EDA_fd$coefs) %in% common_IDs], each = length(tt))
        )
    }
    if(HR) {
        ylab <- 'Heart Rate'
    } else {
        ylab <- 'EDA'
    } 
    
    p1 <- df_plot |> ggplot(aes(x = time, y = obs, colour = ID)) + 
        geom_line(aes(linetype = 'obs'), linewidth = 0.3) + 
        geom_line(aes(y = est, linetype = 'est'), linewidth = 0.3) + 
        facet_wrap(~ID, ncol = 5, scales = "free_y") + # , scales = "free_y"
        theme_bw() + 
        scale_color_discrete(labels = 1:length(unique(df_plot$ID))) + 
        theme(strip.background = element_blank(),
              strip.text.x = element_blank(),
              panel.grid.minor.x = element_blank(),
              axis.text.x = element_text(size = 8),
              axis.text.y = element_text(size = 8)
             ) + 
        labs(x = 'Time', y = ylab) + 
        scale_linetype_manual(name='Curve', values = c('dashed', 'solid'), 
                              labels = c('estimated', 'observed'))
    ggsave(paste0(path_plot, '/model_samples.pdf'), width = 12, height = 7)
    
    # add to graphs vertical lines indicating segments
    important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
    #=========================================
    n_beta <- length(model_concurrent$betaestlist)
    message('Plotting the beta functions ...')
    for (j in 1:n_beta) {
        df_beta <- data.frame(time = tt, 
                              beta = c(eval.fd(model_concurrent$betaestlist[[j]]$fd, tt)))
        p_beta <- df_beta |> ggplot(aes(x = time, y = beta)) + 
            geom_line(col = 'deepskyblue2', linewidth = 1) + 
            theme_bw() + 
            labs(x = expression(t), y = bquote(widehat(beta)[.(j-1)]*'(t)')) + 
            geom_hline(yintercept = 0, linetype = 'dashed', col = 'grey2', alpha = 0.7) + 
            theme(panel.grid = element_blank(),
                  axis.text.x = element_text(angle = 55, vjust = 1, hjust = 1, size = 7)) + 
            geom_vline(xintercept = important_times, linewidth = 0.2,
                       col = 'grey', linetype = 'dashed') +  
            scale_x_continuous(breaks = important_times,
                               labels = Times_of_segments$Time_point)
        assign(paste0('p_beta_', j-1), p_beta)
        ggsave(paste0(path_plot, '/beta_', j-1 , '.pdf'), plot = p_beta, width = 12, height = 7)
    }
    #=========================================
    ## Functional R^2
    message('Calculating the functional R^2 ...')
    tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
    nomin <- mean.fd((outcome - yhatfd)^2)
    denom <- mean.fd((center.fd(outcome))^2)
    Rvalues <- 1 - eval.fd(tt, nomin)/eval.fd(tt, denom)
    # sequence of knots ... set them to every 30 second (for all curves the same)
    breaks <- seq(rangeval[1], rangeval[2], by = 30)
    bbasis <- create.bspline.basis(rangeval = rangeval, norder = 4, breaks = breaks)
    curv.Lfd <- int2Lfd(2) 
    curv.fdPar <- fdPar(bbasis, curv.Lfd, 1e-1)
    Rvalues_smooth <- smooth.basis(tt, Rvalues, curv.fdPar)
    Rvalues_sm <- eval.fd(Rvalues_smooth$fd, tt)
    # Calculate RMSE, integrated R2 and max of R2
    RMSE <- eval.fd(tt, nomin) |> mean() |> sqrt()
    maxR2 <- max(Rvalues)
    integratedR2 <- metric.lp(fdata(Rvalues_smooth$fd), 
                              fdata(rep(0, length(fdata(Rvalues_smooth$fd)$argvals)), 
                                    fdata(Rvalues_smooth$fd)$argvals)) |> c()
    #=========================================
    message('Plotting the functional R^2 ...')
    plot_R2 <- data.frame(time = tt, R2 = c(Rvalues_sm)) |>
        ggplot(aes(x = time, y = R2)) +
        geom_line(col = 'deepskyblue2', linewidth = 0.8) + 
        geom_hline(aes(yintercept = 0), linetype = 'dashed', col = 'grey2',
                   alpha = 0.7, linewidth = 0.4) + 
        theme_bw() +
        theme(panel.grid = element_blank(),
              axis.text.x = element_text(angle = 55, vjust = 1, hjust = 1, size = 7)) + 
        geom_vline(xintercept = important_times, linewidth = 0.2, 
                   col = 'grey', linetype = 'dashed') +  
        scale_x_continuous(breaks = important_times,
                           labels = Times_of_segments$Time_point) + 
        labs(x = expression(t), y = expression(R^2*(t)))
    scales <- layer_scales(plot_R2)$y$range$range
    plot_R2 <- plot_R2 + 
        annotate("text", x = 20, y = scales[2] - 0.01 * ceiling(2*(scales[2] - scales[1])), 
                 label = paste0('RMSE = ', round(RMSE, 4)), 
                 size = 4, vjust = "inward", hjust = "inward") +
        annotate("text", x = 20, y = scales[2] - 0.035 * ceiling(2*(scales[2] - scales[1])), 
                 label = paste0('max(R^2) =' ,round(maxR2, 4)), 
                size = 4, vjust = "inward", hjust = "inward") + 
        annotate("text", x = 20, y = scales[2] - 0.06 * ceiling(2*(scales[2] - scales[1])), 
                 label = paste0('Integrated R^2 = ', round(integratedR2, 4)), 
                 size = 4, vjust = "inward", hjust = "inward")
    
    ggsave(paste0(path_plot, '/R2.pdf'), plot = plot_R2, width = 12, height = 7)
    #=========================================
    message('Calculating the functional F-ratio test ...')
    # F-Ratio
    F.res <- Fperm.fd(outcome, 
                      model_concurrent$xfdlist, 
                      model_concurrent$betalist, 
                      nperm = nperm, argvals = tt, plotres = FALSE)
    #=========================================
    message('Plotting the results of the functional F-ratio test ...')
    df_res_metrics <- data.frame(RMSE = RMSE,
                                 maxR2 = maxR2,
                                 integratedR2 = integratedR2,
                                 pval = F.res$pval, 
                                 qval = F.res$qval, 
                                 Fobs = F.res$Fobs)
    options(ggplot2.discrete.colour = c("deepskyblue2", "grey3", 'tomato'))
    plot_Fres <- data.frame(time = tt, F = F.res$Fvals, p = F.res$pvals.pts, q = F.res$qvals.pts) |>
        ggplot(aes(x = time, y = F)) +
        geom_line(aes(col = ' observed F statistic', linetype = ' observed F statistic'),
                  linewidth = 0.8) + 
        geom_hline(aes(yintercept = 0), linetype = 'dashed', col = 'grey2', 
                   alpha = 0.7, linewidth = 0.4) + 
        theme_bw() +
        theme(panel.grid = element_blank(),
              axis.text.x = element_text(angle = 55, vjust = 1, hjust = 1, size = 7),
              legend.position = 'bottom') + 
        geom_vline(xintercept = important_times, linewidth = 0.2, col = 'grey', linetype = 'dashed') +  
        scale_x_continuous(breaks = important_times,
                           labels = Times_of_segments$Time_point) + 
        labs(x = expression(t), y = expression(F*(t)), col = 'Curve:', linetype = 'Curve:') + 
        geom_line(aes(y = q, col = 'pointwise 0.05 critical value', 
                      linetype = 'pointwise 0.05 critical value')) + 
        geom_hline(aes(yintercept = F.res$qval, col = 'maximum 0.05 critical value', 
                       linetype = 'maximum 0.05 critical value'))
    scales <- layer_scales(plot_Fres)$y$range$range
    plot_Fres <- plot_Fres + 
        annotate("text", x = 20, y = scales[2] - 0.01 * ceiling(2*(scales[2] - scales[1])), 
                 label = paste0('p-value = ', round(df_res_metrics$pval, 4)), 
                 family = 'serif', fontface = 'plain', size = 4, vjust = "inward", hjust = "inward") +
        annotate("text", x = 20, y = scales[2] - 0.035 * ceiling(2*(scales[2] - scales[1])), 
                 label = paste0('q-value = ', round(df_res_metrics$qval, 4)), 
                 family = 'serif', fontface = 'plain', size = 4, vjust = "inward", hjust = "inward") + 
        annotate("text", x = 20, y = scales[2] - 0.06 * ceiling(2*(scales[2] - scales[1])), 
                 label = paste0('Observed F-statistic = ', round(df_res_metrics$Fobs, 4)), 
                 family = 'serif', fontface = 'plain', size = 4, vjust = "inward", hjust = "inward")
    
    ggsave(paste0(path_plot, '/F_res.pdf'), plot = plot_Fres, width = 12, height = 7)
    #=========================================
    
    message('DONE :-)')
    return(list(model = model_concurrent,
                df_res_metrics = df_res_metrics,
                plots = list(p1, plot_Fres, plot_R2, p_beta_0, p_beta_1)))
}

########################################################################################
## Function for Bootstrap CI for parametric functions
########################################################################################

bootstrap_CI <- function(N_repeats = 100, beta_BS, n_beta, model_concurrent, path_plot, lenght_tt = 1001) {
    N_repeats_NA <- N_repeats - sum(is.na(beta_BS[1, , 1]))
    message(paste0('Plotting the bootstrap CIs for beta functions (from ', N_repeats_NA, 
                   ' bootstrap samples) ...'))
    beta_BSnew <- array(data = NA, dim = c(lenght_tt, N_repeats_NA, n_beta))
    
    for(j in 1:n_beta) {
        beta_BSnew[, , j] <- beta_BS[, , j] |> 
        as.data.frame() |>
        select_if(~ !any(is.na(.))) |> 
        as.matrix()
    }

    for (j in 1:n_beta) {
        df_beta <- data.frame(time = tt, 
                              beta = c(eval.fd(model_concurrent$betaestlist[[j]]$fd, tt)))
        p_beta_CI <- df_beta |> ggplot(aes(x = time, y = beta)) + 
            geom_line(col = 'deepskyblue2', linewidth = 1) + 
            theme_bw() + 
            labs(x = expression(t), y = bquote(widehat(beta)[.(j-1)]*'(t)')) + 
            geom_hline(yintercept = 0, linetype = 'dashed', col = 'grey2', alpha = 0.7) + 
            theme(panel.grid = element_blank(),
                  axis.text.x = element_text(angle = 55, vjust = 1, hjust = 1, size = 7)) + 
            geom_vline(xintercept = important_times, linewidth = 0.2, 
                       col = 'grey', linetype = 'dashed') +  
            scale_x_continuous(breaks = important_times,
                               labels = Times_of_segments$Time_point) + 
            geom_line(aes(x = time, 
                          y = 2*beta - apply(beta_BSnew[, , j], 1, quantile, probs = 0.025)), 
                      col = 'black') + 
            geom_line(aes(x = time, 
                          y = 2*beta - apply(beta_BSnew[, , j], 1, quantile, probs = 0.975)),
                      col = 'black')
        plot(p_beta_CI)
        ggsave(paste0(path_plot, '/beta_', j-1 , '_CI', '.pdf'), 
               plot = p_beta_CI, width = 12, height = 7)
    }
    
    message('DONE :-)')

    return(list(beta_BS = beta_BSnew, N_repeats_NA = N_repeats_NA))
}

Global envelopes

The GET package provides central regions (i.e. global envelopes) and global envelope tests with intrinsic graphical interpretation. The central regions can be constructed from (functional) data. The tests are Monte Carlo or permutation tests, which demand simulations from the tested null model. The methods are applicable for any multivariate vector data and functional data (after discretization).

We use GET package for constructing $100(1-\alpha)\%$ global envelope for test statistic of $H_0: \beta_j(t) = 0$.

plot_GET <- function(beta_num, tt, model_concurrent, res, beta_BSnew, path_plot, title = '') {
    
    df_beta <- data.frame(time = tt, beta = c(eval.fd(model_concurrent$betaestlist[[beta_num]]$fd, tt)))
    
    p1 <- plot(res, 
               sign.col="tomato",
               digits = 6) + 
        theme_bw() + 
        labs(x = expression(t), y = bquote(widehat(beta)[.(beta_num - 1)](t))) + # expression(widehat(beta)[beta_num - 1](t))
        geom_hline(yintercept = 0, linetype = 'dashed', col = 'grey2', alpha = 0.7) + 
        theme(panel.grid = element_blank(),
              axis.text.x = element_text(angle = 55, vjust = 1, hjust = 1, size = 7),
              legend.position = "bottom") + 
        geom_vline(xintercept = important_times, linewidth = 0.2, col = 'grey', linetype = 'dashed') +  
        scale_x_continuous(breaks = important_times,
                           labels = Times_of_segments$Time_point,
                           expand = c(0.01, 0.01)) +
        geom_line(data = df_beta, aes(x = time, y = beta), col = 'deepskyblue2', linewidth = 1) + 
        geom_line(data = df_beta, aes(x = time, 
                                      y = 2*beta - apply(beta_BSnew[, , beta_num], 1, quantile, probs = 0.975)),
                  col = 'grey', linewidth = 0.8) + 
        geom_line(data = df_beta, aes(x = time,
                                      y = 2*beta - apply(beta_BSnew[, , beta_num], 1, quantile, probs = 0.025)),
                  col = 'grey', linewidth = 0.8) + 
        ggtitle(label = title, 
                subtitle = paste0("Graphical functional GLM: p = ", round(attr(res, "p"), 6)))
    
    ggsave(paste0(path_plot, '/beta', beta_num - 1, '_GET.pdf'), width = 20, height = 10, dpi = 300)

    return(p1)
}

GET_function <- function(J, outcome, model_1, nsim, model_concurrent,
                         beta_BSnew, path_plot, sex = FALSE, lenght_tt = 1001) {
    rangeval <- outcome$basis$rangeval
    tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) # 1001 
    # for outcome
    eval0 <- eval.fd(outcome, evalarg = tt)
    rownames(eval0) <- tt
    data_GET0 <- curve_set(obs = eval0, r = tt)
    # create curve_set
    my_curve_set <- list(Y = data_GET0)
    # for covariates
    ncovariates <- length(names(model_1$covariates))
    for (j in 1:ncovariates) {
        cov <- model_1$covariates[[names(model_1$covariates)[j]]]
        evalj <- eval.fd(cov, evalarg = tt)
        rownames(evalj) <- tt
        assign(paste0('data_GET', j), curve_set(obs = evalj, r = tt))
        my_list <- list(curve_set(obs = evalj, r = tt))
        names(my_list) <- paste0('covariate', j, '_fd')
        my_curve_set <- c(my_curve_set, my_list)
    }
    ############################################################################
    ## Create formulas and curve_set
    # defining formula of the model
    formula.full <- paste0('Y ~ ')
    for(j in 1:(ncovariates - 1)) {formula.full <- paste0(formula.full, 'covariate', j, '_fd+')}
    formula.full <- paste0(formula.full, 'covariate', ncovariates, '_fd')

    # delete the covariate of interest
    if(sex) {
        formula.reduced <- formula.full
        formula.full <- paste0(formula.full, '+Sex')
    } else {
        formula.reduced <- gsub(paste0('covariate', J, '_fd\\+'), '', formula.full)
        if(formula.full == formula.reduced) {
            formula.reduced <- sub(paste0('\\+covariate', J, '_fd'), '', formula.full)}
    }
    formula.full <- as.formula(formula.full)
    formula.reduced <- as.formula(formula.reduced)
    ############################################################################
    ## Now, we calculate and plot the global envelope.
    if(sex) {
            res <- graph.flm(nsim = nsim, # Increase the number of simulations 
                     formula.full = formula.full,
                     formula.reduced = formula.reduced, 
                     curve_sets = my_curve_set,
                     factors = data.frame(Sex = factor(Sex)),
                     GET.args = list(typeone = 'fwer',
                                     alpha = 0.05, central = 'mean'))
    } else {
            res <- graph.flm(nsim = nsim, # Increase the number of simulations 
                     formula.full = formula.full,
                     formula.reduced = formula.reduced, 
                     curve_sets = my_curve_set,
                     GET.args = list(typeone = 'fwer',
                                     alpha = 0.05, central = 'mean'))
    }
    ############################################################################
    ## Plot the envelope
    p1 <- plot_GET(beta_num = J + 1, tt = tt, model_concurrent = model_concurrent,
                   res = res, beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, 
                   title = paste('Model: covariate of interest =', names(model_1$covariates)[J]))

    return(list(res = res, plot = p1))
}

MODELS for Heart Rate

Now, we want to model heart rate on other covariates. We use the functions defined above. For new model, we only change the first cell below and the second cell then computes everything for us. Especially, we have to specify:

• outcome ... fd object
• covariates ... named list of the covariates
• path_plot ... path where to save the figures
• basis_params ... list of the parameters used for defining B-spline basis for each covariate and intercept
• N_repeats ... number of bootstrapped sampled used to construct pointwise CI's, it should be at least 1000
• nperm ... number of permutations for permutation $F$-test, it should be at least 200
• nsim ... number of simulations for calculating Global Envelope Test, it should be at least 2499

# Set the numbers for all models
N_repeats <- 101#1001
nperm <- 200
nsim <- 2499
lenght_tt <- 501

HR ~ air + noise

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- HR_fd
covariates <- list(altitude = altitude_fd, 
                   noise = noise_fd)
path_plot <- 'figures/model_HR_alt_noise_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 90, norder = 4, lambda = 1e2),
                     noise = list(nbetabasis = 90, norder = 4, lambda = 1e2))

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, 
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 39.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Warning message in `^.fd`((outcome - yhatfd), 2):
"The maximum error exceeds the tolerance level."
Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 240 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	8.736482	0.4111378	6.871452	0.01	0.4733055	0.6124866

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 8, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

HR ~ alt + noise + Sex (const basis for sex)

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

NOTE: If we define also some scalar variable, we have to specify the basis parameters for corresponding parametric function. It is done by `basis_params`.

- If we specify for the name of the factor corresponding list of parameters, then the <b>B-splines</b> of specified order will be created
- Otherwise (if we do not specify the basis parameters for factor), the <b>constant basis</b> will be used for this parametric function.

• Be careful, the code is slightly different for cases with factors.

# Omit NA values
participant_info <- participant_info |> na.omit()

outcome <- HR_fd
covariates <- list(altitude = altitude_fd, 
                   noise = noise_fd)
path_plot <- 'figures/model_HR_alt_noise_Sex'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e6),
                     altitude = list(nbetabasis = 90, norder = 4, lambda = 1e2),
                     noise = list(nbetabasis = 90, norder = 4, lambda = 1e2))

factors <- list(Sex = participant_info$Sex |> as.factor())

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params,
                            factors = factors)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}
for (fact in names(factors)) {
    assign(fact, factors[[fact]][participant_info$ID %in% (model_1$common_IDs |> substr(4, 9))] |> as.numeric())
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, 
                            basis_params = basis_params, nperm = nperm, factors = factors, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        if(!is.na(factors[1])) {for (fact in names(factors)) {
            assign(paste0(fact, '_BS'), 
                   factors[[fact]][participant_info$ID %in% (model_1$common_IDs |> substr(4, 9))][BS_sample] |> 
                   as.numeric())}}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS'))
        if(!is.na(factors[1])) {for(nam in names(factors)) {formula_BS <- paste0(formula_BS, '+', nam, '_BS')}}
        formula_BS <- as.formula(formula_BS)
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Warning message in `^.fd`((outcome - yhatfd), 2):
"The maximum error exceeds the tolerance level."
Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 38 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Plotting the bootstrap CIs for beta functions (from 50 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	8.89276	0.3533194	6.522793	0.1	0.7696907	0.6040062

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, sex = FALSE, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

GET_res <- GET_function(J = j+1, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, sex = TRUE, lenght_tt = lenght_tt)
GET_results[[j+1]] <- GET_res

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
            (GET_results[[3]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

HR ~ alt + noise + Sex (B-spline for sex)

- First, we have to define some variables. - Then, execute the cell below. It should compute everything :)

NOTE: If we define also some scalar variable, we have to specify the basis parameters for corresponding parametric function. It is done by `basis_params`.

- If we specify for the name of the factor corresponding list of parameters, then the <b>B-splines</b> of specified order will be created
- Otherwise (if we do not specify the basis parameters for factor), the <b>constant basis</b> will be used for this parametric function.

• Be careful, the code is slightly different for cases with factors.

outcome <- HR_fd
covariates <- list(altitude = altitude_fd, 
                   noise = noise_fd)
path_plot <- 'figures/model_HR_alt_noise_Sex_Bspl_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e6),
                     altitude = list(nbetabasis = 90, norder = 4, lambda = 1e2),
                     noise = list(nbetabasis = 90, norder = 4, lambda = 1e2),
                     Sex = list(nbetabasis = 90, norder = 4, lambda = 1e2))

factors <- list(Sex = participant_info$Sex |> as.factor())

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params,
                            factors = factors)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}
for (fact in names(factors)) {
    assign(fact, factors[[fact]][participant_info$ID %in% (model_1$common_IDs |> 
                                                           substr(4, 9))] |> as.numeric())
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, 
                            basis_params = basis_params, nperm = nperm, factors = factors, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        if(!is.na(factors[1])) {for (fact in names(factors)) {
            assign(paste0(fact, '_BS'), 
                   factors[[fact]][participant_info$ID %in% (model_1$common_IDs |> substr(4, 9))][BS_sample] |> 
                   as.numeric())}}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS'))
        if(!is.na(factors[1])) {for(nam in names(factors)) {formula_BS <- paste0(formula_BS, '+', nam, '_BS')}}
        formula_BS <- as.formula(formula_BS)
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 38.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 388 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	8.518559	0.379981	9.999879	0.035	0.5320388	0.5997903

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, sex = FALSE, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

GET_res <- GET_function(J = j+1, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, sex = TRUE, lenght_tt = lenght_tt)
GET_results[[j+1]] <- GET_res

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
            (GET_results[[3]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

HR ~ alt + noise + temp (Empatica)

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- HR_fd
covariates <- list(altitude = altitude_fd, 
                   noise = noise_fd,
                   temperature = temperature_fd)
path_plot <- 'figures/model_HR_alt_noise_tempEmpatica_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 90, norder = 4, lambda = 1e2),
                     noise = list(nbetabasis = 90, norder = 4, lambda = 1e2),
                     temperature = list(nbetabasis = 90, norder = 4, lambda = 1e2))

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, 
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 33.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 310 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	8.567088	0.4293899	9.358159	0.085	0.7230028	0.6613453

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

HR ~ alt + noise + temp (Entrant)

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- HR_fd
covariates <- list(altitude = altitude_fd, 
                   noise = noise_fd,
                   temperature = air_temperature_ENT_fd)
path_plot <- 'figures/model_HR_alt_noise_tempEntrant_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 90, norder = 4, lambda = 1e2),
                     noise = list(nbetabasis = 90, norder = 4, lambda = 1e2),
                     temperature = list(nbetabasis = 90, norder = 4, lambda = 1e2))

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, 
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 24.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 400 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Smallest eigenvalues:
 [1]  0.7833585  0.7707040  0.6411206  0.5989976  0.5591936  0.5567340
 [7]  0.4314782  0.4308269  0.3292914 -0.2052906

Largest  eigenvalues:
 [1] 71305842 68558264 63966446 63807462 62130543 60536319 59385986 59044419
 [9] 58049990 57661764

Smallest eigenvalues:
 [1]  0.71853851  0.66259093  0.62569180  0.60368678  0.55828907  0.53387336
 [7]  0.35931978  0.28792571  0.23412785 -0.02906518

Largest  eigenvalues:
 [1] 71740708 68564664 64559704 63913320 62362347 60651116 60397994 59151830
 [9] 58500236 57794954

Smallest eigenvalues:
 [1]  0.710052060  0.618438059  0.611693430  0.596946399  0.585326044
 [6]  0.505858641  0.467334208  0.450768258  0.378575725 -0.006726297

Largest  eigenvalues:
 [1] 73331066 69249948 65354311 65085678 63167356 61412096 61283824 59682595
 [9] 57963532 57747546

Smallest eigenvalues:
 [1]  0.7244335  0.7151224  0.5995001  0.5602164  0.5355778  0.4924939
 [7]  0.4578872  0.3087752  0.2930759 -0.1939169

Largest  eigenvalues:
 [1] 71495511 67957762 64014011 63836671 62613106 60914767 59288142 59087033
 [9] 58063514 57856818

Smallest eigenvalues:
 [1]  0.7279014  0.6492877  0.6290261  0.5610432  0.5528180  0.4826807
 [7]  0.4282515  0.3683406  0.2521219 -0.1287820

Largest  eigenvalues:
 [1] 72077437 68198721 64455298 63964059 62946666 60980525 60214498 60068511
 [9] 58064986 57517102

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	8.332604	0.6563847	15.7536	0.04	1.331577	1.469169

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

HR ~ alt + n + t + acc

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- HR_fd
covariates <- list(altitude = altitude_fd, 
                   noise = noise_fd,
                   temperature = temperature_fd,
                   acceleration = acceleration_fd)
path_plot <- 'figures/model_HR_alt_noise_temp_acc_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     noise = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     temperature = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     acceleration = list(nbetabasis = 80, norder = 4, lambda = 1e3))

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, 
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 32.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 542 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Smallest eigenvalues:
 [1]  0.8716439  0.8501062  0.7929519  0.7713887  0.6455789  0.5548213
 [7]  0.5194145  0.4788490 -0.4087386 -1.0159171

Largest  eigenvalues:
 [1] 109094934 103323420  97119957  94954556  94213710  91296769  88575342
 [8]  88373363  87993404  87132788

Smallest eigenvalues:
 [1]  0.8557968106  0.7229404645  0.6594665701  0.5557379678  0.5422057556
 [6]  0.4321785672  0.3714286997  0.2567776285 -0.0004305333 -0.4461854063

Largest  eigenvalues:
 [1] 107788521 103895440  97704523  94911701  94800499  91854015  88973768
 [8]  88530748  87937287  86863972

Smallest eigenvalues:
 [1]  0.95617144  0.83615029  0.77603592  0.72014785  0.61883550  0.59588516
 [7]  0.57500011  0.48375912  0.47367886 -0.07217484

Largest  eigenvalues:
 [1] 107029316 104565286  98917906  94797645  94227685  92569418  89524993
 [8]  89240025  87865751  87181746

Smallest eigenvalues:
 [1]  0.88903281  0.85415649  0.83938379  0.66807084  0.63514111  0.59359886
 [7]  0.52903317  0.40630874  0.38543263 -0.02795208

Largest  eigenvalues:
 [1] 108777428 103540862  97800530  95763571  93832821  91213188  88964505
 [8]  88594098  88370138  87006314

Smallest eigenvalues:
 [1]  0.84517789  0.80242398  0.78417866  0.74331729  0.65735267  0.50320455
 [7]  0.48770975  0.47987454  0.07809825 -2.90820653

Largest  eigenvalues:
 [1] 107606289 102983787  97583320  94480015  94310069  91581818  89544119
 [8]  88368008  87381864  86752878

Smallest eigenvalues:
 [1]  0.8767251  0.7641281  0.6903513  0.6899957  0.6759859  0.6012802
 [7]  0.5681353  0.4129215  0.2298728 -0.3584217

Largest  eigenvalues:
 [1] 107118755 104322380  98145549  94592468  94477774  92135811  89324916
 [8]  88446711  87472383  86947660

Smallest eigenvalues:
 [1]  0.9425468  0.8593926  0.8020653  0.6709320  0.6411257  0.5624229
 [7]  0.5281958  0.3182029  0.2251623 -2.3065338

Largest  eigenvalues:
 [1] 109381624 102855028  97403627  95094153  93216803  91042402  88693590
 [8]  88262843  88219053  86680832

Smallest eigenvalues:
 [1]  0.9793056  0.8830834  0.8528803  0.7423535  0.7366995  0.6568983
 [7]  0.5380016  0.5306911  0.4647761 -0.9306622

Largest  eigenvalues:
 [1] 106774425 103657270  97533434  94344429  93753823  91646752  88686610
 [8]  88561281  86967833  86690831

Smallest eigenvalues:
 [1]  0.8620713  0.8345827  0.7921674  0.7864393  0.7653780  0.7149577
 [7]  0.5435019  0.2804479  0.2590612 -0.6677662

Largest  eigenvalues:
 [1] 108347208 103382835  97389200  94668865  93726606  91721318  89061022
 [8]  88501653  87204644  86440562

Smallest eigenvalues:
 [1]  0.9248331  0.6657690  0.6508995  0.6476453  0.6139276  0.5751912
 [7]  0.5529175  0.1137819  0.1129087 -0.4302189

Largest  eigenvalues:
 [1] 107884656 103136876  96894110  94266256  94158391  91295424  88743480
 [8]  88210669  86920306  86605328

Smallest eigenvalues:
 [1]  0.9367047  0.8178849  0.7746082  0.7375337  0.6664622  0.5742880
 [7]  0.5233158  0.4224464  0.1813183 -0.5176218

Largest  eigenvalues:
 [1] 108482198 101209235  96599139  94288358  92808975  90257072  87507470
 [8]  87483956  87129999  86260201

Smallest eigenvalues:
 [1]  0.7259332  0.6515320  0.5377519  0.5130425  0.5025229  0.4464642
 [7]  0.4102184  0.2321810  0.1791797 -2.1334504

Largest  eigenvalues:
 [1] 107900317 103756697  98097775  94472480  94077132  91873205  89605613
 [8]  88812775  87459066  86974019

Smallest eigenvalues:
 [1]  0.7756044  0.7713757  0.6778960  0.6680832  0.6666396  0.5664970
 [7]  0.3704883  0.3122338  0.2164667 -0.2031463

Largest  eigenvalues:
 [1] 106579960 102699521  97292159  94277333  93782746  91450928  89095276
 [8]  88500515  87313442  86978433

Smallest eigenvalues:
 [1]  0.91335919  0.89520322  0.87913816  0.83613568  0.81550818  0.65470353
 [7]  0.61304205  0.58381315  0.52573348 -0.06385793

Largest  eigenvalues:
 [1] 109255818 102699872  96524215  94837443  94009624  91089688  88594344
 [8]  88125984  88060248  86595372

Smallest eigenvalues:
 [1]  0.8775120  0.8293961  0.8105373  0.7200255  0.6885267  0.6219314
 [7]  0.5301660  0.4469277  0.1792715 -2.0455835

Largest  eigenvalues:
 [1] 108624441 102834392  97500082  94720128  93733308  91457423  89161646
 [8]  88303223  87771817  86908930

Smallest eigenvalues:
 [1]  0.7521986  0.7140749  0.6393041  0.6341570  0.4694921  0.4609641
 [7]  0.4565301  0.3118130 -0.2560743 -1.0004415

Largest  eigenvalues:
 [1] 109813170 104552660  97754487  95956241  94953492  91573470  89263114
 [8]  89036468  88834676  87443726

Smallest eigenvalues:
 [1]  0.84292248  0.83022099  0.70296779  0.63382788  0.60175781  0.59602276
 [7]  0.56356554  0.17243779  0.06940894 -0.87560339

Largest  eigenvalues:
 [1] 111111281 104172734  98278983  96055219  94836706  92110016  89538795
 [8]  89360785  89176574  87808022

Smallest eigenvalues:
 [1]  0.80474852  0.75327496  0.69504463  0.67465972  0.65300462  0.57327132
 [7]  0.48274075  0.23477979  0.03917412 -0.40234313

Largest  eigenvalues:
 [1] 106621807 103648986  97663072  93845629  93748058  91372162  88790057
 [8]  87687497  86934356  86068218

Smallest eigenvalues:
 [1]  1.00569653  0.92170723  0.86554213  0.82924199  0.78461078  0.65505115
 [7]  0.62696409  0.61083886  0.52060238 -0.07317702

Largest  eigenvalues:
 [1] 108020603 103256367  97347436  94733080  94180548  91801077  88468679
 [8]  88400840  87312882  86835531

Smallest eigenvalues:
 [1]  0.9828879  0.8888334  0.8733402  0.8216811  0.8128000  0.7098531
 [7]  0.6284019  0.5901828  0.5794624 -0.5336554

Largest  eigenvalues:
 [1] 107810962 103853571  97670558  94828284  94640803  92014184  88713559
 [8]  88658728  87821305  87013622

Smallest eigenvalues:
 [1]  0.86106846  0.72612204  0.66710711  0.59103210  0.50407716  0.44237890
 [7]  0.31378560  0.04838675 -0.41357046 -1.21846072

Largest  eigenvalues:
 [1] 107911500 101461426  96554062  94116748  92651142  89533877  88434473
 [8]  87705250  87221475  86587759

Smallest eigenvalues:
 [1]  1.0105503  0.9272241  0.8232121  0.6689654  0.6675312  0.6307643
 [7]  0.5613469  0.5076451  0.3327870 -0.7584954

Largest  eigenvalues:
 [1] 108595086 102713623  97737496  95261716  93786521  91373556  88580367
 [8]  88349848  87812232  87136291

Smallest eigenvalues:
 [1]  0.67186094  0.59062408  0.57712804  0.51831994  0.48281029  0.33969755
 [7]  0.19649300  0.04754508 -0.45909282 -7.88695366

Largest  eigenvalues:
 [1] 109859402 102163601  97898935  94423681  93532238  90602329  88491583
 [8]  87810057  87651098  87075944

Smallest eigenvalues:
 [1]  0.9691789  0.8993445  0.8745925  0.8147007  0.7282038  0.6765138
 [7]  0.5023434  0.3951217  0.3560023 -0.4517029

Largest  eigenvalues:
 [1] 106687716 101620679  96230323  93384956  93292999  90444369  88224084
 [8]  87363053  86451488  86001756

Smallest eigenvalues:
 [1]  0.8269466  0.6486635  0.5877420  0.5833506  0.5580785  0.5562149
 [7]  0.3167155  0.1897060  0.1119832 -0.2710390

Largest  eigenvalues:
 [1] 110083820 103888411  98725361  96988817  94606953  92121870  89489991
 [8]  89410307  89123731  87590916

Smallest eigenvalues:
 [1]  0.90259676  0.77598750  0.76610736  0.73986927  0.70359734  0.56244895
 [7]  0.50755074  0.21551415 -0.01288411 -0.37890855

Largest  eigenvalues:
 [1] 109972615 104150154  98416980  97195654  95009565  92483433  89644301
 [8]  89290875  88739858  87603347

Smallest eigenvalues:
 [1]  0.8249515  0.8056391  0.7462270  0.7058730  0.5916069  0.5387958
 [7]  0.5069774  0.4396740  0.1689024 -0.4893813

Largest  eigenvalues:
 [1] 107866296 103029059  97481412  94368401  93955912  91523955  89456441
 [8]  88214044  87416701  86802248

Smallest eigenvalues:
 [1]  1.0108922  1.0074571  0.7852222  0.7610551  0.7448131  0.7382305
 [7]  0.7157412  0.6635559  0.4472582 -0.9911224

Largest  eigenvalues:
 [1] 109974759 102489800  97306224  94942024  93895458  91133827  88863288
 [8]  88283750  88112620  87416503

Smallest eigenvalues:
 [1]  0.7517393  0.7205585  0.7067084  0.6406682  0.5487647  0.5431366
 [7]  0.4959984  0.4772563 -0.5758258 -0.7563566

Largest  eigenvalues:
 [1] 109151133 103322879  98304579  95473427  93879987  91448782  89447386
 [8]  89014655  88615177  87876250

Smallest eigenvalues:
 [1]  0.7648631  0.6427379  0.6021311  0.5652321  0.4304333  0.4168429
 [7]  0.3955647  0.3789174  0.2004489 -0.1222338

Largest  eigenvalues:
 [1] 108807190 103618677  97468941  96203635  93682485  91491469  89030734
 [8]  88771061  88480784  87021496

Smallest eigenvalues:
 [1]  0.7599520  0.6508359  0.6405970  0.6228885  0.6104181  0.4975251
 [7]  0.4713674  0.4455729  0.3979905 -1.1733023

Largest  eigenvalues:
 [1] 106528919 102604497  97430072  93867185  93142475  91316857  88800696
 [8]  88112860  87031399  86447180

Smallest eigenvalues:
 [1]  0.8313580  0.7744583  0.7732968  0.7473390  0.7223690  0.5250136
 [7]  0.4067012  0.3953674  0.1247483 -0.0459836

Largest  eigenvalues:
 [1] 108266457 104298619  98306048  94997368  94655852  92181544  89046244
 [8]  88313367  87643053  86786942

Smallest eigenvalues:
 [1]  1.0552175  0.9608836  0.9083536  0.8137891  0.7781124  0.7438965
 [7]  0.6948925  0.5189620  0.4813227 -1.0088539

Largest  eigenvalues:
 [1] 106699382 103106029  97778397  94321857  94104653  92054902  89669240
 [8]  88138439  86955873  86566445

Smallest eigenvalues:
 [1]  0.8944665  0.8242692  0.8182314  0.7297219  0.7265837  0.4879771
 [7]  0.3421240  0.2953817  0.1839575 -0.1180448

Largest  eigenvalues:
 [1] 109727803 102722836  97390325  96205036  93920377  91170760  88597655
 [8]  88435746  88083203  86942749

Smallest eigenvalues:
 [1]  0.83615608  0.78956872  0.76253242  0.67900651  0.64088357  0.42124548
 [7]  0.40264341  0.38268260  0.04521849 -0.72919639

Largest  eigenvalues:
 [1] 110624173 103817345  97698846  96733444  94965707  91729065  89678882
 [8]  89352591  88281902  87754046

Smallest eigenvalues:
 [1]  0.7984311  0.6197636  0.5600151  0.4993678  0.4878135  0.4169297
 [7]  0.3508084  0.2233203 -0.7349728 -2.2766328

Largest  eigenvalues:
 [1] 109481613 103874477  97868626  96117700  93884409  91367848  89188963
 [8]  89098061  88235056  87095535

Smallest eigenvalues:
 [1]  0.8706013173  0.8610741155  0.8597516267  0.7058094619  0.7050977434
 [6]  0.6072916516  0.5770936741  0.4804878217  0.2032625075 -0.0006889913

Largest  eigenvalues:
 [1] 108647480 103905178  97762464  95010765  94988390  92074367  89101300
 [8]  88216332  87757327  86968930

Smallest eigenvalues:
 [1]  0.8811104  0.8738058  0.8170923  0.8132223  0.6630131  0.6149969
 [7]  0.5533124  0.5485668  0.4056408 -0.1229492

Largest  eigenvalues:
 [1] 107731888 102078202  96846730  94246720  93245361  90368466  88533930
 [8]  88296384  87380286  87166346

Smallest eigenvalues:
 [1]  0.7682205  0.7445157  0.7171476  0.6187419  0.5623426  0.5067172
 [7]  0.4341715  0.4123718  0.3190856 -1.8207411

Largest  eigenvalues:
 [1] 107640565 102984281  97826348  94136615  93362157  91212927  88176374
 [8]  87611097  87375017  86125369

Smallest eigenvalues:
 [1]  0.9086733  0.8761694  0.8598913  0.8198902  0.7888336  0.6401377
 [7]  0.5215863  0.5155420  0.4402819 -0.0659769

Largest  eigenvalues:
 [1] 107956720 102803663  97290066  94485231  94188649  91494736  88401617
 [8]  87895718  87272025  86170483

Smallest eigenvalues:
 [1]  0.84292621  0.70832028  0.61463364  0.56821280  0.55563854  0.52773288
 [7]  0.28009234  0.05289292 -0.05679742 -2.37513446

Largest  eigenvalues:
 [1] 106622952 100943621  96184452  92970191  92206616  89956206  87962146
 [8]  87517159  86609039  86195159

Smallest eigenvalues:
 [1]  0.9445260  0.9012139  0.8809718  0.7002910  0.5812220  0.4543793
 [7]  0.4532511  0.2788804  0.1409139 -2.7322759

Largest  eigenvalues:
 [1] 106348106 102030765  96271945  93779141  93600659  90729851  88830193
 [8]  87159364  86641443  85782495

Smallest eigenvalues:
 [1]  0.715098616  0.603784026  0.534936737  0.524906215  0.492624719
 [6]  0.388362880  0.371912083  0.308755573  0.006834966 -0.100082967

Largest  eigenvalues:
 [1] 108238956 104836047  99076862  95388642  95146622  92931486  90134222
 [8]  89923436  87911276  87768348

Smallest eigenvalues:
 [1]  1.0149198  1.0059602  0.8672876  0.7763581  0.7610714  0.7305590
 [7]  0.6649024  0.6030967  0.3805226 -0.7769863

Largest  eigenvalues:
 [1] 108091745 103411413  97674256  94206935  93922509  91348762  88889415
 [8]  88143305  87328540  86392998

Smallest eigenvalues:
 [1]  0.9363154  0.8928282  0.8694252  0.7960278  0.6835573  0.6244205
 [7]  0.4167354  0.1195476  0.1111607 -0.2391994

Largest  eigenvalues:
 [1] 111119932 102565753  97477410  96667283  93406596  90814147  89402807
 [8]  88874007  87762711  87423207

Smallest eigenvalues:
 [1]  0.9948398  0.8636861  0.7134741  0.6179233  0.6024991  0.4973910
 [7]  0.4704489  0.4570190  0.2309826 -0.6427265

Largest  eigenvalues:
 [1] 106053130 101295585  95852877  93766987  92595916  89879398  87954128
 [8]  87310051  86850808  85685300

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	8.334506	0.5575056	12.40295	0.145	1.010932	0.8306072

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

HR ~ alt + n + t + speed

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- HR_fd
covariates <- list(altitude = altitude_fd, 
                   noise = noise_fd,
                   temperature = temperature_fd,
                   speed = speed_fd)
path_plot <- 'figures/model_HR_alt_noise_temp_speed_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     noise = list(nbetabasis = 80, norder = 4, lambda = 1e2),
                     temperature = list(nbetabasis = 80, norder = 4, lambda = 1e2),
                     speed = list(nbetabasis = 80, norder = 4, lambda = 1e3))

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, 
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 33.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Warning message in `^.fd`((outcome - yhatfd), 2):
"The maximum error exceeds the tolerance level."
Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 564 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Smallest eigenvalues:
 [1]  1.0260844  0.8850395  0.8527031  0.7607098  0.6484172  0.6220947
 [7]  0.5689357  0.5204373  0.4821186 -0.2135256

Largest  eigenvalues:
 [1] 111292628 106391819  99912218  98491447  96219015  93536679  91141423
 [8]  90742941  90323719  88660331

Smallest eigenvalues:
 [1]  0.72480756  0.66212416  0.64015007  0.51878428  0.30657979  0.30349219
 [7]  0.05977739 -0.04465672 -0.05489741 -2.59177779

Largest  eigenvalues:
 [1] 111069597 107283939 101037517  98450846  97160601  94742259  91837582
 [8]  91750634  91114466  89927348

Smallest eigenvalues:
 [1]  0.9896444  0.9567728  0.7725702  0.7046511  0.6103521  0.6019973
 [7]  0.5425109  0.4490726 -0.3471343 -3.3548327

Largest  eigenvalues:
 [1] 111971226 106306345 100410422  98008927  96709072  93850089  91988684
 [8]  91303526  90924326  89900760

Smallest eigenvalues:
 [1]  0.9950635  0.9368923  0.9173444  0.7566277  0.7159751  0.6610207
 [7]  0.6201743  0.5521210  0.5049739 -1.1948875

Largest  eigenvalues:
 [1] 110438519 105460913  99511703  96955325  96373603  93585482  91114736
 [8]  89880426  89655335  88132952

Smallest eigenvalues:
 [1]  0.9138107  0.7388487  0.7257594  0.6922668  0.6873405  0.6527690
 [7]  0.5939962  0.5627636  0.3623862 -9.4456780

Largest  eigenvalues:
 [1] 111959090 106495268  99939505  97357324  96505140  94431107  91072984
 [8]  90859248  89858603  88832396

Smallest eigenvalues:
 [1]  0.8453914  0.8245527  0.7799956  0.7175125  0.6794408  0.6790913
 [7]  0.6564376  0.5695283  0.5469496 -6.9659224

Largest  eigenvalues:
 [1] 108513693 105519891  99609804  96607707  95886515  93357145  90975607
 [8]  90271077  89119314  88215681

Smallest eigenvalues:
 [1]  1.0591489  0.9908519  0.8512991  0.7022406  0.6480885  0.5905481
 [7]  0.4689820  0.4608132  0.4031816 -0.8504813

Largest  eigenvalues:
 [1] 109848300 107622594 100636571  98121131  97406051  94873051  92641225
 [8]  91618842  90250749  90027947

Smallest eigenvalues:
 [1]  1.0113352  0.9536303  0.9119895  0.8274812  0.8210721  0.7474070
 [7]  0.6550981  0.5867596  0.4382541 -6.5011028

Largest  eigenvalues:
 [1] 110877385 106418603 100413849  97074814  96974339  94268070  92096816
 [8]  90812457  89899473  89152499

Smallest eigenvalues:
 [1]  0.7630203  0.7117793  0.6974708  0.5821329  0.4940877  0.4416742
 [7]  0.3754807  0.3633591  0.3402837 -1.1495654

Largest  eigenvalues:
 [1] 110570292 106116736 100219641  97580343  96601399  94164385  91362909
 [8]  90891895  90189757  88915499

Smallest eigenvalues:
 [1]  1.1059502  1.0683969  0.8071105  0.7856602  0.7493517  0.6975260
 [7]  0.6798917  0.5879784  0.5100844 -1.6672398

Largest  eigenvalues:
 [1] 110236997 105851771  99765222  97195790  96549388  93874802  91621234
 [8]  90378918  89967770  88737910

Smallest eigenvalues:
 [1]  1.0560185  1.0083466  0.7872252  0.7453351  0.7309675  0.7263321
 [7]  0.6552442  0.5169476  0.5125468 -2.5284843

Largest  eigenvalues:
 [1] 111759423 105943058  99958979  97829738  96810556  93615174  90944910
 [8]  90872741  90463838  88924170

Smallest eigenvalues:
 [1]  1.00628848  0.83676896  0.74353673  0.69981542  0.66294780  0.65849707
 [7]  0.56537478  0.39021780  0.15072678 -0.06560649

Largest  eigenvalues:
 [1] 111223048 107493811 100640330  97666189  97612014  94426402  92149132
 [8]  90786527  90618194  89064547

Smallest eigenvalues:
 [1]  0.82888694  0.82486744  0.71224421  0.65278997  0.59096664  0.57302021
 [7]  0.53765383  0.42462305  0.19872887 -0.07518924

Largest  eigenvalues:
 [1] 111197003 105726889 100116679  97762711  97464013  94238117  90733479
 [8]  90339740  90264015  88405722

Smallest eigenvalues:
 [1]  0.9116630  0.8184469  0.7042238  0.6559777  0.6436006  0.5267276
 [7]  0.4675035  0.3276056  0.3164901 -0.2225504

Largest  eigenvalues:
 [1] 114081538 106110897 101181454  98816706  96608529  94091968  91481729
 [8]  91322737  91116411  89795590

Smallest eigenvalues:
 [1]  0.9980381  0.8910770  0.8857321  0.8394874  0.8091502  0.6951349
 [7]  0.6566401  0.6112221  0.5062307 -0.2206848

Largest  eigenvalues:
 [1] 113702811 106149821 100766888  98780009  96906247  93795690  91948460
 [8]  91533659  90733578  90239053

Smallest eigenvalues:
 [1]  0.9402103  0.8589109  0.6467004  0.6399532  0.5898160  0.5737218
 [7]  0.5311028  0.4980165  0.4068249 -2.5285333

Largest  eigenvalues:
 [1] 112013032 107484975 101417326  98839748  97832264  95340579  91481803
 [8]  91236967  91189333  89202455

Smallest eigenvalues:
 [1]  0.7933143  0.7494045  0.6984910  0.6391679  0.6329033  0.4975231
 [7]  0.3970231  0.3276468  0.2171648 -0.3020071

Largest  eigenvalues:
 [1] 111665500 105992849 100236956  97844674  97005908  94481299  91987821
 [8]  90914552  90311839  89343834

Smallest eigenvalues:
 [1]  0.8985577  0.8549494  0.7844898  0.7343894  0.6354818  0.6076425
 [7]  0.4703076  0.4189014  0.3723014 -0.7689090

Largest  eigenvalues:
 [1] 112993537 107346476 101009968  98902961  97269432  94865593  91768924
 [8]  91665537  91098885  89626611

Smallest eigenvalues:
 [1]  0.82546659  0.82276089  0.62292421  0.59010519  0.52630715  0.51336255
 [7]  0.40316934  0.30180909  0.03687301 -0.65095018

Largest  eigenvalues:
 [1] 113358585 107886021 101625759  98960875  97895762  95082207  92225915
 [8]  92187712  91889422  90448448

Smallest eigenvalues:
 [1]  0.9122774  0.8732275  0.7813472  0.5744615  0.5255296  0.5130228
 [7]  0.4761624  0.3948829  0.3649221 -2.1933804

Largest  eigenvalues:
 [1] 111973718 107468642 101432724  98094667  97905231  94779298  92699059
 [8]  91936048  91149962  90875092

Smallest eigenvalues:
 [1]  0.6815760  0.6254511  0.6243723  0.5997641  0.5230832  0.5161512
 [7]  0.4759508  0.4446396  0.2675388 -1.1575794

Largest  eigenvalues:
 [1] 113103702 106038167 100196112  98646220  96898944  94032762  91515073
 [8]  91056817  90629761  89255102

Smallest eigenvalues:
 [1]  0.789897972  0.784382009  0.683992253  0.584833503  0.573968564
 [6]  0.508396435  0.421500243  0.242206822  0.088902116 -0.002352464

Largest  eigenvalues:
 [1] 112155723 104808176  99446884  98681943  95408184  92793297  90786592
 [8]  90638434  90422962  89077528

Smallest eigenvalues:
 [1]  1.0463911  0.8171793  0.7386587  0.7029084  0.6625931  0.5797579
 [7]  0.5101602  0.4849994  0.4533082 -0.1486453

Largest  eigenvalues:
 [1] 113483630 105509167  99862731  99513876  95618208  92424710  92113388
 [8]  90814949  90214303  89044501

Smallest eigenvalues:
 [1]  0.8601488020  0.6915628779  0.6449047739  0.6296918043  0.5407655949
 [6]  0.5182576266  0.4894039867  0.3037491285  0.0273445701 -0.0009680657

Largest  eigenvalues:
 [1] 112598601 106822330 101073674  98667594  97337561  94635741  92086114
 [8]  91475405  91266345  90035580

Smallest eigenvalues:
 [1]  0.8874836  0.8723000  0.8208359  0.7236003  0.6223821  0.5895829
 [7]  0.5475264  0.4176873  0.3526485 -0.2878256

Largest  eigenvalues:
 [1] 110490616 104926841  98800527  96984658  95893710  93230474  90507314
 [8]  90489775  89798207  88803799

Smallest eigenvalues:
 [1]  1.05335309  0.99475937  0.82243429  0.80725686  0.73613982  0.71715506
 [7]  0.67146915  0.63986518  0.62480456 -0.02430108

Largest  eigenvalues:
 [1] 111302141 106452887 100697659  98331619  97297166  94499320  92364333
 [8]  90869486  90450578  89133444

Smallest eigenvalues:
 [1]  0.8152167  0.6978276  0.6808726  0.6699467  0.6600201  0.5803814
 [7]  0.5456787  0.5186091  0.4899459 -0.9435758

Largest  eigenvalues:
 [1] 112810177 106568539 100676372  99503059  96722134  94136193  91604000
 [8]  91370231  90984009  89557056

Smallest eigenvalues:
 [1]  0.87417492  0.78829167  0.65104729  0.58983668  0.57080091  0.56017820
 [7]  0.42210846  0.40800803  0.17191411 -0.03490206

Largest  eigenvalues:
 [1] 115228833 106852856 100872305 100612593  96668994  93944870  93133607
 [8]  91547886  91099573  89870287

Smallest eigenvalues:
 [1]  1.0421748  0.9817670  0.8979474  0.7135620  0.6765490  0.6556969
 [7]  0.6043825  0.6018187  0.4389780 -0.5168323

Largest  eigenvalues:
 [1] 109488187 108031512 101236633  97874966  96436230  95061262  91791919
 [8]  90742249  89733278  89075070

Smallest eigenvalues:
 [1]  0.66410406  0.63008117  0.44675415  0.44276185  0.43490092  0.36210114
 [7]  0.36065442  0.06512088 -0.68429152 -5.46802925

Largest  eigenvalues:
 [1] 111395077 106520544 100813573  98410671  97114953  94708924  91534507
 [8]  91129181  90969331  88982751

Smallest eigenvalues:
 [1]  1.05607197  0.97657931  0.94210397  0.89807917  0.82917942  0.77739581
 [7]  0.74458676  0.67188543  0.27173511 -0.01372373

Largest  eigenvalues:
 [1] 112181315 106175825 100114010  98511977  96683015  93941844  91084646
 [8]  90688504  90661510  88738164

Smallest eigenvalues:
 [1]  1.1429093  1.1120269  1.0372100  0.9346440  0.9095105  0.7489668
 [7]  0.7312088  0.7108722  0.6998953 -2.7443250

Largest  eigenvalues:
 [1] 110407360 106062556  99698106  96947761  96714957  93805261  91392568
 [8]  91116145  89470132  88638925

Smallest eigenvalues:
 [1]  0.83001031  0.70062883  0.60878181  0.56505925  0.51739158  0.45835171
 [7]  0.37423004  0.08768986 -0.22078140 -8.54102379

Largest  eigenvalues:
 [1] 111314821 106422047 100126522  98179475  97317316  94130163  91769598
 [8]  91714855  90879757  89852963

Smallest eigenvalues:
 [1]  1.0256507  0.9123795  0.8720874  0.8595631  0.6163933  0.6050374
 [7]  0.5943788  0.4717390  0.2093141 -0.2056350

Largest  eigenvalues:
 [1] 111431510 105446503  99584960  98434487  96181945  93618419  90579169
 [8]  90485731  89964174  88201526

Smallest eigenvalues:
 [1]   0.7844244   0.7480633   0.6155423   0.5491966   0.4699574   0.4126140
 [7]   0.2547411   0.1456164   0.1093533 -13.9338254

Largest  eigenvalues:
 [1] 111752712 106734192 100390558  98354552  97565986  94538159  91840314
 [8]  91698931  90949547  89868911

Smallest eigenvalues:
 [1]  0.86448777  0.71902679  0.65863933  0.52573217  0.52028122  0.46881391
 [7]  0.44462569  0.43431567  0.38501281 -0.02163295

Largest  eigenvalues:
 [1] 110449945 106456899 100414361  97016898  96844385  94496205  91570406
 [8]  90955824  89795802  89515734

Smallest eigenvalues:
 [1]  0.8077533  0.7210238  0.7046503  0.6085655  0.5154150  0.4638999
 [7]  0.4070571  0.4037090 -0.5578822 -2.9755371

Largest  eigenvalues:
 [1] 112973608 106556216 100691312  98152280  96881222  94703967  92021864
 [8]  90876640  90683992  89404057

Smallest eigenvalues:
 [1]  1.0773007  0.9626993  0.9391143  0.7244120  0.6689677  0.6444892
 [7]  0.6404767  0.5692663  0.5009240 -1.1511150

Largest  eigenvalues:
 [1] 111311852 105232210  99928039  98265507  96039031  93148420  90556313
 [8]  90488658  90308898  88917255

Smallest eigenvalues:
 [1]   0.7981970   0.7137126   0.5524738   0.5143721   0.4631009   0.4315507
 [7]   0.3440508   0.3307966  -0.6640709 -13.6530744

Largest  eigenvalues:
 [1] 112401409 106226143  99606786  98302071  97346257  94324572  91229649
 [8]  90974595  90884715  88957844

Smallest eigenvalues:
 [1]  0.829813872  0.808524245  0.671348323  0.540293260  0.483241813
 [6]  0.435728941  0.268804002 -0.007331811 -0.479030577 -9.594758667

Largest  eigenvalues:
 [1] 111347621 106199593 100142393  97726908  97365430  94082117  91829816
 [8]  90732757  90601758  89054039

Smallest eigenvalues:
 [1]  0.9615530  0.8850449  0.7495478  0.6728715  0.5648177  0.5490488
 [7]  0.4949402  0.4868193  0.3929350 -2.9092752

Largest  eigenvalues:
 [1] 111631000 107777313 101684344  98172664  98168006  95857725  92842954
 [8]  91670704  90774020  90117877

Smallest eigenvalues:
 [1]  0.8739108  0.8275594  0.7757406  0.7607616  0.6420070  0.6336824
 [7]  0.6080127  0.5084099  0.4949343 -0.1608341

Largest  eigenvalues:
 [1] 111466445 106320177 100208899  97248736  97064845  94351587  91498086
 [8]  91260856  90024937  89551921

Smallest eigenvalues:
 [1]  0.9988479  0.9883082  0.7596602  0.7435862  0.6155986  0.5804031
 [7]  0.5332565  0.5265821  0.5217056 -1.3656965

Largest  eigenvalues:
 [1] 109425389 104497885  99229765  95947142  95519276  93010176  90788547
 [8]  90328333  88918384  88640162

Smallest eigenvalues:
 [1]  0.9249039  0.8676555  0.7875298  0.6754646  0.6264638  0.5906099
 [7]  0.5557671  0.4618144  0.2376553 -1.7922688

Largest  eigenvalues:
 [1] 111799604 106481838 100838188  98745987  97461329  94701464  92312035
 [8]  91490629  91128327  89711698

Smallest eigenvalues:
 [1]  0.8542768  0.8471045  0.8358482  0.8149381  0.7840356  0.7230181
 [7]  0.5723058  0.4746535 -0.6272396 -0.7254714

Largest  eigenvalues:
 [1] 112916722 105809923 100571340  99337329  95684253  92882721  91557154
 [8]  90806729  90118652  88788615

Smallest eigenvalues:
 [1]  0.8952134  0.7104466  0.7028589  0.6619203  0.6394758  0.6334800
 [7]  0.4738881  0.4188225  0.4144207 -1.6640274

Largest  eigenvalues:
 [1] 109818254 107122122 100135355  97670024  97110970  94890048  92215405
 [8]  90651234  89891877  88795194

Smallest eigenvalues:
 [1]  0.73032461  0.69048295  0.68040785  0.62712556  0.53470399  0.49439651
 [7]  0.48178364  0.46440751  0.45518368 -0.06228659

Largest  eigenvalues:
 [1] 113741631 107359730 101493407  99947294  97539029  95205164  92292266
 [8]  91682973  91591967  90074837

Smallest eigenvalues:
 [1]  1.1409923  0.9902209  0.8965798  0.8457491  0.7979157  0.7376543
 [7]  0.5407625  0.4906326  0.3232874 -0.1901821

Largest  eigenvalues:
 [1] 113122387 107849352 101228100  99163997  97610249  94451043  92199002
 [8]  91649456  91511862  89988175

Smallest eigenvalues:
 [1]  0.7365103  0.7299214  0.7217137  0.6310214  0.5889902  0.5509948
 [7]  0.5200066  0.4028569  0.1723160 -0.2521258

Largest  eigenvalues:
 [1] 112282350 106863390 100634214  98628405  97045471  94335103  91719497
 [8]  91339914  91035716  89156143

Smallest eigenvalues:
 [1]   0.9953283   0.9550616   0.9046692   0.8810875   0.7491354   0.6954332
 [7]   0.6133449   0.5778792   0.4657114 -11.5932692

Largest  eigenvalues:
 [1] 115262997 106115067 100363224 100263218  96762338  93914858  93042521
 [8]  91098684  90521522  89630432

Smallest eigenvalues:
 [1]  0.8755228  0.7926383  0.7431564  0.7347429  0.6041977  0.5518729
 [7]  0.4817466  0.4594325  0.4559424 -0.5008348

Largest  eigenvalues:
 [1] 111744869 105403438  99730886  98834732  95880066  92957791  90983171
 [8]  90840638  90655121  89001006

Smallest eigenvalues:
 [1]  0.9870905  0.9110886  0.7091675  0.6884389  0.6824216  0.6533060
 [7]  0.6234503  0.5830949  0.5056994 -1.5022314

Largest  eigenvalues:
 [1] 111183425 106865713 100001688  97427979  97016915  93682849  91273023
 [8]  91100640  90224315  89268923

Smallest eigenvalues:
 [1]   0.66395357   0.60793105   0.57882042   0.52678373   0.50563976
 [6]   0.50326024   0.47520678   0.03497791  -0.38520771 -13.55494233

Largest  eigenvalues:
 [1] 112005687 105771346  99958139  98339602  96475076  93959460  91161788
 [8]  90873326  90332974  88527218

Smallest eigenvalues:
 [1]  8.612330e-01  7.900377e-01  7.213975e-01  6.609407e-01  5.753306e-01
 [6]  4.741194e-01  4.497456e-01  3.307483e-01  1.070042e-01 -2.753446e-05

Largest  eigenvalues:
 [1] 114049019 105874335 100464193  99395650  96301079  93511106  92348214
 [8]  91402268  90907022  89852610

Smallest eigenvalues:
 [1]  0.86054413  0.73613501  0.65624374  0.60028953  0.53086601  0.49756083
 [7]  0.48957512  0.48883735  0.06621942 -0.58732263

Largest  eigenvalues:
 [1] 112433380 105897861 100790155  98732772  96148610  93674740  91456774
 [8]  91265290  91105945  89916993

Smallest eigenvalues:
 [1]  0.8012861  0.7290541  0.7232635  0.6832502  0.4737090  0.2344541
 [7]  0.1750941  0.1655950 -1.1288695 -7.8812476

Largest  eigenvalues:
 [1] 110638199 104722979 100053841  96568931  96511229  93853308  91165033
 [8]  90395093  89407024  88855949

Smallest eigenvalues:
 [1]  0.5730275  0.5275477  0.5120175  0.4519950  0.4352719  0.3681492
 [7]  0.1351852  0.1267968 -0.4436056 -7.6377639

Largest  eigenvalues:
 [1] 110469913 105820725  99412132  96832030  96679789  94094500  91461632
 [8]  90423132  89457170  88259902

Smallest eigenvalues:
 [1]  1.0706439  1.0525352  0.8663157  0.8285159  0.7517212  0.7228777
 [7]  0.5999208  0.5636557  0.5250552 -1.1117627

Largest  eigenvalues:
 [1] 110844220 106252000  99683618  98070848  96565745  93726388  90722164
 [8]  90681828  90548851  88799347

Smallest eigenvalues:
 [1]  1.1207215  1.0769947  0.9522244  0.8363761  0.7829118  0.7821836
 [7]  0.6731551  0.5910142  0.5884217 -0.7990171

Largest  eigenvalues:
 [1] 111822654 105906098  99686805  97954426  96749647  93803503  91546730
 [8]  90774389  90605444  88835072

Smallest eigenvalues:
 [1]  0.8833443  0.8007969  0.7652360  0.6710414  0.5886209  0.5375649
 [7]  0.5348174  0.4319573 -0.4827065 -0.7530039

Largest  eigenvalues:
 [1] 113792372 107892590 101206171  99526757  97841155  94945158  92345784
 [8]  92291016  91524278  90563002

Smallest eigenvalues:
 [1]  0.7906509  0.6334079  0.6174079  0.5935930  0.5500160  0.4343821
 [7]  0.4083412  0.3817616  0.1963990 -0.3138231

Largest  eigenvalues:
 [1] 111494610 107200857 101227038  97918306  97902035  95052182  92481215
 [8]  91533816  90786087  89657430

Smallest eigenvalues:
 [1]  1.0689002  0.7848512  0.7804397  0.6903064  0.6452717  0.6367489
 [7]  0.6143130  0.4779349  0.4564593 -0.5095508

Largest  eigenvalues:
 [1] 111788285 106539667 101261873  97643777  97156546  94560648  91217421
 [8]  91075781  90423546  89327671

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	8.263548	0.7573061	14.61197	0	1.078832	2.865932

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

HR ~ alt + n + t + steps

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- HR_fd
covariates <- list(altitude = altitude_fd, 
                   noise = noise_fd,
                   temperature = temperature_fd,
                   steps = steps_fd)
path_plot <- 'figures/model_HR_alt_noise_temp_steps_N200'
basis_params <- list(beta_0 = list(nbetabasis = 80, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     noise = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     temperature = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     steps = list(nbetabasis = 80, norder = 4, lambda = 1e3))

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, 
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 32.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 570 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Smallest eigenvalues:
 [1]  0.9348751  0.8093196  0.8040542  0.7777050  0.7055800  0.5354735
 [7]  0.4280335  0.3952667  0.3673367 -0.4506395

Largest  eigenvalues:
 [1] 110560798 104438156  98471328  96510822  94369583  91943003  89734160
 [8]  89271913  88979213  87500760

Smallest eigenvalues:
 [1]  0.9148198  0.8080296  0.7935495  0.7855616  0.6945535  0.6615462
 [7]  0.6457396  0.5180668  0.4906340 -2.6355302

Largest  eigenvalues:
 [1] 107141197 104661043  99030811  94902669  94330151  92672700  89609511
 [8]  89340768  87971457  87278558

Smallest eigenvalues:
 [1]  0.5842274  0.5086076  0.4276569  0.3914728  0.2094963  0.1706714
 [7]  0.1555966  0.1434095 -0.4481483 -1.9866377

Largest  eigenvalues:
 [1] 107717260 103076063  97696149  94584135  94411817  91685513  89632686
 [8]  88475584  87476908  86849211

Smallest eigenvalues:
 [1]  0.9255135  0.9183308  0.7152333  0.5882397  0.5748553  0.5303885
 [7]  0.4825541  0.4037417  0.3994518 -0.3085808

Largest  eigenvalues:
 [1] 109857448 103755034  97556038  97168865  93847394  90903460  90038486
 [8]  89105322  88709232  87529164

Smallest eigenvalues:
 [1]  0.8858831  0.8239709  0.6139123  0.5783001  0.5405536  0.4838569
 [7]  0.4161177  0.3826504 -0.1580680 -0.1818739

Largest  eigenvalues:
 [1] 109663136 103770360  97920493  97006402  93993462  91034069  89768646
 [8]  89496821  89214865  87683496

Smallest eigenvalues:
 [1]  0.986934769  0.906741179  0.794638082  0.790531278  0.774610658
 [6]  0.703182994  0.597410578  0.583205167  0.575475314 -0.009657942

Largest  eigenvalues:
 [1] 109091658 103369129  97840566  95746264  93960993  91035176  88798408
 [8]  88737081  88320345  87187357

Smallest eigenvalues:
 [1]  0.82383862  0.80594310  0.65756364  0.52734114  0.44892800  0.26086729
 [7]  0.21487300  0.03755222 -0.10412527 -2.24442264

Largest  eigenvalues:
 [1] 108594474 101307301  96706243  94392361  92917794  90363345  87603931
 [8]  87582122  87231534  86366033

Smallest eigenvalues:
 [1]  1.0097999  0.9277245  0.8833997  0.8709712  0.7470745  0.6625220
 [7]  0.5858319  0.5222761  0.3458447 -0.6465332

Largest  eigenvalues:
 [1] 109365157 102797979  96631264  94939915  94117613  91189978  88692480
 [8]  88210259  88154308  86698700

Smallest eigenvalues:
 [1]  0.8821917  0.8566059  0.8546108  0.8477908  0.7738026  0.6348665
 [7]  0.5683213  0.4619029  0.3276785 -0.8170213

Largest  eigenvalues:
 [1] 111219897 104266556  98389482  96155883  94940092  92211097  89625330
 [8]  89461874  89270509  87912253

Smallest eigenvalues:
 [1]  0.9519004  0.8774986  0.8714826  0.6573351  0.5987138  0.4794838
 [7]  0.4568477  0.4489152 -0.2750028 -6.4406371

Largest  eigenvalues:
 [1] 106176322 101827521  96030586  94085328  93106426  90332269  87754106
 [8]  87147891  86805069  85559873

Smallest eigenvalues:
 [1]  0.70611147  0.63904316  0.59769181  0.56182159  0.46654091  0.38750647
 [7]  0.08588930  0.08241867 -0.03336646 -0.83554004

Largest  eigenvalues:
 [1] 108708031 102810434  97851080  95366421  93893256  91481478  88669002
 [8]  88456015  87913262  87243465

Smallest eigenvalues:
 [1]  0.787667992  0.786164541  0.724675825  0.648467100  0.603139918
 [6]  0.495925831  0.405797963  0.369148802 -0.005448678 -0.194699930

Largest  eigenvalues:
 [1] 107419741 101992909  96248653  95104978  92745036  90418279  88290100
 [8]  87697173  87554001  86302378

Smallest eigenvalues:
 [1]  1.0425054  0.8836607  0.7949276  0.7516601  0.7330903  0.6955937
 [7]  0.5514973  0.5250823  0.4932373 -0.2625946

Largest  eigenvalues:
 [1] 107257342 102287179  96669942  94007831  93932913  90778352  88099904
 [8]  87959913  86918076  86421720

Smallest eigenvalues:
 [1]  0.8449660  0.8358558  0.7799953  0.6674715  0.6550824  0.4692654
 [7]  0.4641032  0.4049352  0.3684635 -1.5083540

Largest  eigenvalues:
 [1] 109489098 103049835  97521799  95675749  94178813  91542625  88816175
 [8]  88787423  88528986  87287311

Smallest eigenvalues:
 [1]  0.86402274  0.82285041  0.82047166  0.79914112  0.66068689  0.60334841
 [7]  0.57842039  0.50972973  0.27782894 -0.03728339

Largest  eigenvalues:
 [1] 106788677 102523146  96787327  93900386  93887870  91157660  88536411
 [8]  87691715  86981931  86125157

Smallest eigenvalues:
 [1]  0.6902443  0.6887146  0.6476250  0.6437710  0.5685211  0.4726260
 [7]  0.4638292  0.3926920  0.3828357 -3.6519680

Largest  eigenvalues:
 [1] 104854669 102225329  96842499  93698710  92400994  91526331  89233891
 [8]  87358422  86091170  86034217

Smallest eigenvalues:
 [1]  0.9595052  0.9399287  0.8237670  0.7804078  0.7151511  0.5967222
 [7]  0.5175085  0.4995102 -0.3495336 -0.5565257

Largest  eigenvalues:
 [1] 109909455 102736085  97554445  96406653  94102402  91513439  89284159
 [8]  89070005  88956348  87571208

Smallest eigenvalues:
 [1]  0.9106840  0.8991241  0.7210108  0.6807789  0.6672419  0.5762042
 [7]  0.5459487  0.5132373  0.4124881 -0.2897281

Largest  eigenvalues:
 [1] 109459214 104703848  98646210  96377760  94276849  91804835  89392342
 [8]  89089093  89054151  87807454

Smallest eigenvalues:
 [1]  0.9383827  0.9123978  0.7408325  0.7190509  0.6547596  0.5662811
 [7]  0.5521328  0.5399948  0.4293418 -0.1883691

Largest  eigenvalues:
 [1] 108526729 102895243  97390691  94579088  93758015  91165300  88226305
 [8]  88198559  87639885  86570278

Smallest eigenvalues:
 [1]  0.9126121  0.8322896  0.7882769  0.7779469  0.6923482  0.5720599
 [7]  0.4627222  0.4573269  0.4384198 -1.7239175

Largest  eigenvalues:
 [1] 110753874 103597558  97892843  95900892  94357848  91700757  89265051
 [8]  88846774  88722629  87533543

Smallest eigenvalues:
 [1]  0.98807060  0.92472976  0.88191590  0.76558622  0.75873238  0.58895431
 [7]  0.57706534  0.53905494  0.53262966 -0.01002251

Largest  eigenvalues:
 [1] 110933982 104055425  98504863  96799838  94741497  91719515  89651802
 [8]  89494385  89248682  87823686

Smallest eigenvalues:
 [1]  0.9669601  0.8357802  0.7996964  0.7628540  0.6595044  0.5478379
 [7]  0.5262466  0.5245446  0.4519131 -0.2540084

Largest  eigenvalues:
 [1] 109899230 103324056  97702827  95839754  94530136  91638618  89350749
 [8]  88860696  88750190  87802656

Smallest eigenvalues:
 [1]  0.9042244  0.8254569  0.8169962  0.7228478  0.7066670  0.6504461
 [7]  0.5831069  0.4994867  0.4503487 -0.2249093

Largest  eigenvalues:
 [1] 110835537 105489454  99078364  96641977  95433460  92669628  90021975
 [8]  89833432  88940373  87262268

Smallest eigenvalues:
 [1]  0.8078271  0.7262409  0.6239240  0.5586248  0.5290175  0.4931768
 [7]  0.4309517  0.3622649  0.3594863 -0.5018356

Largest  eigenvalues:
 [1] 111273343 103142987  98579238  96744422  93811785  91122572  89526270
 [8]  89005590  88413278  87448124

Smallest eigenvalues:
 [1]  0.7645423  0.6542116  0.6452031  0.6106405  0.4857393  0.4606741
 [7]  0.4221937  0.3605441  0.3127330 -0.5698418

Largest  eigenvalues:
 [1] 108912549 103706042  97580975  96304339  93783456  91591109  89108729
 [8]  88864949  88580762  87123471

Smallest eigenvalues:
 [1]  1.0150695  0.9808378  0.9434159  0.8148177  0.8063113  0.7582341
 [7]  0.6801490  0.5021209  0.3306220 -1.0327082

Largest  eigenvalues:
 [1] 107578659 102803587  97037622  94823226  93524125  90819146  88582703
 [8]  88219136  87628719  86437670

Smallest eigenvalues:
 [1]  0.8370708  0.8315579  0.7314729  0.6732884  0.6229784  0.5589385
 [7]  0.3736938  0.3717455  0.3085594 -1.3044376

Largest  eigenvalues:
 [1] 109609236 103466190  96992804  95965258  94431977  91521651  89162525
 [8]  88762898  87970055  86418844

Smallest eigenvalues:
 [1]  0.80875084  0.75502958  0.72595540  0.65685373  0.59638425  0.54621251
 [7]  0.51905116  0.47063072  0.39610270 -0.05887288

Largest  eigenvalues:
 [1] 109354229 104421536  98076640  95163044  93979409  91547264  88624426
 [8]  88600186  88071506  87008412

Smallest eigenvalues:
 [1]   0.26041013   0.20739104   0.10838255   0.01584623   0.01019292
 [6]  -0.02560742  -0.57417992  -0.66026131  -1.52878029 -40.92491042

Largest  eigenvalues:
 [1] 108164207 101042177  96353509  93164105  93097169  90198547  88092729
 [8]  87992806  86405320  85840998

Smallest eigenvalues:
 [1]  0.48481067  0.45796668  0.35056824  0.34659635  0.29132789  0.21766116
 [7]  0.19342659  0.06038247 -0.19053152 -2.02191309

Largest  eigenvalues:
 [1] 107616232 103667421  97110900  95353017  94095340  91431200  89144407
 [8]  88586923  87875430  86966556

Smallest eigenvalues:
 [1]  0.7432947  0.7106206  0.6790812  0.6452983  0.5125927  0.4494981
 [7]  0.4363445  0.3188098  0.2902803 -0.4335392

Largest  eigenvalues:
 [1] 108346038 104931074  99182983  95491965  95242805  93033787  90216357
 [8]  90017434  88009962  87863187

Smallest eigenvalues:
 [1]  0.9713218  0.9501582  0.8288115  0.7367016  0.7119248  0.6741525
 [7]  0.5509152  0.4596668  0.3893768 -1.3398669

Largest  eigenvalues:
 [1] 110826878 102449973  97311640  96663915  93242202  90686551  89324789
 [8]  88323651  88025755  86538732

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	8.262888	0.7368767	13.81651	0	1.107147	2.366921

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

HR ~ alt + body_temp

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- HR_fd
covariates <- list(altitude = altitude_fd, 
                   temp_body = body_temperature_ENT_fd
                  )
path_plot <- 'figures/model_HR_alt_temp_body_ENT_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 90, norder = 4, lambda = 1e2),
                     temp_body = list(nbetabasis = 90, norder = 4, lambda = 1e2)
                    )

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, 
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 34.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 204 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	8.464485	0.4787502	8.416988	0.005	0.5999727	0.7783512

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

HR ~ alt + noise + body_temp

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- HR_fd
covariates <- list(altitude = altitude_fd, 
                   noise = noise_fd,
                   temp_body = body_temperature_ENT_fd
                  )
path_plot <- 'figures/model_HR_alt_noise_temp_body_ENT_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 90, norder = 4, lambda = 1e2),
                     noise = list(nbetabasis = 90, norder = 4, lambda = 1e2),
                     temp_body = list(nbetabasis = 90, norder = 4, lambda = 1e2)
                    )

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, 
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 28.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Warning message in `^.fd`((outcome - yhatfd), 2):
"The maximum error exceeds the tolerance level."
Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 312 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Smallest eigenvalues:
 [1]  0.539498014  0.481587315  0.466305475  0.437374808  0.423081170
 [6]  0.416107218  0.372700653  0.135696735  0.006281957 -0.138226310

Largest  eigenvalues:
 [1] 86591494 79305369 75904835 75903568 73050436 70546791 70340435 69256091
 [9] 68852466 68001938

Smallest eigenvalues:
 [1]  0.7871032  0.7759548  0.7505842  0.7300239  0.7022145  0.6841254
 [7]  0.6208750  0.3874420  0.2507688 -0.4148149

Largest  eigenvalues:
 [1] 85316977 81111829 75469702 75196362 73542269 71739741 70842454 69201781
 [9] 68697465 67763252

Smallest eigenvalues:
 [1]  0.80509361  0.62147414  0.60884550  0.51355545  0.50798118  0.46064036
 [7]  0.42764667  0.41545691  0.26171675 -0.07306901

Largest  eigenvalues:
 [1] 84593325 80735953 75726240 75647435 73409556 71349813 70057060 69544465
 [9] 69193163 68082936

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	8.399143	0.5332019	11.20614	0.045	0.917515	0.9335229

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

HR ~ alt + noise + PM25

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- HR_fd
covariates <- list(altitude = altitude_fd, 
                   noise = noise_fd,
                   pollution = pollution25_fd
                  )
path_plot <- 'figures/model_HR_alt_noise_pollution25_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 90, norder = 4, lambda = 1e2),
                     noise = list(nbetabasis = 90, norder = 4, lambda = 1e2),
                     pollution = list(nbetabasis = 90, norder = 4, lambda = 1e2)
                    )

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, 
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 23.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 404 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	7.68567	0.4495668	9.376699	0.645	1.478112	0.6997994

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

HR ~ alt + temp + PM25

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- HR_fd
covariates <- list(altitude = altitude_fd, 
                   temperature = temperature_fd,
                   pollution = pollution25_fd
                  )
path_plot <- 'figures/model_HR_alt_temp_pollution25_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 90, norder = 4, lambda = 1e2),
                     temperature = list(nbetabasis = 90, norder = 4, lambda = 1e2),
                     pollution = list(nbetabasis = 90, norder = 4, lambda = 1e2)
                    )

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, 
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 27.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 408 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	7.68485	0.3932684	9.166168	0.43	1.099246	0.6483349

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

HR ~ alt + noise + PM1

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- HR_fd
covariates <- list(altitude = altitude_fd, 
                   noise = noise_fd,
                   pollution = pollution1_fd
                  )
path_plot <- 'figures/model_HR_alt_noise_pollution1_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 90, norder = 4, lambda = 1e2),
                     noise = list(nbetabasis = 90, norder = 4, lambda = 1e2),
                     pollution = list(nbetabasis = 90, norder = 4, lambda = 1e2)
                    )

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, 
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 23.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 366 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	7.666164	0.4508731	9.603953	0.625	1.40222	0.7105318

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

HR ~ alt + temp + PM1

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- HR_fd
covariates <- list(altitude = altitude_fd, 
                   temperature = temperature_fd,
                   pollution = pollution1_fd
                  )
path_plot <- 'figures/model_HR_alt_temp_pollution1_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 90, norder = 4, lambda = 1e2),
                     temperature = list(nbetabasis = 90, norder = 4, lambda = 1e2),
                     pollution = list(nbetabasis = 90, norder = 4, lambda = 1e2)
                    )

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, 
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 27.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 352 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	7.685915	0.3931867	9.208156	0.445	1.140291	0.6481669

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

HR ~ alt + n + t + acc + body_temp

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- HR_fd
covariates <- list(altitude = altitude_fd, 
                   noise = noise_fd,
                   temp_air = temperature_fd,
                   acceleration = acceleration_fd,
                   temp_body = body_temperature_ENT_fd
                  )
path_plot <- 'figures/model_HR_alt_noise_temp_body_acc_N200'
basis_params <- list(beta_0 = list(nbetabasis = 80, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 60, norder = 4, lambda = 1e4),
                     noise = list(nbetabasis = 60, norder = 4, lambda = 1e4),
                     temp_air = list(nbetabasis = 60, norder = 4, lambda = 1e4),
                     acceleration = list(nbetabasis = 60, norder = 4, lambda = 1e4),
                     temp_body = list(nbetabasis = 60, norder = 4, lambda = 1e4)
                    )

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, 
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 22.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Warning message in `^.fd`((outcome - yhatfd), 2):
"The maximum error exceeds the tolerance level."
Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 572 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Smallest eigenvalues:
 [1]  0.40499922  0.38575140  0.37330254  0.26565527  0.23669670  0.17909644
 [7]  0.12022384  0.09929447  0.08027420 -0.11493198

Largest  eigenvalues:
 [1] 100409811  97227921  91487178  86785043  85852388  85144134  83623236
 [8]  82165859  81042210  79393144

Smallest eigenvalues:
 [1]  0.2896454  0.2590102  0.2439697  0.2321240  0.2290729  0.1828896
 [7] -0.0313414 -0.1371232 -0.3849387 -0.5804426

Largest  eigenvalues:
 [1] 100808344  96841614  91198062  86431656  85943120  83915587  83387010
 [8]  82001826  80104350  78836155

Smallest eigenvalues:
 [1]  0.34340896  0.31374410  0.30799138  0.30188452  0.16692150  0.10970465
 [7]  0.10787023  0.10430705  0.07349305 -0.35782804

Largest  eigenvalues:
 [1] 98998981 97747862 90844333 87274935 85958850 84079228 83692096 81517025
 [9] 80656001 78344453

Smallest eigenvalues:
 [1]  0.4154001  0.3227800  0.2822608  0.2239209  0.1902423  0.1851140
 [7]  0.1452747 -0.0386263 -0.5144615 -0.6734427

Largest  eigenvalues:
 [1] 100272007  96658609  90982856  86232050  85414936  83509473  82852874
 [8]  80933528  79872321  77840072

Smallest eigenvalues:
 [1]  0.28349125  0.25350768  0.23627961  0.23420214  0.14783177  0.06159823
 [7] -0.22543440 -0.26380441 -0.66641794 -0.80658187

Largest  eigenvalues:
 [1] 99921871 95973474 90119595 85836159 85625488 83783373 82185000 81153194
 [9] 79525736 77847237

Smallest eigenvalues:
 [1]  0.26664951  0.24789935  0.23927021  0.22353279  0.08824512  0.03968938
 [7] -0.02912113 -0.03549294 -0.04997009 -0.30938845

Largest  eigenvalues:
 [1] 99858036 96284862 90176795 86150933 84898962 83611760 82670891 81121819
 [9] 79803881 77908207

Smallest eigenvalues:
 [1]  0.3576000  0.2964083  0.2899710  0.2643327  0.2310401  0.2042095
 [7]  0.2004565 -0.1296703 -0.3233978 -0.3329375

Largest  eigenvalues:
 [1] 98347651 95861863 89801871 86052759 83374693 82947858 82476556 81049617
 [9] 79757305 77507778

Smallest eigenvalues:
 [1]  0.28357528  0.26952505  0.21067696  0.20116957  0.12406344  0.12300721
 [7]  0.11386965  0.11091921 -0.09569219 -0.37868482

Largest  eigenvalues:
 [1] 98350647 97306176 91600206 86753737 85259916 84500186 83997789 82468014
 [9] 80710666 79569331

Smallest eigenvalues:
 [1]  0.263166072  0.237117695  0.208720269  0.143722317  0.120915211
 [6]  0.039572040  0.008137819 -0.213259223 -0.518664559 -0.625044333

Largest  eigenvalues:
 [1] 99488573 96535090 90412637 85771308 85272740 83149055 82303012 80166252
 [9] 79834294 77076658

Smallest eigenvalues:
 [1]  0.33087316  0.29332091  0.27808402  0.27482848  0.25179347  0.15599007
 [7]  0.14410473  0.10239065 -0.08174326 -0.21962707

Largest  eigenvalues:
 [1] 102186745  97446340  90956431  86962187  86539180  85433882  82809867
 [8]  82165291  80491122  79498119

Smallest eigenvalues:
 [1]  0.32318669  0.32285306  0.30964775  0.29741764  0.25589597  0.19427749
 [7]  0.17653953  0.17303152  0.06828234 -0.46645893

Largest  eigenvalues:
 [1] 99040849 97851975 91097719 87526657 85065703 84148649 83722832 81542100
 [9] 80103623 78123498

Smallest eigenvalues:
 [1]  0.35801185  0.30127014  0.22429455  0.20322895  0.18909833  0.14920184
 [7]  0.01073892 -0.13422249 -0.51128543 -0.56308417

Largest  eigenvalues:
 [1] 101821747  96632987  90457961  87408137  85869193  84000093  82612171
 [8]  81512880  79850050  78532413

Smallest eigenvalues:
 [1]  0.26128199  0.23391728  0.22453912  0.18306532  0.15426175  0.12829706
 [7]  0.10083483 -0.01364102 -0.19001718 -0.82815413

Largest  eigenvalues:
 [1] 101383832  98167018  91742215  87654212  87407813  85339515  84344031
 [8]  83007846  81529559  80168045

Smallest eigenvalues:
 [1]  0.31409117  0.30780545  0.29623860  0.28759548  0.25229695  0.24897994
 [7]  0.09010427  0.06366506 -0.16982046 -0.29850493

Largest  eigenvalues:
 [1] 99146203 96817646 90911458 86848025 84581118 83574627 83385542 81185516
 [9] 79975257 77685279

Smallest eigenvalues:
 [1]  0.43664323  0.42304255  0.38684613  0.36953838  0.35607809  0.30589877
 [7]  0.26394911  0.23545676  0.08685125 -0.16888413

Largest  eigenvalues:
 [1] 98870968 95686778 89625885 85858336 84157315 82808052 82153344 80306759
 [9] 79325757 77124002

Smallest eigenvalues:
 [1]  0.37760263  0.36183604  0.35465511  0.34773687  0.30503724  0.18599247
 [7]  0.12593031  0.09374236  0.02984161 -0.50944468

Largest  eigenvalues:
 [1] 99559108 96302892 89969866 86747295 84890903 84089648 83025149 81769868
 [9] 80015468 78514005

Smallest eigenvalues:
 [1]  0.31249005  0.29108176  0.26181397  0.24792714  0.14131434  0.09839221
 [7]  0.08009540 -0.07223220 -0.11408439 -0.16809780

Largest  eigenvalues:
 [1] 100290671  96992885  91168376  86220127  85375749  84346296  83125511
 [8]  82075253  80510177  79083207

Smallest eigenvalues:
 [1]  0.45213367  0.43621775  0.38318628  0.38197710  0.25267327  0.23193849
 [7]  0.10383533  0.06100657  0.01787862 -0.49939169

Largest  eigenvalues:
 [1] 98876202 97412122 90817865 86427420 85819873 83917984 83743106 81336712
 [9] 80313145 78341465

Smallest eigenvalues:
 [1]  0.4692218  0.4283286  0.4187500  0.3970100  0.3378676  0.2969187
 [7]  0.2932013  0.2397879  0.1354956 -0.2109869

Largest  eigenvalues:
 [1] 100886663  95740984  89824820  86109135  86009369  84042650  82235463
 [8]  81442361  79527111  78273939

Smallest eigenvalues:
 [1]  0.37721892  0.36178260  0.35926790  0.35914786  0.34806129  0.15178651
 [7]  0.01312851 -0.20305815 -0.24056860 -0.52847045

Largest  eigenvalues:
 [1] 99889486 97219354 90535407 87016701 86173941 84167110 83585594 81133749
 [9] 80391273 77805138

Smallest eigenvalues:
 [1]  0.44956212  0.43113748  0.34794090  0.30565046  0.24509971  0.21539892
 [7]  0.07626997  0.05901595 -0.09107371 -0.47723095

Largest  eigenvalues:
 [1] 98198568 96031354 89701386 85572522 85326996 83119099 82826619 80704813
 [9] 79369560 77406174

Smallest eigenvalues:
 [1]  0.405926625  0.390693620  0.363323656  0.265052771  0.260446920
 [6]  0.212611893  0.210829100  0.207717460 -0.006217537 -0.190462800

Largest  eigenvalues:
 [1] 100571932  96218987  89712430  86118059  84899480  83828761  82379222
 [8]  81111765  79804814  78306279

Smallest eigenvalues:
 [1]  0.29379923  0.26671983  0.23145690  0.19418080  0.16178844  0.15327418
 [7]  0.09182310  0.06621997 -0.03902393 -0.52312589

Largest  eigenvalues:
 [1] 99708647 97342367 91226684 86766161 85076191 83926140 83336027 81235030
 [9] 80382298 77858810

Smallest eigenvalues:
 [1]  0.4597979  0.4400163  0.3935718  0.3930541  0.2982237  0.2616361
 [7]  0.2411777  0.2285961 -0.0936151 -0.1470789

Largest  eigenvalues:
 [1] 100221320  97644767  91205674  86963075  85906252  83946978  83421463
 [8]  81224812  80232309  78459953

Smallest eigenvalues:
 [1]  0.31131033  0.27871188  0.27793978  0.24675938  0.24035070  0.17052164
 [7]  0.11874112  0.03552373  0.02022545 -0.37477601

Largest  eigenvalues:
 [1] 99914935 95425913 88887608 85756304 84965721 82859509 82581920 80668768
 [9] 78918687 77560808

Smallest eigenvalues:
 [1]  0.41072865  0.35380235  0.31152920  0.29829745  0.23563424  0.11042764
 [7]  0.08595452  0.05026712 -0.15045173 -0.45095803

Largest  eigenvalues:
 [1] 101414690  97422242  91455291  86947924  86485376  85623497  83209668
 [8]  82526556  80722420  79643316

Smallest eigenvalues:
 [1]  0.37661155  0.37492003  0.34053816  0.30530303  0.26060679  0.21956300
 [7]  0.11159119 -0.01691463 -0.05754314 -0.35915150

Largest  eigenvalues:
 [1] 100032000  97177861  90538020  87066209  85476424  84061138  83201690
 [8]  81225165  80587492  78374163

Smallest eigenvalues:
 [1]  0.47085305  0.44047079  0.43447665  0.40189831  0.36420557  0.33735926
 [7]  0.22780838  0.08806813  0.05957222 -0.13675461

Largest  eigenvalues:
 [1] 101322005  96967969  90697528  86841509  85685407  84402577  82715288
 [8]  81463851  80039088  78318791

Smallest eigenvalues:
 [1]  0.21245253  0.20660722  0.15106556  0.14926415  0.14852636  0.07290937
 [7]  0.04075537 -0.03508697 -0.25371986 -1.00928473

Largest  eigenvalues:
 [1] 99377370 97364407 90517905 87248111 85765702 84061761 83485525 81571040
 [9] 80306468 77945996

Smallest eigenvalues:
 [1]  0.45938470  0.45013613  0.43499194  0.40525092  0.30883185  0.30497477
 [7]  0.11091883  0.05602612 -0.17371783 -0.35642733

Largest  eigenvalues:
 [1] 100093563  96594256  90858245  86693456  84745672  83656362  83409091
 [8]  81165828  80256990  77908107

Smallest eigenvalues:
 [1]  0.314093203  0.306725501  0.248874030  0.245209039  0.196328915
 [6]  0.071010672  0.017277817  0.015906990 -0.006597346 -0.116304159

Largest  eigenvalues:
 [1] 97810937 97059264 90505453 86121661 84460474 83446259 82893943 80476818
 [9] 80068860 77597445

Smallest eigenvalues:
 [1]  0.39031490  0.37796342  0.34930858  0.34212798  0.24005479  0.14761918
 [7]  0.14685534  0.14405352  0.03708517 -0.49935565

Largest  eigenvalues:
 [1] 97808153 95028026 89383658 85206158 83530010 83239709 82104279 80491410
 [9] 79405177 77566529

Smallest eigenvalues:
 [1]  0.25923598  0.25236320  0.22232473  0.19899237  0.15081010  0.06844456
 [7]  0.06605889 -0.18679572 -0.23041843 -1.71139873

Largest  eigenvalues:
 [1] 99248883 97087692 90240480 86687804 85881591 84761920 82525057 81493474
 [9] 79870491 78450471

Smallest eigenvalues:
 [1]  0.39836078  0.39526171  0.38738993  0.28226396  0.27607376  0.25607851
 [7]  0.23984362  0.15642635  0.08866805 -0.31615196

Largest  eigenvalues:
 [1] 97346160 95663274 89495304 86036390 83882987 83232543 82291795 81095326
 [9] 79277744 77979753

Smallest eigenvalues:
 [1]  0.313284458  0.310829996  0.252046172  0.251562527  0.164256148
 [6]  0.051978263  0.020428095 -0.001386579 -0.279840232 -0.338049989

Largest  eigenvalues:
 [1] 100228039  97118594  91513487  86092541  85488439  83970107  83272567
 [8]  81460678  80637422  78614630

Smallest eigenvalues:
 [1]  0.41080465  0.38001527  0.34669900  0.27227910  0.25363763  0.22499337
 [7]  0.22173489  0.19278159  0.06858431 -0.13090833

Largest  eigenvalues:
 [1] 99784818 96452165 89471537 86187067 85389388 82963293 82590269 80235532
 [9] 79325819 76987017

Smallest eigenvalues:
 [1]  0.458498097  0.456589721  0.420246750  0.388439121  0.378101419
 [6]  0.337765963  0.296999919  0.217440473  0.009250704 -0.190879226

Largest  eigenvalues:
 [1] 100691810  95796460  89999010  86217049  85069473  83425480  82333258
 [8]  81148756  79405296  78030491

Smallest eigenvalues:
 [1]  0.403401895  0.396575899  0.339065942  0.205026448  0.169466699
 [6]  0.166501472  0.039562486 -0.006456898 -0.259688163 -0.719661342

Largest  eigenvalues:
 [1] 100090304  96358671  90795176  86035637  85179572  83495549  82961045
 [8]  81037517  80231164  77902914

Smallest eigenvalues:
 [1]  0.33489898  0.31948839  0.29983695  0.25278292  0.19677031  0.16581440
 [7]  0.13645739  0.11775408  0.06606754 -0.16810145

Largest  eigenvalues:
 [1] 98743753 97532819 90754413 87076455 84323844 83731923 83425970 81180890
 [9] 80474875 78012914

Smallest eigenvalues:
 [1]  0.40085074  0.37300348  0.35643040  0.30709310  0.24466219  0.22871078
 [7]  0.17313416  0.09851080 -0.01197968 -0.09208119

Largest  eigenvalues:
 [1] 98984981 96334258 89806810 86920017 84933597 83461642 82764242 80822350
 [9] 80074287 77738362

Smallest eigenvalues:
 [1]  0.3727153070  0.3637305411  0.3104891141  0.3004390483  0.2582798690
 [6]  0.2524897325  0.2217216022  0.0590810246  0.0008437753 -0.5295404927

Largest  eigenvalues:
 [1] 102554803  96016389  90802808  85931817  85779304  84139036  82359364
 [8]  81643848  79764004  78420441

Smallest eigenvalues:
 [1]  0.51737863  0.49984632  0.49172217  0.44882690  0.36934854  0.31030308
 [7]  0.20670276  0.19453192  0.05975679 -0.17234306

Largest  eigenvalues:
 [1] 100643915  96202406  89708965  86066398  85655332  83543294  82502070
 [8]  80890705  79784241  77857469

Smallest eigenvalues:
 [1]  0.34296124  0.29873743  0.25007675  0.23902385  0.23552444  0.15602640
 [7]  0.04632341  0.03537650 -0.18118070 -0.59643524

Largest  eigenvalues:
 [1] 100279656  96075210  90156225  85551588  85335796  83629207  82431881
 [8]  81213635  79271178  77872124

Smallest eigenvalues:
 [1]  0.2680535  0.2304919  0.2177748  0.2030088  0.1828213  0.1433360
 [7] -0.1148718 -0.1805616 -0.2355844 -0.4479960

Largest  eigenvalues:
 [1] 100585063  97121171  91481766  86700314  84762150  83679646  83439441
 [8]  81317150  80348024  77973821

Smallest eigenvalues:
 [1]  0.37671217  0.37430604  0.36117745  0.35001678  0.27092440  0.21888527
 [7]  0.13756463  0.08396045 -0.13767705 -1.06654921

Largest  eigenvalues:
 [1] 100419108  96840975  90098389  86800322  86181572  84249606  82990260
 [8]  81572909  80277651  78647144

Smallest eigenvalues:
 [1]  0.4074080  0.3967413  0.3701096  0.3528831  0.3421448  0.2849518
 [7]  0.2314174  0.2147500  0.1423941 -0.1060413

Largest  eigenvalues:
 [1] 99929547 96218963 89662323 86087950 85504517 83409500 82483543 80675760
 [9] 79848095 77632442

Smallest eigenvalues:
 [1]  0.45419145  0.43425036  0.42495091  0.30142881  0.25420232  0.18762717
 [7]  0.17765908  0.08862725  0.05584173 -0.32046316

Largest  eigenvalues:
 [1] 101742773  97032644  90796846  86502784  86468291  84108359  82736303
 [8]  81529986  80130655  78987724

Smallest eigenvalues:
 [1]  0.31431116  0.30401229  0.29482882  0.23339797  0.21266297  0.20039933
 [7]  0.10415410  0.08946401  0.08474100 -0.23343580

Largest  eigenvalues:
 [1] 98699953 97228258 90868236 86363864 84901020 83731627 82939562 80978494
 [9] 79817840 77912238

Smallest eigenvalues:
 [1]  0.3240336  0.2967009  0.2927913  0.2874111  0.1889279  0.1860270
 [7]  0.1061618  0.0133811 -0.1831504 -0.3977991

Largest  eigenvalues:
 [1] 98365216 96987410 90187599 86346175 84725479 83790222 83591403 81479119
 [9] 80228266 78448412

Smallest eigenvalues:
 [1]  0.26495640  0.26489071  0.22371769  0.21272452  0.21092455  0.13450794
 [7]  0.07568175 -0.11308530 -0.25355568 -0.38785730

Largest  eigenvalues:
 [1] 100491773  95592483  89483865  85601483  85489499  82743754  82566395
 [8]  80384907  79315528  77336978

Smallest eigenvalues:
 [1]  0.20849775  0.20253732  0.19351602  0.09609910 -0.05523809 -0.25221580
 [7] -0.26257271 -0.34160063 -0.59292528 -0.85442338

Largest  eigenvalues:
 [1] 103198308  95716266  90003891  86909666  85829582  83603974  82528480
 [8]  81540857  80021167  78695613

Smallest eigenvalues:
 [1]  0.27124006  0.22904853  0.22640671  0.19259504  0.17670303  0.11733140
 [7]  0.03183786  0.00249886 -0.60376701 -0.80894782

Largest  eigenvalues:
 [1] 100673602  97409450  91515394  87079070  85942614  84881373  84089383
 [8]  82481464  81464515  79423696

Smallest eigenvalues:
 [1]  0.274472616  0.230702312  0.200248548  0.154492050  0.150924328
 [6]  0.095856745  0.035929818  0.004475167 -0.145421725 -0.624190552

Largest  eigenvalues:
 [1] 101538431  97484694  91723375  87624019  86213488  84619455  83642029
 [8]  81979964  80760794  79012205

Smallest eigenvalues:
 [1]  0.41310806  0.39554402  0.38618436  0.31271958  0.24652824  0.20700732
 [7]  0.20154068  0.12364335 -0.08561735 -0.88749876

Largest  eigenvalues:
 [1] 99271555 97350853 91114716 86844757 85247488 84041997 83368549 81021300
 [9] 80452200 77773715

Smallest eigenvalues:
 [1]  0.4775575  0.4416685  0.4174721  0.3846210  0.3787343  0.2681676
 [7]  0.2461911  0.2069391  0.1219360 -0.4126579

Largest  eigenvalues:
 [1] 99493125 97104916 90511072 86636753 85750709 83731296 83284917 81289769
 [9] 80087007 78325864

Smallest eigenvalues:
 [1]  0.321047589  0.256578596  0.246271330  0.241456877  0.233125494
 [6]  0.146518835  0.115333127  0.005539807 -0.668371730 -0.792509817

Largest  eigenvalues:
 [1] 101061241  97283880  90959774  87238111  87045290  85133011  83521049
 [8]  82210550  80981195  79148486

Smallest eigenvalues:
 [1]  0.31502864  0.29885731  0.27042688  0.25000756  0.13478598  0.09440181
 [7] -0.05863189 -0.18305294 -0.20343206 -0.40745947

Largest  eigenvalues:
 [1] 101666259  96161519  90160730  86162939  86149603  83021845  82876465
 [8]  80622416  79911005  77607571

Smallest eigenvalues:
 [1]  0.32321599  0.29765039  0.28275263  0.23299141  0.20687585  0.14359639
 [7] -0.05513066 -0.09088349 -0.13955483 -0.68653307

Largest  eigenvalues:
 [1] 101167422  96969937  91183942  86732446  86210555  84643096  83458690
 [8]  82176422  80460081  78838903

Smallest eigenvalues:
 [1]  0.443018052  0.433213211  0.409304825  0.341968996  0.322748177
 [6]  0.272489144  0.269587057  0.061893489 -0.005889398 -0.031154854

Largest  eigenvalues:
 [1] 99387816 96943807 90141891 86317755 85904622 83114595 82768579 80480453
 [9] 79807087 77596674

Smallest eigenvalues:
 [1]  0.46888194  0.44823053  0.43925039  0.43603113  0.24706506  0.17091920
 [7]  0.15326666  0.10653323  0.04191861 -0.08799794

Largest  eigenvalues:
 [1] 100689112  96678238  90632215  86676106  85667570  84646780  83016529
 [8]  81922957  80678611  79055828

Smallest eigenvalues:
 [1]  0.44876530  0.42748719  0.40161040  0.37347764  0.30731749  0.26952745
 [7]  0.22240745  0.14723311  0.04313528 -0.10656128

Largest  eigenvalues:
 [1] 98249151 96912514 90282710 86542644 84940550 83840127 83274650 81297173
 [9] 79972219 78152178

Smallest eigenvalues:
 [1]  0.31051564  0.28985408  0.21245428  0.19608185  0.06897631 -0.03223848
 [7] -0.20209307 -0.29525275 -0.50162766 -0.83945699

Largest  eigenvalues:
 [1] 102471592  95172423  90001053  85932613  84847533  83312912  82309420
 [8]  81264859  79268381  78158983

Smallest eigenvalues:
 [1]  0.3963428  0.3612168  0.3544779  0.3079443  0.2922775  0.2840457
 [7]  0.2465732 -0.1109756 -0.3454127 -0.3639729

Largest  eigenvalues:
 [1] 101169130  95860693  90048167  86057373  85187984  83554025  83163367
 [8]  81272632  79953091  78011318

Smallest eigenvalues:
 [1]  0.36818786  0.34443605  0.34330245  0.26352006  0.23837803  0.22697530
 [7]  0.14965625  0.13984745 -0.01714207 -0.43932538

Largest  eigenvalues:
 [1] 100897932  97004602  90779091  87101643  85714829  83326501  82823537
 [8]  80798358  79924877  77934946

Smallest eigenvalues:
 [1]  0.339465543  0.328428933  0.313407795  0.286559421  0.285598306
 [6]  0.257465199  0.245470759  0.101111314  0.003669218 -0.488906157

Largest  eigenvalues:
 [1] 98608666 97029308 89942148 86443380 85436910 83758391 83302106 81346349
 [9] 79992980 78036444

Smallest eigenvalues:
 [1]  0.37813408  0.34924592  0.31326803  0.30185522  0.29897284  0.18525517
 [7]  0.17236735  0.07706857  0.04655103 -0.12091970

Largest  eigenvalues:
 [1] 102004511  97017037  90977195  86504296  86201110  83728273  82671964
 [8]  81132065  79690198  78114046

Smallest eigenvalues:
 [1]  0.38849735  0.37753133  0.35391690  0.31472925  0.28686815  0.27276788
 [7]  0.25271352  0.07130709 -0.09001781 -0.17834236

Largest  eigenvalues:
 [1] 102031990  96016037  90345615  86672013  85583433  83557185  82368742
 [8]  81169442  79501202  77805902

Smallest eigenvalues:
 [1]  0.27817447  0.23720392  0.20269332  0.19309593  0.15496230  0.14107932
 [7]  0.13863626  0.05970453 -0.08667786 -1.31664468

Largest  eigenvalues:
 [1] 98720336 95742280 89441213 85926938 84031525 82934738 82394779 80367454
 [9] 79323556 77139984

Smallest eigenvalues:
 [1]  0.32259028  0.28718578  0.26595576  0.25182607  0.16949987  0.04819654
 [7] -0.01027395 -0.06673669 -0.08626667 -0.36186837

Largest  eigenvalues:
 [1] 99952323 96661136 90322810 86416946 85510766 83445283 82947620 80869633
 [9] 80217725 77739396

Smallest eigenvalues:
 [1]  0.35591690  0.35300928  0.33931493  0.33493348  0.32307042  0.23847879
 [7]  0.21540666  0.20364584  0.14205951 -0.06026108

Largest  eigenvalues:
 [1] 99380047 96549841 90846855 86132381 84728796 84440209 83158418 81662943
 [9] 80311703 78714208

Smallest eigenvalues:
 [1]  0.26642410  0.25581797  0.19490048  0.18147550  0.02421292  0.02406712
 [7] -0.18875475 -0.37089817 -0.43742610 -0.97236271

Largest  eigenvalues:
 [1] 99596398 97418785 91183505 86463696 86015405 83764300 83372938 81328489
 [9] 80340177 78348409

Smallest eigenvalues:
 [1]  0.50025117  0.39843823  0.39083446  0.38194174  0.34848935  0.32932914
 [7]  0.16617195  0.15689723 -0.05260435 -0.24970872

Largest  eigenvalues:
 [1] 100722078  96645060  90070229  86863546  86137152  84310195  82370754
 [8]  81308418  79738294  78343637

Smallest eigenvalues:
 [1]  0.302375575  0.215083527  0.212562528  0.207308069  0.112655653
 [6]  0.098919665  0.023181595  0.002992639 -0.343116301 -0.644366724

Largest  eigenvalues:
 [1] 99098176 96956999 90859297 86238772 85401493 83888217 83449735 81208517
 [9] 80144778 78045204

Smallest eigenvalues:
 [1]  0.4588222  0.4267511  0.4176553  0.3883630  0.3876748  0.3333641
 [7]  0.2769433  0.1446222 -0.1176175 -0.2994323

Largest  eigenvalues:
 [1] 100619958  95844347  90052100  85989164  85545683  83143355  82574198
 [8]  80609272  79758716  77496234

Smallest eigenvalues:
 [1]  0.33950745  0.33447094  0.28815610  0.28027972  0.27819773  0.25111271
 [7]  0.22168267 -0.05237228 -0.40712417 -0.53493874

Largest  eigenvalues:
 [1] 100328398  96955095  90529150  86355623  86257038  84516084  83221751
 [8]  81809060  80030567  78563354

Smallest eigenvalues:
 [1]  0.13205679  0.10842634  0.10184721  0.05648537  0.05537725  0.03935342
 [7] -0.04814956 -0.15145606 -0.46596589 -0.51276531

Largest  eigenvalues:
 [1] 98397788 96448275 91300422 87783670 84602707 83604751 83320197 80990146
 [9] 80446167 77637415

Smallest eigenvalues:
 [1]  0.37175172  0.36527311  0.35833299  0.34443991  0.28026019  0.16409954
 [7]  0.11544373  0.06779821  0.02316705 -0.07093374

Largest  eigenvalues:
 [1] 99246119 96932624 90886803 86423134 84647982 84472074 83318966 81882594
 [9] 80477566 78975551

Smallest eigenvalues:
 [1]  0.27593798  0.26882660  0.23980222  0.14942382  0.12214058  0.11610548
 [7] -0.04505453 -0.13823081 -0.25462989 -0.27196716

Largest  eigenvalues:
 [1] 99125996 96724292 90308229 86466196 85676195 83707786 82898440 81049550
 [9] 80025062 78385729

Smallest eigenvalues:
 [1]  0.46648745  0.44837094  0.44158263  0.38085923  0.37186917  0.36568731
 [7]  0.24770157  0.19141239  0.13837776 -0.05683146

Largest  eigenvalues:
 [1] 99184202 95162005 89384377 85143910 84033476 83283302 81551453 80593881
 [9] 78864748 77402415

Smallest eigenvalues:
 [1]  0.4097244  0.3178153  0.2667854  0.2208578  0.2162445  0.2145888
 [7]  0.2131585  0.2129423 -0.2270495 -0.3191023

Largest  eigenvalues:
 [1] 98267567 96969484 91068004 86251795 84569527 83941578 82942608 81363583
 [9] 79556860 78335908

Smallest eigenvalues:
 [1]  0.36672967  0.35645687  0.24224017  0.22070704  0.19904944  0.11382517
 [7] -0.04024551 -0.47150064 -0.48852963 -1.31912532

Largest  eigenvalues:
 [1] 102767114  97981184  91472173  87761712  87100613  84927348  83899368
 [8]  82282737  81009300  79417094

Smallest eigenvalues:
 [1]  0.23481631  0.21982836  0.21048491  0.20896228  0.17719247  0.16246698
 [7]  0.05035253  0.03924741 -0.23450144 -0.53293250

Largest  eigenvalues:
 [1] 99201337 97207139 90949668 86617499 85234546 83954489 83374533 81478305
 [9] 80429618 78465224

Smallest eigenvalues:
 [1]  0.428617258  0.404801171  0.352566605  0.343006154  0.318883414
 [6]  0.299959035  0.251958770  0.027442156  0.001942045 -0.021128535

Largest  eigenvalues:
 [1] 99849052 96876335 90948052 86187186 85290238 83852206 83051997 80916079
 [9] 80277180 78115014

Smallest eigenvalues:
 [1]  0.42917812  0.34589424  0.30366688  0.30155517  0.22992807  0.15943113
 [7]  0.14776920  0.13517865  0.01593799 -0.05816734

Largest  eigenvalues:
 [1] 97592284 96163709 89712024 86025829 84427021 83327239 82778989 80733220
 [9] 79637038 77675034

Smallest eigenvalues:
 [1]  0.35942367  0.31197655  0.28768258  0.28370090  0.24594165  0.22076058
 [7]  0.14438131  0.04239094 -0.28719232 -0.29265377

Largest  eigenvalues:
 [1] 97728963 96755149 89852528 86188725 85089459 84056946 82507876 81235969
 [9] 79375947 78028877

Smallest eigenvalues:
 [1]  0.39862900  0.38488347  0.38423546  0.34398073  0.23361275  0.20624471
 [7]  0.17135076 -0.08379514 -0.10908396 -0.29689802

Largest  eigenvalues:
 [1] 100015111  96198242  90135451  86473997  85553230  83700278  82394531
 [8]  80882895  79455733  77791560

Smallest eigenvalues:
 [1]  0.3449952  0.3298586  0.3245529  0.2909400  0.2390100  0.2389493
 [7]  0.1978010  0.1556460  0.1414455 -0.4161229

Largest  eigenvalues:
 [1] 98744302 97436351 90896911 87079748 85401945 84653689 83164328 81787636
 [9] 79703793 78337059

Smallest eigenvalues:
 [1]  0.34646422  0.33304773  0.27320820  0.26040558  0.16977101  0.14595103
 [7]  0.14507878  0.08576811 -0.29135459 -0.48845203

Largest  eigenvalues:
 [1] 99725346 96755847 90421569 86459429 86073479 85096212 82979874 82401938
 [9] 80075619 79147807

Smallest eigenvalues:
 [1]  0.399628029  0.393430955  0.275768994  0.190936404  0.186153069
 [6]  0.090511332  0.086989351  0.032912539  0.006328245 -0.268763860

Largest  eigenvalues:
 [1] 99212951 96764403 90393656 86633321 84308560 83662643 82933602 80904224
 [9] 79764997 77515016

Smallest eigenvalues:
 [1]  0.229245847  0.211035407  0.108199259  0.105259863  0.078437317
 [6]  0.005624065 -0.017416658 -0.052969226 -0.091139899 -0.572878304

Largest  eigenvalues:
 [1] 99176070 96365984 90069536 86293296 84661507 83017050 82798501 80657583
 [9] 79703400 77576040

Smallest eigenvalues:
 [1]  0.35344173  0.35169601  0.29651357  0.27540075  0.27252579  0.26509883
 [7]  0.20889515  0.05811856  0.02331890 -0.10848214

Largest  eigenvalues:
 [1] 98382937 98063424 91433626 87865870 84661230 84474282 84152148 81791083
 [9] 80819320 78358589

Smallest eigenvalues:
 [1]  0.484711937  0.464397795  0.460029971  0.420550638  0.406648248
 [6]  0.400444451  0.359702533  0.084779176  0.004643896 -0.047970685

Largest  eigenvalues:
 [1] 101225338  96972709  90329182  86917538  86420219  84570882  82842403
 [8]  81433132  80246810  78521589

Smallest eigenvalues:
 [1]  0.3223312  0.3133303  0.2807783  0.2803595  0.2403501  0.2273902
 [7]  0.2010201  0.1799303 -0.1146300 -0.3789557

Largest  eigenvalues:
 [1] 99949663 96225238 89792217 85646782 85150469 83132908 82070292 80598308
 [9] 79427113 77892896

Smallest eigenvalues:
 [1]  0.47336466  0.46521729  0.36163158  0.33729698  0.28877477  0.27263974
 [7]  0.26381791  0.04073367 -0.14707974 -0.39364029

Largest  eigenvalues:
 [1] 103199770  95985428  90592673  86330967  86195579  84203549  82718886
 [8]  81858016  80143574  78686127

Smallest eigenvalues:
 [1]  0.37142294  0.36150721  0.34485164  0.33796501  0.23220514  0.21711344
 [7]  0.19104552  0.08555758 -0.01702987 -0.11570236

Largest  eigenvalues:
 [1] 100380630  97297920  90908858  86553787  85991789  84456289  83410405
 [8]  81562282  80451831  78390035

Smallest eigenvalues:
 [1]  0.40325161  0.38671779  0.36522420  0.36169364  0.34129946  0.31401020
 [7]  0.15019437  0.07127135 -0.06730594 -0.10579871

Largest  eigenvalues:
 [1] 97958304 96367686 89511740 86404848 84161861 83593581 81725710 79599455
 [9] 79326443 76174294

Smallest eigenvalues:
 [1]  0.3454119  0.3141145  0.2817877  0.2618520  0.2094059  0.1405137
 [7]  0.1085651  0.1018783  0.0129301 -0.2010862

Largest  eigenvalues:
 [1] 99092645 96833885 90078243 86563662 85529709 83759886 82688125 80690387
 [9] 79903493 77705498

Smallest eigenvalues:
 [1]  0.35816381  0.32277173  0.28796838  0.27088540  0.26608905  0.21362866
 [7]  0.07612091 -0.18094776 -0.36042107 -0.41707999

Largest  eigenvalues:
 [1] 102140772  97459499  91441244  87070662  86537204  84638888  83683507
 [8]  82434922  80806133  79590165

Smallest eigenvalues:
 [1]  0.3900280  0.3794089  0.3408131  0.2658394  0.2499082  0.2268678
 [7]  0.1885378 -0.1821073 -0.4017061 -0.4515327

Largest  eigenvalues:
 [1] 101527335  98048617  91368555  87531320  87407152  85608090  83857224
 [8]  82691862  81010480  79581223

Smallest eigenvalues:
 [1]  0.41773987  0.41482266  0.34549022  0.32593907  0.32140120  0.31795387
 [7]  0.23161854  0.20562727  0.05054392 -0.04718841

Largest  eigenvalues:
 [1] 97937332 96448687 88911231 86568001 84569052 83264606 83027001 80605480
 [9] 79370689 77487846

Smallest eigenvalues:
 [1]  0.28515622  0.25645770  0.25611474  0.24955606  0.18851065  0.17321769
 [7]  0.07821665  0.06115378 -0.22768348 -0.23824025

Largest  eigenvalues:
 [1] 99411744 96361726 90513547 86067230 84638625 83030218 82757730 80648661
 [9] 79923228 77621022

Smallest eigenvalues:
 [1]  0.34563097  0.33164010  0.22131756  0.19967235  0.12474336  0.09391956
 [7]  0.07950065  0.07577933 -0.10071544 -0.12849286

Largest  eigenvalues:
 [1] 101275703  97744200  91455978  87027251  85638049  84041800  83247070
 [8]  81237680  80171061  78136540

Smallest eigenvalues:
 [1]  0.27885939  0.26903588  0.24111008  0.15190376  0.14045656  0.06802534
 [7]  0.02984304 -0.01374009 -0.10950806 -0.35652718

Largest  eigenvalues:
 [1] 96732182 96008539 90080271 86338523 83744566 83118807 82943695 80824075
 [9] 79658306 77262902

Smallest eigenvalues:
 [1]  0.30063993  0.29631723  0.26422534  0.25198386  0.23796207  0.21666162
 [7]  0.16106770  0.07951774  0.07603121 -0.14976514

Largest  eigenvalues:
 [1] 99349475 96807543 89822579 86664030 84745144 84373236 82828176 81678797
 [9] 79798081 78380596

Smallest eigenvalues:
 [1]  0.23714340  0.23196729  0.19928415  0.19618710  0.15868110  0.05805298
 [7]  0.02658923 -0.12856663 -0.40083258 -1.09621734

Largest  eigenvalues:
 [1] 102310945  96894070  91732140  86170335  86045650  84815626  83080521
 [8]  82608263  80401031  79414190

Smallest eigenvalues:
 [1]  0.44912469  0.44233099  0.39630960  0.38307006  0.32344334  0.23107470
 [7]  0.15981179  0.10479993  0.08017396 -0.16215229

Largest  eigenvalues:
 [1] 99787233 96072598 89631967 86805850 85006367 82995240 82750786 80358447
 [9] 79635028 77243902

Smallest eigenvalues:
 [1]  0.410139102  0.404092112  0.381775714  0.377532893  0.225243378
 [6]  0.211265833  0.084522730  0.009718151  0.007250021 -0.276611646

Largest  eigenvalues:
 [1] 99400195 95612316 89754342 85402281 84884448 83279824 81998921 80347792
 [9] 79370841 77578389

Smallest eigenvalues:
 [1]  0.3813101  0.3298211  0.3000051  0.2511375  0.2162794  0.2089192
 [7]  0.1479285  0.1032967 -0.1170077 -0.3179301

Largest  eigenvalues:
 [1] 98614134 95976906 89515474 85706928 84880284 82618171 82273691 80062633
 [9] 79119409 77137317

Smallest eigenvalues:
 [1]  0.46342904  0.43755500  0.42007454  0.36745766  0.31590176  0.21377818
 [7]  0.20594263  0.16125315 -0.06850554 -0.11062541

Largest  eigenvalues:
 [1] 101107260  96378627  89747632  86250886  85744330  83754362  82451631
 [8]  81004998  79924346  78168508

Smallest eigenvalues:
 [1]  0.42806610  0.35104938  0.34807065  0.33608485  0.32924065  0.32150001
 [7]  0.12192950  0.09759104 -0.11167794 -0.12932110

Largest  eigenvalues:
 [1] 101863909  96600821  90460738  86826807  86509823  83840549  82997354
 [8]  81126448  80352413  77987962

Smallest eigenvalues:
 [1]  0.46642828  0.43716392  0.41653242  0.35934138  0.34451162  0.26536333
 [7]  0.24551153  0.19147015 -0.03646138 -0.20826431

Largest  eigenvalues:
 [1] 101148232  96209533  90165562  86331613  86262233  83957635  82406434
 [8]  81230696  80000994  78540599

Smallest eigenvalues:
 [1]  0.41867637  0.35632334  0.32348462  0.29727318  0.26370391  0.23843074
 [7]  0.05770251  0.01608767 -0.04406826 -0.06623116

Largest  eigenvalues:
 [1] 99067657 97274783 89824284 87491919 84956223 83659899 83041310 80570791
 [9] 80228711 77649236

Smallest eigenvalues:
 [1]  0.40137864  0.38889178  0.32479432  0.28334003  0.23415514  0.21112442
 [7]  0.15482432  0.13196442  0.08640855 -0.02693301

Largest  eigenvalues:
 [1] 99225450 97495805 90639545 87379316 84616902 84490204 83031376 81565079
 [9] 80564035 78902048

Smallest eigenvalues:
 [1]  0.37749948  0.32018202  0.25589822  0.23955210  0.20192800  0.19452190
 [7]  0.18201782  0.10355985  0.03731818 -0.11208304

Largest  eigenvalues:
 [1] 97979360 97894039 90476967 86722291 84597340 83632611 83166905 80616679
 [9] 79966049 77690294

Smallest eigenvalues:
 [1]  0.41368735  0.39047570  0.37636921  0.31446144  0.28392998  0.23814518
 [7]  0.23457630  0.09824392  0.02206441 -0.47102990

Largest  eigenvalues:
 [1] 98477698 96729576 90160366 86031238 85221928 84301004 83022716 81504286
 [9] 79789946 78356040

Smallest eigenvalues:
 [1]  0.4582915  0.4526640  0.4477887  0.3260148  0.2338115  0.2171097
 [7]  0.1875100  0.1685598  0.1240071 -0.1775180

Largest  eigenvalues:
 [1] 99537990 95261451 88646861 85289071 85190289 83163762 81449084 80406964
 [9] 78673950 77266300

Smallest eigenvalues:
 [1]  0.29072789  0.25287336  0.20523249  0.14288510  0.13876403  0.10296366
 [7]  0.08840748  0.04641719 -0.09422410 -0.11852544

Largest  eigenvalues:
 [1] 97068277 97033652 89758553 86316113 84719321 83697925 83522616 81160675
 [9] 79791413 77940896

Smallest eigenvalues:
 [1]  0.44985814  0.43500943  0.40978109  0.40632485  0.38812908  0.26480478
 [7]  0.18500513  0.10175388 -0.01181772 -0.35115980

Largest  eigenvalues:
 [1] 97997905 96678050 89959320 86772646 84430445 83714198 82997980 80678323
 [9] 80142563 77525440

Smallest eigenvalues:
 [1]  0.4681510  0.4376518  0.3697904  0.3582608  0.2599015  0.2271657
 [7]  0.2088376  0.1370148  0.0591722 -0.1053801

Largest  eigenvalues:
 [1] 98967244 97296109 91160059 86691282 85550954 84333765 83896686 81614048
 [9] 80714976 78781936

Smallest eigenvalues:
 [1]  0.32957192  0.29182676  0.27535905  0.19788924  0.16317191  0.09712017
 [7]  0.03730400 -0.27289352 -0.31904753 -0.43021397

Largest  eigenvalues:
 [1] 98607638 95288019 88621986 85227057 85026377 82546346 82434277 79991302
 [9] 79106433 76986539

Warning message in eigchk(Cmat):
"Near singularity in coefficient matrix."

Log10 Eigenvalues range from
 -4.01547907717633  to  8.00597875797177 

Smallest eigenvalues:
 [1]  0.259196756  0.249313642  0.245617617  0.156883606  0.150873072
 [6]  0.145698999  0.142372167  0.048984983 -0.001109882 -0.368079432

Largest  eigenvalues:
 [1] 98428021 97154830 90642423 86405619 85353201 83761097 83270055 81105276
 [9] 80385156 77886461

Smallest eigenvalues:
 [1]  0.218090767  0.121425792  0.114296346  0.045727397  0.041379965
 [6] -0.003286548 -0.028108202 -0.187746522 -0.562315609 -0.592506110

Largest  eigenvalues:
 [1] 99596110 96981560 90879063 86128246 85879332 83918849 83408812 81133967
 [9] 80392608 78211117

Smallest eigenvalues:
 [1]  0.340409402  0.329469676  0.281608910  0.185865752  0.171685812
 [6]  0.051564640 -0.007178453 -0.055688562 -0.056088263 -0.553729613

Largest  eigenvalues:
 [1] 98191868 97711970 90821438 87257403 85301549 84000131 83799543 81620805
 [9] 79801215 77950779

Smallest eigenvalues:
 [1]  0.41901044  0.31445856  0.22145064  0.19501874  0.18265206  0.12606786
 [7]  0.08121955  0.04241358 -0.08525668 -0.47532918

Largest  eigenvalues:
 [1] 101452127  96229412  90025195  86563982  85949159  83206074  82698738
 [8]  80698715  79814370  77690384

Smallest eigenvalues:
 [1]  0.36589845  0.31460653  0.30165254  0.26968992  0.18332818  0.18253122
 [7]  0.16222568 -0.07051108 -0.10201134 -0.56752033

Largest  eigenvalues:
 [1] 100345586  95951680  89654108  85661932  85616600  83112509  82923643
 [8]  80971772  79476273  77533271

Smallest eigenvalues:
 [1]  0.30367654  0.25207404  0.23254472  0.20109111  0.14811054  0.12419306
 [7]  0.11494188 -0.01170954 -0.27181657 -0.41077600

Largest  eigenvalues:
 [1] 99749597 96537618 90289641 86278266 85663294 84271923 82436051 81188901
 [9] 79917477 78304015

Smallest eigenvalues:
 [1]  0.441025453  0.439462083  0.372571162  0.356677027  0.313013594
 [6]  0.238547668  0.224046403  0.114471136 -0.009674968 -0.216150694

Largest  eigenvalues:
 [1] 99423634 97126305 90111197 87378814 85234403 84026160 83441953 81183508
 [9] 80435248 78147033

Smallest eigenvalues:
 [1]  0.435486334  0.417198161  0.416554776  0.281058376  0.250670057
 [6]  0.221277008 -0.006368029 -0.020031754 -0.057307928 -0.098471958

Largest  eigenvalues:
 [1] 101151130  96454685  90734231  86074600  85779590  83379060  83183615
 [8]  80978031  80294962  78070886

Smallest eigenvalues:
 [1]  0.3868220  0.3789579  0.3492270  0.3008169  0.2778945  0.1397108
 [7]  0.1292415  0.1276767 -0.1417223 -0.1463796

Largest  eigenvalues:
 [1] 98537937 96762464 90757702 86031794 84791344 83451552 82980380 80702426
 [9] 80039246 77768034

Smallest eigenvalues:
 [1]  0.29351778  0.27087740  0.26718787  0.26605354  0.22760828  0.20951933
 [7]  0.19888023 -0.05679158 -0.30420524 -0.44577242

Largest  eigenvalues:
 [1] 100159453  96992049  90676823  86239631  85490874  83871612  83486783
 [8]  81140006  80405209  77949290

Smallest eigenvalues:
 [1]  0.31210121  0.29676468  0.25489653  0.23534481  0.17556597  0.16176963
 [7]  0.03296527  0.01299031 -0.18791658 -0.35607091

Largest  eigenvalues:
 [1] 99397434 97293203 90616232 86721129 85171874 83821442 83595709 81165285
 [9] 80439179 77802061

Smallest eigenvalues:
 [1]  0.44224582  0.42063060  0.34986328  0.28829221  0.26456858  0.17754717
 [7]  0.06869811 -0.02368882 -0.05822343 -0.18000631

Largest  eigenvalues:
 [1] 100176069  96083635  90083969  86154758  85814355  84081751  83145709
 [8]  81473333  79964269  78332991

Smallest eigenvalues:
 [1]  0.39516742  0.39346730  0.32435771  0.32200876  0.25218728  0.21258067
 [7]  0.20579027  0.17422558  0.14710203 -0.07944606

Largest  eigenvalues:
 [1] 100089600  96755063  90572390  86365563  85497599  84368517  82957708
 [8]  81793504  80565545  78988086

Smallest eigenvalues:
 [1]  0.40028543  0.38825149  0.38467744  0.33513049  0.23741795  0.16506795
 [7]  0.15223137  0.06039350 -0.08664239 -0.63461905

Largest  eigenvalues:
 [1] 100974040  95560400  90147006  85332818  85197571  83739983  82137404
 [8]  81294257  79754662  78118248

Smallest eigenvalues:
 [1]  0.35454367  0.33639411  0.32766083  0.21714687  0.21073165  0.16153351
 [7]  0.12030570 -0.02118556 -0.32053854 -0.70574110

Largest  eigenvalues:
 [1] 102797605  96038489  90289079  86135019  85528318  83840614  82470316
 [8]  81482985  79839376  78382400

Smallest eigenvalues:
 [1]  0.42505074  0.41775639  0.38500489  0.34631109  0.30725052  0.28323056
 [7]  0.27981238  0.01403913 -0.08137273 -0.19322242

Largest  eigenvalues:
 [1] 101146142  97185577  90824185  86915344  86135074  85141001  83529662
 [8]  82569490  80712207  79505298

Smallest eigenvalues:
 [1]  0.36993710  0.33028816  0.32731964  0.30314400  0.29631073  0.23479809
 [7]  0.22525067  0.17854997 -0.02560994 -0.33201960

Largest  eigenvalues:
 [1] 101537599  96759784  90779334  86691465  85695453  83566135  82399410
 [8]  80841092  79787019  77824691

Smallest eigenvalues:
 [1]  0.39317939  0.38106219  0.35141570  0.31858379  0.30698009  0.29446393
 [7]  0.18572891 -0.08385814 -0.37576226 -0.81780937

Largest  eigenvalues:
 [1] 101632568  97059712  91065745  86937685  86578448  84346382  83291725
 [8]  82065876  80466212  79022467

Smallest eigenvalues:
 [1]  0.274190097  0.273652479  0.269222208  0.221017930  0.198924658
 [6]  0.075026662  0.027345104 -0.007483765 -0.100049567 -0.497888488

Largest  eigenvalues:
 [1] 98584708 97446450 90632336 86973782 84999799 84589347 83649732 81868079
 [9] 80368028 78672134

Smallest eigenvalues:
 [1]  0.3101156  0.2812338  0.2456275  0.1587053  0.1463317  0.1416373
 [7]  0.1080058 -0.1902076 -0.2473457 -0.4326882

Largest  eigenvalues:
 [1] 99429831 97094677 90262642 87200701 85896901 84955079 83849676 82164157
 [9] 80679518 79107106

Smallest eigenvalues:
 [1]  0.3768285  0.3357103  0.3141694  0.2925934  0.2366395  0.2290650
 [7]  0.2248386 -0.1920549 -0.6268244 -1.1577079

Largest  eigenvalues:
 [1] 100698618  98277135  91954786  87682044  86362721  84821749  84195523
 [8]  82018964  81399394  78944049

Smallest eigenvalues:
 [1]  0.27115226  0.26225686  0.23556787  0.21404877  0.21369164  0.19097448
 [7]  0.09825333 -0.17105229 -0.19535816 -0.31331510

Largest  eigenvalues:
 [1] 98839831 96840745 90272247 86289392 85331896 83712982 83259072 81305740
 [9] 79824444 77964753

Smallest eigenvalues:
 [1]  0.43994736  0.41874154  0.41299847  0.37380041  0.36380660  0.27293547
 [7]  0.21963153  0.03603612  0.01513694 -0.14864908

Largest  eigenvalues:
 [1] 100534921  95727116  89930214  85946800  85176071  82924403  82643602
 [8]  80475202  79670474  77212527

Smallest eigenvalues:
 [1]  0.37339401  0.31331646  0.30025620  0.26233953  0.19805133  0.19268086
 [7]  0.16568904  0.16402035  0.15988226 -0.02653874

Largest  eigenvalues:
 [1] 99876619 96975475 90615390 86793615 85588170 85155821 82839841 81981010
 [9] 80144016 78950471

Smallest eigenvalues:
 [1]  0.45169361  0.42740031  0.40597492  0.30450009  0.25938436  0.25381492
 [7]  0.19369093  0.09081850 -0.01894558 -0.20198622

Largest  eigenvalues:
 [1] 99522168 97166023 91031916 86468292 85417465 83634230 83324316 81009755
 [9] 80189476 78008132

Smallest eigenvalues:
 [1]  0.39817549  0.39519547  0.39221453  0.38811775  0.36246929  0.32616827
 [7]  0.25142713 -0.02559785 -0.06004750 -0.23770886

Largest  eigenvalues:
 [1] 99744542 95693085 89581587 85256937 84939759 83143348 82386383 80688494
 [9] 79278589 77590351

Smallest eigenvalues:
 [1]  0.359905443  0.325037405  0.291494018  0.281458375  0.217112446
 [6]  0.171013565  0.128861815  0.002151916 -0.337760144 -0.844361298

Largest  eigenvalues:
 [1] 100414942  96298376  90398512  86556588  85386919  83363472  82773181
 [8]  80511355  80129484  77506910

Smallest eigenvalues:
 [1]  0.42442600  0.41862708  0.39623058  0.30843689  0.29572071  0.28974822
 [7]  0.26471727  0.21085550 -0.06701425 -0.11128117

Largest  eigenvalues:
 [1] 99411075 97052472 90548873 86640969 85210319 84162671 83359419 81251740
 [9] 80423633 78252416

Smallest eigenvalues:
 [1]  0.37204263  0.31101989  0.30180413  0.29831277  0.27741850  0.22178133
 [7]  0.19367054  0.05446480  0.02483204 -0.15069950

Largest  eigenvalues:
 [1] 99681516 96245110 89766699 85887664 85290315 83825828 83287701 81642721
 [9] 79680228 78333747

Smallest eigenvalues:
 [1]  0.20700142  0.20185063  0.16721312  0.13012804  0.12607157  0.07549707
 [7]  0.06044686 -0.03663962 -0.45028358 -0.46509576

Largest  eigenvalues:
 [1] 99224611 98412673 91950906 88898837 85056550 84291883 84032718 81732058
 [9] 81246291 78230725

Smallest eigenvalues:
 [1]  0.41415410  0.41070569  0.38841230  0.35190471  0.34318967  0.33497720
 [7]  0.31396779  0.13813861  0.06721334 -0.40984924

Largest  eigenvalues:
 [1] 102480511  96341023  90656572  86504746  85769980  84498323  82468282
 [8]  81431207  80231301  78591154

Smallest eigenvalues:
 [1]  0.19026154  0.18460442  0.16440288  0.08446663  0.07973830  0.04368909
 [7] -0.20650268 -0.50374943 -0.97668665 -1.34700643

Largest  eigenvalues:
 [1] 99419544 96974443 90713130 86659997 86041423 84914576 83379350 82146695
 [9] 80870567 78976427

Smallest eigenvalues:
 [1]  0.35283779  0.33383613  0.28385606  0.22260731  0.21650760  0.20013846
 [7]  0.11291193  0.08583090  0.03724823 -0.17760326

Largest  eigenvalues:
 [1] 100467844  96447283  90985143  85734951  85578596  83458516  82948051
 [8]  80929081  80098863  78261205

Smallest eigenvalues:
 [1]  0.236674925  0.196333432  0.161101419  0.154485210  0.148593147
 [6]  0.001363579 -0.054575175 -0.218659529 -0.239224331 -0.319684180

Largest  eigenvalues:
 [1] 98654472 96511516 90432937 86989104 83578022 83519580 83344136 81134569
 [9] 80482244 77798489

Smallest eigenvalues:
 [1]  0.27084644  0.26036264  0.25183650  0.18144729  0.17232211  0.06987502
 [7] -0.05134286 -0.14784944 -0.31974606 -0.88826172

Largest  eigenvalues:
 [1] 100830801  96525537  90347329  86367571  86343278  83334634  83048460
 [8]  80617674  79981559  77431122

Smallest eigenvalues:
 [1]  0.26597564  0.25545233  0.25422201  0.20097502  0.19228524  0.06237084
 [7]  0.02574948 -0.04988070 -0.16662011 -0.30599645

Largest  eigenvalues:
 [1] 100387250  97974410  92176227  86913227  86051673  84896058  84166721
 [8]  82300726  81108437  79282069

Smallest eigenvalues:
 [1]  0.12090349  0.12038161  0.05659220  0.04976744  0.04688604 -0.06617030
 [7] -0.08217257 -0.08786815 -0.36310615 -0.46025389

Largest  eigenvalues:
 [1] 98481114 97609636 91229827 87477480 84689035 84265687 83322298 80827046
 [9] 80386709 77432665

Smallest eigenvalues:
 [1]  0.38647404  0.37604123  0.35281657  0.33201684  0.26623796  0.25973318
 [7]  0.22703667  0.11396106  0.05159202 -0.47088056

Largest  eigenvalues:
 [1] 99501508 96328063 90155692 86246068 85579232 83976769 82560282 81227234
 [9] 79607062 78104189

Smallest eigenvalues:
 [1]  0.29119720  0.26434436  0.25256430  0.22992220  0.22007386 -0.01779067
 [7] -0.10912288 -0.17256624 -0.94253995 -1.05241811

Largest  eigenvalues:
 [1] 100415818  96706330  91068024  86237538  85585364  83614060  83399271
 [8]  81319682  80282550  78011859

Smallest eigenvalues:
 [1]  0.423685212  0.358641430  0.343763630  0.319606363  0.312285656
 [6]  0.296451951  0.207879709  0.200301236  0.055839325 -0.003057454

Largest  eigenvalues:
 [1] 100288672  97451207  90624361  86487833  86480907  84075663  82663891
 [8]  81065809  79917246  78404547

Smallest eigenvalues:
 [1]  0.48887791  0.47736292  0.47717636  0.40620722  0.38931696  0.30925282
 [7]  0.30522812  0.26944861  0.22118918 -0.05669037

Largest  eigenvalues:
 [1] 99604403 96612206 89782802 86549668 85355365 83377167 82826510 80954125
 [9] 79594004 77735367

Smallest eigenvalues:
 [1]  0.31091702  0.20454303  0.19548475  0.16798131  0.14324054  0.13499058
 [7]  0.11177758  0.06977989  0.03012750 -1.05817888

Largest  eigenvalues:
 [1] 98664826 95220723 89134537 84799410 84293536 82256106 81908737 79854974
 [9] 78989336 76987559

Smallest eigenvalues:
 [1]  0.47139123  0.44564922  0.34291217  0.31928703  0.26539900  0.25404080
 [7]  0.19000088 -0.06733429 -0.08730505 -0.08809411

Largest  eigenvalues:
 [1] 101154751  96193456  90300361  85892165  84743259  83525548  82228703
 [8]  80938436  79551917  77625983

Smallest eigenvalues:
 [1]  0.4165684  0.3753378  0.3727181  0.3675855  0.3445250  0.3163810
 [7]  0.2568659  0.1335433 -0.1439579 -0.1823380

Largest  eigenvalues:
 [1] 100459529  97326496  90649900  86870869  86290559  84135404  83321036
 [8]  81284806  80583012  78344475

Smallest eigenvalues:
 [1]  0.3751088  0.3082582  0.2846152  0.2792904  0.2686102  0.2338961
 [7]  0.1976973  0.1067882 -0.1758633 -0.2869967

Largest  eigenvalues:
 [1] 100841028  96342942  90384275  86756271  86021714  84386337  82714464
 [8]  81519286  79566105  78210183

Smallest eigenvalues:
 [1]  0.2829990  0.2522599  0.2184583  0.1879066  0.1744687  0.1448572
 [7] -0.0211150 -0.2006961 -0.6272395 -0.9162553

Largest  eigenvalues:
 [1] 100977867  95839336  89392211  85839543  85769670  84015581  81990927
 [8]  81001702  79528786  77551917

Smallest eigenvalues:
 [1]  0.475675549  0.467663150  0.456874355  0.370401681  0.235164824
 [6]  0.230000107  0.219340425  0.179321869 -0.002527997 -0.085619389

Largest  eigenvalues:
 [1] 99617461 96208817 90199621 86034682 84857763 83693803 82693278 81082954
 [9] 79805478 78084052

Smallest eigenvalues:
 [1]  0.39890223  0.37849095  0.33083518  0.28708106  0.27494527  0.21151717
 [7]  0.21115159  0.04594424 -0.05599630 -0.18966230

Largest  eigenvalues:
 [1] 100807540  96351997  89994850  86798510  84867925  83644332  82571762
 [8]  80854733  79935247  78008363

Smallest eigenvalues:
 [1]  0.5398797  0.5119049  0.4910498  0.4553929  0.4285348  0.2442247
 [7]  0.2236218  0.2174147  0.1126432 -0.3077161

Largest  eigenvalues:
 [1] 101200087  95790897  90034271  85986469  85847795  83187038  82401688
 [8]  80625825  79780671  77577992

Smallest eigenvalues:
 [1]  0.362285239  0.256392152  0.255136133  0.245801268  0.207630656
 [6]  0.195891292  0.181043293  0.138143577 -0.008728413 -0.117895179

Largest  eigenvalues:
 [1] 98470545 96261078 89847389 85761141 83907744 83296823 82809204 80816730
 [9] 79469960 77323357

Smallest eigenvalues:
 [1]  0.34336671  0.28823191  0.28575239  0.19940711  0.17702827  0.10689894
 [7]  0.04083368 -0.02516718 -0.33429302 -0.37126126

Largest  eigenvalues:
 [1] 100816047  97275356  90641160  86584665  86227590  83461191  83278439
 [8]  80850998  80070177  77714746

Smallest eigenvalues:
 [1]  0.41378131  0.36194406  0.35018541  0.28551934  0.23192564  0.22591458
 [7]  0.11763455  0.09582884  0.00310396 -0.01600872

Largest  eigenvalues:
 [1] 98708699 95775077 89480775 85942675 84075112 83085320 82173690 80247674
 [9] 79422784 77203818

Smallest eigenvalues:
 [1]  0.27804713  0.26595776  0.19451082  0.14815892  0.05245555 -0.02131120
 [7] -0.25594283 -0.29253821 -0.67270772 -1.02913831

Largest  eigenvalues:
 [1] 101592160  97387017  91371384  87529858  86632848  85122233  84170164
 [8]  82426578  80882461  79414976

Smallest eigenvalues:
 [1]  0.42846211  0.42494961  0.34954212  0.34437638  0.32930869  0.26364152
 [7]  0.17359267  0.03940581 -0.19278295 -0.22221333

Largest  eigenvalues:
 [1] 99367496 96556598 90188138 86356102 84729359 83219631 82956413 80639491
 [9] 80087819 77638602

Smallest eigenvalues:
 [1]  0.38347536  0.35627308  0.29812688  0.27801859  0.27726729  0.23347794
 [7]  0.14519985  0.11876596 -0.05414279 -0.37327979

Largest  eigenvalues:
 [1] 98662275 95949085 89943937 85899151 83978626 83047907 82738688 80351334
 [9] 79685022 76946097

Smallest eigenvalues:
 [1]  0.36760940  0.35120392  0.29705876  0.26535126  0.26328126  0.21654292
 [7]  0.10906304  0.08295381  0.06830809 -0.40073066

Largest  eigenvalues:
 [1] 100180406  96550872  90443392  86362852  85413691  83688184  82578241
 [8]  80817413  79731402  77872326

Smallest eigenvalues:
 [1]  0.38170315  0.37559237  0.36337744  0.32469500  0.29244703  0.24883401
 [7]  0.21256052  0.05151235 -0.03317623 -0.59633988

Largest  eigenvalues:
 [1] 98931766 95469050 88882223 85298399 84134462 83206474 82250343 80501442
 [9] 79144870 77529246

Smallest eigenvalues:
 [1]  0.38711372  0.37310976  0.36558909  0.33357093  0.26801582  0.20142193
 [7]  0.16883399  0.14218216 -0.03222853 -0.13851576

Largest  eigenvalues:
 [1] 99850233 96314294 90129294 86497378 84695458 84464230 82792624 81811295
 [9] 80161330 78718575

Smallest eigenvalues:
 [1]  0.36374899  0.34638654  0.33119650  0.32025008  0.28654127  0.22596740
 [7]  0.16369697  0.04255003  0.04026850 -0.25951160

Largest  eigenvalues:
 [1] 101080853  97264752  91372453  86560250  86456136  84456539  83286847
 [8]  81890568  80527971  78804341

Smallest eigenvalues:
 [1]  0.40008244  0.38841572  0.37563787  0.34217453  0.23345082  0.21731559
 [7]  0.20292146  0.18104199  0.04963511 -0.10371434

Largest  eigenvalues:
 [1] 99949754 96065104 89948613 85835089 85632412 84052498 82515558 81440915
 [9] 79544129 78206953

Smallest eigenvalues:
 [1]  0.39189412  0.38527035  0.34313987  0.23559510  0.21788875  0.14420221
 [7]  0.13312286 -0.02473703 -0.18785820 -0.93056149

Largest  eigenvalues:
 [1] 101790662  96728218  90819899  87261941  86637686  83852840  83254602
 [8]  81599388  80311863  78417057

Smallest eigenvalues:
 [1]  0.22945440  0.22142444  0.21661571  0.16272737  0.10505681  0.04489440
 [7] -0.02834395 -0.11923691 -0.17255477 -0.62328909

Largest  eigenvalues:
 [1] 100371869  97800458  91808555  87087175  85993068  84630821  83914020
 [8]  82150836  80805313  78848494

Smallest eigenvalues:
 [1]  0.43512981  0.40665327  0.39082725  0.36193407  0.35078444  0.32496774
 [7]  0.15677982  0.14423356  0.01115005 -0.08789770

Largest  eigenvalues:
 [1] 98701410 96935267 90284678 86701902 84186580 82993401 82806822 80113616
 [9] 79753318 76824208

Smallest eigenvalues:
 [1]  0.26578445  0.25326925  0.23449873  0.19144536  0.15726074  0.09172629
 [7]  0.08388444  0.02972164 -0.05190195 -0.26329349

Largest  eigenvalues:
 [1] 99349327 97548308 90339028 87245524 85546253 84704440 83350332 81904533
 [9] 80563672 79247307

Smallest eigenvalues:
 [1]  0.3291675  0.3003846  0.2786729  0.2738109  0.2270862  0.2182747
 [7]  0.1610270  0.1142171 -0.8554455 -1.0663738

Largest  eigenvalues:
 [1] 99969800 97443247 91385442 86977193 86457271 85121186 83831034 82599073
 [9] 80601561 79283089

Smallest eigenvalues:
 [1]  0.23199575  0.18891530  0.15278536  0.07700010  0.06983587  0.01985868
 [7] -0.07025673 -0.15438599 -0.17489595 -0.27130823

Largest  eigenvalues:
 [1] 98781228 95791103 88722173 86296463 84588981 82609053 82165344 79994644
 [9] 79162039 76743440

Smallest eigenvalues:
 [1]  0.21003141  0.18659366  0.17602103  0.16742998  0.10466265  0.09722515
 [7]  0.08369750 -0.07968870 -0.12272959 -0.59606422

Largest  eigenvalues:
 [1] 101553756  97654027  91221148  87325615  85964083  84750796  82765272
 [8]  81837507  80152298  78869539

Smallest eigenvalues:
 [1]  0.39666680  0.37590317  0.28062674  0.26315180  0.26131842  0.25456757
 [7]  0.21612607  0.21070172  0.09646027 -0.22958180

Largest  eigenvalues:
 [1] 100726104  97266231  91184593  86351371  86295989  84103027  82942359
 [8]  81510741  80175890  78702522

Smallest eigenvalues:
 [1]  0.31633471  0.25496171  0.24492725  0.21529846  0.21337277  0.16928994
 [7]  0.13148027  0.11199629 -0.01804806 -0.62813112

Largest  eigenvalues:
 [1] 99136049 97697681 90943238 87284800 85083236 84497460 83812058 81765659
 [9] 80812411 78596535

Smallest eigenvalues:
 [1]  0.4161065  0.3966191  0.3665883  0.3600131  0.3499192  0.3053255
 [7]  0.3043102  0.2941767  0.2515397 -0.3789164

Largest  eigenvalues:
 [1] 100225901  95869246  90078775  85976774  85191818  82808699  82631040
 [8]  80208728  79722232  77482020

Smallest eigenvalues:
 [1]  0.29922866  0.29013662  0.28053669  0.27181468  0.22721597  0.19815085
 [7]  0.17241151 -0.01949369 -0.03403402 -0.21495175

Largest  eigenvalues:
 [1] 97967019 96156356 90067926 85552537 83862494 82888748 82723462 80291827
 [9] 79835304 77292909

Smallest eigenvalues:
 [1]  0.3216793  0.3192788  0.3079577  0.2921470  0.2861906  0.2628851
 [7]  0.2381517  0.2088655 -0.2276861 -0.4686292

Largest  eigenvalues:
 [1] 101213840  96885018  90111947  86731120  85309532  84599300  83318794
 [8]  81808539  80349690  78703592

Smallest eigenvalues:
 [1]  0.3214139  0.3023930  0.2834594  0.2475218  0.2466521  0.2261063
 [7]  0.1787387  0.1585157  0.1222383 -0.4262098

Largest  eigenvalues:
 [1] 98712233 96508625 90052198 86634799 84837275 82949584 82842958 80425813
 [9] 79494438 77104164

Smallest eigenvalues:
 [1]  0.46254130  0.32133495  0.31749391  0.30695002  0.29268884  0.17404896
 [7]  0.14812832  0.06587111  0.03210534 -0.18469517

Largest  eigenvalues:
 [1] 99331776 97827517 91298883 87693021 84989739 84289132 83429365 81092415
 [9] 80644269 77499566

Smallest eigenvalues:
 [1]  0.412889258  0.347453092  0.340124119  0.300958369  0.275975566
 [6]  0.220822725 -0.007434993 -0.022930492 -0.104674844 -0.307833345

Largest  eigenvalues:
 [1] 99985361 96023806 90046714 86387080 85146789 83105020 82882379 80671102
 [9] 79934272 77514683

Smallest eigenvalues:
 [1]  0.375020467  0.358525063  0.341763082  0.306006194  0.283169903
 [6]  0.231242161  0.198312888  0.007256288 -0.003244579 -0.243174567

Largest  eigenvalues:
 [1] 100021546  96563865  90699336  85919483  85901413  84166078  83033402
 [8]  81395802  80027518  78306189

Smallest eigenvalues:
 [1]  0.36530870  0.33538903  0.32586180  0.31922281  0.21224283  0.21145359
 [7]  0.18008291  0.11365012 -0.09954352 -0.15536536

Largest  eigenvalues:
 [1] 98316566 96213754 89640733 85782453 84929365 83379526 83229353 80727682
 [9] 79676267 77648032

Smallest eigenvalues:
 [1]  0.4582382  0.4200222  0.4082777  0.3439409  0.2634010  0.2533368
 [7]  0.2293562  0.1810232 -0.1092063 -0.2340864

Largest  eigenvalues:
 [1] 98306494 95589119 89318153 85821222 83663165 82947160 82602594 80421398
 [9] 79366316 76901517

Smallest eigenvalues:
 [1]  0.35144551  0.33198170  0.33065923  0.31326850  0.28276695  0.24514249
 [7] -0.03281605 -0.19137565 -0.61688945 -0.77482055

Largest  eigenvalues:
 [1] 99480227 97025066 90620121 86676811 85963513 83899927 83289270 80862336
 [9] 80393081 77619514

Smallest eigenvalues:
 [1]  0.4154858  0.3815868  0.3220493  0.3179277  0.3162152  0.2845961
 [7]  0.2263959  0.2205937  0.1136755 -0.1710908

Largest  eigenvalues:
 [1] 99186859 95532602 89395318 85300467 85247838 82941904 82012811 80628258
 [9] 78706338 77203631

Smallest eigenvalues:
 [1]  0.41615203  0.37707605  0.36047194  0.17221318  0.13724036  0.13582418
 [7]  0.13023637  0.05293728 -0.20113903 -0.34785317

Largest  eigenvalues:
 [1] 102162469  95735566  89517891  87269639  85280794  83235676  82276005
 [8]  80936718  79204643  77679853

Smallest eigenvalues:
 [1]  0.3994863  0.3992282  0.3642533  0.3290305  0.2579752  0.2373379
 [7]  0.1683926 -0.0420832 -0.1039533 -0.2572223

Largest  eigenvalues:
 [1] 99896820 96181368 89932593 86502697 84685950 83506049 82521069 80730113
 [9] 79562650 77390813

Smallest eigenvalues:
 [1]  0.41035983  0.40646410  0.40512550  0.39692791  0.26199456  0.24860087
 [7]  0.24139778  0.14702915  0.08478759 -0.07098513

Largest  eigenvalues:
 [1] 99670481 96506224 90148483 86043237 85840803 83214937 82918402 80858999
 [9] 79858880 77971787

Smallest eigenvalues:
 [1]  0.347000202  0.344199181  0.315087619  0.287693909  0.175687813
 [6]  0.127912868  0.120181757  0.057190081 -0.009006519 -0.141100665

Largest  eigenvalues:
 [1] 98056011 96404770 90156944 85741641 84533230 83469045 82514584 80344616
 [9] 79861539 77319905

Smallest eigenvalues:
 [1]  0.31306558  0.27892713  0.23333162  0.20461735  0.18944369  0.10929574
 [7]  0.09386942 -0.13956659 -0.36082364 -1.11787213

Largest  eigenvalues:
 [1] 101336268  97049279  90810913  86534350  86338783  84178218  82927568
 [8]  81514715  79989224  78269626

Smallest eigenvalues:
 [1]  0.29307189  0.28111630  0.25421351  0.18754356  0.16336131  0.11358028
 [7]  0.03905137 -0.19453378 -0.31177664 -0.52945666

Largest  eigenvalues:
 [1] 100129472  96260617  90483092  86668798  85442631  84209223  82697721
 [8]  81488669  79925814  78107352

Smallest eigenvalues:
 [1]  0.12702860  0.11906627  0.08365494  0.08265123  0.07673187  0.03975713
 [7] -0.07808367 -0.14527752 -0.24044438 -0.63567854

Largest  eigenvalues:
 [1] 97405243 96542842 89786693 85994773 85030976 83597721 82781746 81193204
 [9] 79635487 77884657

Smallest eigenvalues:
 [1]  0.3464688  0.3064337  0.3051792  0.3027974  0.2934510  0.1808576
 [7] -0.1113322 -0.1985794 -0.2103916 -0.5316172

Largest  eigenvalues:
 [1] 100551761  96781814  91111007  87277807  84836640  83959345  83532685
 [8]  81139180  80360906  77501914

Smallest eigenvalues:
 [1]  0.40292058  0.38526621  0.34944115  0.31246299  0.25810781  0.22784548
 [7]  0.01719268 -0.10578526 -0.13236859 -0.59616293

Largest  eigenvalues:
 [1] 99766137 96347587 89281445 86198011 85278772 83212801 82098563 80289897
 [9] 79291361 77373958

Smallest eigenvalues:
 [1]  0.4633765  0.4075929  0.3790127  0.3535581  0.3509942  0.3017647
 [7]  0.2565188  0.1332860 -0.0841150 -0.5273491

Largest  eigenvalues:
 [1] 99816949 97961584 91446978 87484876 86076947 84188029 83727238 81372019
 [9] 80799387 78436985

Smallest eigenvalues:
 [1]  0.3430210  0.3274314  0.3257035  0.2857321  0.2264250  0.1830879
 [7]  0.1517858  0.1189842 -0.1129485 -0.9711132

Largest  eigenvalues:
 [1] 99093127 95963978 89295297 86406245 84452192 82898741 82685217 80324336
 [9] 79401800 77338301

Smallest eigenvalues:
 [1]  0.39527790  0.39127607  0.35387400  0.32317101  0.30054978  0.27751045
 [7]  0.09715711 -0.05053430 -0.26776845 -0.52062774

Largest  eigenvalues:
 [1] 100985826  96692954  90375031  86720491  85948056  84166287  82543037
 [8]  81420569  79537640  78079147

Smallest eigenvalues:
 [1]  0.38343967  0.38081924  0.30055663  0.27027364  0.24150702  0.23782706
 [7]  0.21326696  0.20748606  0.08765733 -0.25564405

Largest  eigenvalues:
 [1] 100057447  95800009  89786180  85461927  85227780  83446327  81931125
 [8]  80734533  78966587  77246303

Smallest eigenvalues:
 [1]  0.29652574  0.27203556  0.26606878  0.23413065  0.19355386  0.16757500
 [7]  0.01158197 -0.05636534 -0.22215475 -0.38362701

Largest  eigenvalues:
 [1] 100044039  96356941  90534604  85767011  84999943  83245877  82593581
 [8]  80656660  79778857  78028632

Smallest eigenvalues:
 [1]  0.23204359  0.22067409  0.18011525  0.16345270  0.08028338  0.03076562
 [7] -0.03719673 -0.12609204 -0.57744191 -1.81682630

Largest  eigenvalues:
 [1] 102582074  95820926  90097921  87423487  85379266  84413103  82028258
 [8]  81566760  79575945  78671542

Smallest eigenvalues:
 [1]  0.45166991  0.44745100  0.43423239  0.40267643  0.38558276  0.24018359
 [7]  0.22463824 -0.01382489 -0.29946988 -0.43337923

Largest  eigenvalues:
 [1] 100865946  96222523  90016155  86248985  86103043  84243666  83022249
 [8]  81614466  79919868  78312241

Smallest eigenvalues:
 [1]  0.32315683  0.31532212  0.27120714  0.26565123  0.26446407  0.21746149
 [7]  0.04901346 -0.16134939 -0.36713728 -0.36755138

Largest  eigenvalues:
 [1] 99122458 97898161 90597533 87795502 85159682 84444572 84005362 81662863
 [9] 80808099 78553285

Smallest eigenvalues:
 [1]  0.37597041  0.36286674  0.30386485  0.29827873  0.17702349  0.11301322
 [7]  0.08094356 -0.03107875 -0.14068952 -0.49460175

Largest  eigenvalues:
 [1] 98952864 95477958 89887667 86038188 84013230 82761700 82233153 80023278
 [9] 79582295 76982833

Smallest eigenvalues:
 [1]  0.12597992  0.04513590 -0.04890039 -0.07213219 -0.07627277 -0.21394939
 [7] -0.39549316 -0.50071926 -0.56298682 -0.57471745

Largest  eigenvalues:
 [1] 98654871 97201999 91283342 86479210 85523715 83925555 83567606 81273903
 [9] 80350222 78201328

Smallest eigenvalues:
 [1]  0.276598608  0.268721294  0.260447405  0.254317941  0.241952773
 [6]  0.190143882  0.042452456  0.006071576 -0.157321816 -0.251843010

Largest  eigenvalues:
 [1] 100982306  97198985  90669919  86973672  85562286  84500116  83090845
 [8]  81501087  80542988  78154396

Smallest eigenvalues:
 [1]  0.33265075  0.32885275  0.30730838  0.29423247  0.22585955  0.19838492
 [7]  0.16117098  0.04974100 -0.05149819 -0.22451260

Largest  eigenvalues:
 [1] 97773615 96777235 90475121 86783846 83539049 83400043 83184414 81056386
 [9] 80036050 77505075

Smallest eigenvalues:
 [1]  0.312718937  0.309681053  0.274937486  0.253273059  0.231690334
 [6]  0.099959658  0.025005146  0.008546921 -0.579522682 -0.638603196

Largest  eigenvalues:
 [1] 100743080  96248332  90677644  86420883  85693059  84088221  82836185
 [8]  81819577  79915828  78735807

Smallest eigenvalues:
 [1]  0.33645592  0.32279225  0.31011952  0.30446195  0.24947690  0.24943856
 [7]  0.11788043  0.11695098 -0.07846772 -0.21012461

Largest  eigenvalues:
 [1] 100684971  96506237  90482217  86683652  85273124  84073020  83134120
 [8]  81621384  80353984  78557262

Smallest eigenvalues:
 [1]  0.38911709  0.37430428  0.37238149  0.27852723  0.23606819  0.19665507
 [7]  0.14232562  0.09086630  0.08897772 -0.33328594

Largest  eigenvalues:
 [1] 99916481 95907757 89808516 85649656 85422060 84125523 82258463 81293861
 [9] 79413200 78152823

Smallest eigenvalues:
 [1]  0.40634823  0.39723192  0.34518860  0.26826902  0.25036844  0.22548455
 [7]  0.20119042  0.09338915 -0.17348603 -0.21030668

Largest  eigenvalues:
 [1] 100401077  95287422  88853380  85512380  85504708  82619420  81710725
 [8]  80272625  78783452  77129602

Smallest eigenvalues:
 [1]  0.48430968  0.47001574  0.44787245  0.43601338  0.32911416  0.28596273
 [7]  0.26200361  0.22016720 -0.06379419 -0.25833025

Largest  eigenvalues:
 [1] 100523266  97015137  90532238  86498341  85973553  84258108  82872745
 [8]  81394134  80432957  78564814

Smallest eigenvalues:
 [1]  0.38837923  0.37896130  0.36430759  0.35988917  0.34127659  0.19751969
 [7]  0.12653637  0.08903336 -0.01695984 -0.47896245

Largest  eigenvalues:
 [1] 100988971  96588351  90552384  86392669  86124013  84129894  82169323
 [8]  81320872  79299660  78116178

Smallest eigenvalues:
 [1]  0.49024449  0.46949091  0.45607350  0.35711434  0.28386645  0.27041847
 [7]  0.24752663  0.18342243 -0.05472445 -0.06261830

Largest  eigenvalues:
 [1] 100779844  95627929  89129689  86094974  85420246  83303611  81896062
 [8]  80823683  79232247  77819223

Smallest eigenvalues:
 [1]  0.42321529  0.41695157  0.39216309  0.37831099  0.36799435  0.30300748
 [7]  0.25156678  0.24275763  0.07992087 -0.40432720

Largest  eigenvalues:
 [1] 99644241 95286206 89316966 85658165 84302091 83003838 81704517 80506349
 [9] 79056627 77356619

Smallest eigenvalues:
 [1]  0.34817834  0.31605088  0.30693275  0.27688276  0.18149851  0.15739872
 [7]  0.02158334 -0.02329128 -0.17513328 -0.23148561

Largest  eigenvalues:
 [1] 101527880  96250593  90049642  86264788  85919822  84457432  82359297
 [8]  81683126  79658802  78554537

Smallest eigenvalues:
 [1]  0.18485307  0.16092170  0.15001711  0.07913802  0.06921725  0.03837940
 [7]  0.02570691 -0.02465212 -0.20237358 -0.35648977

Largest  eigenvalues:
 [1] 100966335  97179506  91315744  86418678  85564814  84540465  83211789
 [8]  82285852  80862447  79578609

Smallest eigenvalues:
 [1]  0.42165929  0.40243210  0.40210420  0.34802547  0.32175317  0.25084766
 [7]  0.21593482  0.17089007  0.11645095 -0.09180467

Largest  eigenvalues:
 [1] 97748372 96499858 89552987 86799718 84467937 83176536 83044897 80156333
 [9] 79702516 77055607

Smallest eigenvalues:
 [1]  0.38827180  0.34251530  0.28184131  0.23947784  0.23227511  0.18386221
 [7]  0.05640226  0.02499066 -0.21741532 -0.32025736

Largest  eigenvalues:
 [1] 99164812 96240231 89923484 85809514 84395231 82860020 82524677 80336784
 [9] 79514470 77410770

Smallest eigenvalues:
 [1]  0.34302947  0.34182981  0.27248100  0.27091306  0.23122997  0.20878231
 [7]  0.04227076 -0.10340108 -0.13087240 -0.39114792

Largest  eigenvalues:
 [1] 100878133  96885799  90612183  86659998  86032280  85771515  82964210
 [8]  82593016  80631635  79812794

Smallest eigenvalues:
 [1]  0.25356761  0.23879392  0.23383386  0.19953623  0.15848870  0.14271905
 [7]  0.12571647  0.01224474 -0.15947641 -0.36363778

Largest  eigenvalues:
 [1] 98749497 96377162 90369128 86146041 84176250 83223259 83093620 80831556
 [9] 80177213 77625852

Smallest eigenvalues:
 [1]  0.44456767  0.44060360  0.36394276  0.35768201  0.32643542  0.31010307
 [7]  0.23970755  0.12808537 -0.05697475 -0.16550292

Largest  eigenvalues:
 [1] 101129234  97157152  90903101  86757191  85766315  84195084  83058121
 [8]  81725134  80187907  78767996

Smallest eigenvalues:
 [1]  0.26540925  0.23451510  0.20078053  0.18543693  0.16725291  0.11197229
 [7]  0.02752947 -0.06868394 -0.50617854 -0.81610439

Largest  eigenvalues:
 [1] 98324543 96604115 89711853 87178362 84150428 83960289 82990706 80756794
 [9] 80285305 77445213

Smallest eigenvalues:
 [1]  0.28568151  0.27754011  0.25707438  0.21941157  0.20828855 -0.00013390
 [7] -0.05049161 -0.14676752 -0.27230607 -0.39985837

Largest  eigenvalues:
 [1] 100966031  95013983  89634586  85862208  84378557  83301361  82065638
 [8]  81063682  79112131  78252387

Smallest eigenvalues:
 [1]  0.184691033  0.167621781  0.155796873  0.130384275  0.051403602
 [6]  0.049759081  0.009072942 -0.151557707 -0.179620903 -0.209282656

Largest  eigenvalues:
 [1] 99753956 97386549 90544820 86895287 86385577 84584446 83591887 81712832
 [9] 80603307 78768247

Smallest eigenvalues:
 [1]  0.36778600  0.35469351  0.30069769  0.25321614  0.20809725  0.18065364
 [7]  0.17235986  0.10710076 -0.03079384 -0.43534888

Largest  eigenvalues:
 [1] 99182524 96402230 90195937 86273320 84383283 83501295 83272060 81306825
 [9] 80253629 77975324

Smallest eigenvalues:
 [1]  0.33399926  0.31968902  0.31505493  0.31260416  0.24586000  0.23678295
 [7]  0.13240147  0.07774475  0.06793222 -0.06856036

Largest  eigenvalues:
 [1] 100180468  97528473  91604134  86135933  85974659  84680703  83048059
 [8]  82121960  80107418  79139710

Smallest eigenvalues:
 [1]  0.4757747  0.4553701  0.4355483  0.4095840  0.3916077  0.3192264
 [7]  0.2416094  0.2020688  0.1798108 -0.2692753

Largest  eigenvalues:
 [1] 100804652  96065601  89941508  85973485  85945694  83595498  81942275
 [8]  80809735  79604926  77815113

Smallest eigenvalues:
 [1]  0.47734364  0.45145534  0.40431510  0.38796143  0.34586134  0.29092103
 [7]  0.19974862  0.19255734  0.17288024 -0.02851935

Largest  eigenvalues:
 [1] 100976341  97085559  91131335  86845517  86186179  84430567  83195337
 [8]  81622364  80288516  78512993

Smallest eigenvalues:
 [1]  0.31632760  0.31370086  0.28511324  0.20507800  0.18430051 -0.00899935
 [7] -0.06563834 -0.10539771 -0.13831195 -0.36272954

Largest  eigenvalues:
 [1] 100430831  96092760  90665985  85611370  84632059  83116926  82881536
 [8]  80824651  79915380  77723653

Smallest eigenvalues:
 [1]  0.3862668  0.3653550  0.3439284  0.3406631  0.2856466  0.1922455
 [7]  0.1519309  0.1110390  0.1104294 -0.3500123

Largest  eigenvalues:
 [1] 98002826 97171820 90023107 86745494 84755559 83796250 82851972 80975122
 [9] 79907200 77969997

Smallest eigenvalues:
 [1]  0.41514096  0.39727186  0.34381708  0.25630818  0.23747529  0.20419885
 [7]  0.10078711  0.04913593 -0.09320301 -0.10057764

Largest  eigenvalues:
 [1] 99371099 95118565 89424908 85202852 84011995 83033972 82573671 80536753
 [9] 79391444 77652182

Smallest eigenvalues:
 [1]  0.34398659  0.32952786  0.27196761  0.23300557  0.23115483  0.15432715
 [7]  0.03740143 -0.08096112 -0.11260029 -0.20871787

Largest  eigenvalues:
 [1] 99538440 97528581 91529951 86979673 84783102 84372574 83579216 81327616
 [9] 80947081 77999215

Smallest eigenvalues:
 [1]  0.45518257  0.40756718  0.39072914  0.36554424  0.35428706  0.29156589
 [7]  0.22963038  0.15111965  0.05115811 -0.01631632

Largest  eigenvalues:
 [1] 100663844  96382675  90696751  86225390  84957666  83995236  82738361
 [8]  81317435  80103751  78040351

Smallest eigenvalues:
 [1]  0.195197717  0.161341218  0.146352698  0.134936413  0.098163546
 [6]  0.041424516  0.007805326 -0.003949245 -0.189198555 -1.181700339

Largest  eigenvalues:
 [1] 98924237 95332461 89430368 85254513 83958235 82985119 81534868 80408470
 [9] 78827224 77510514

Smallest eigenvalues:
 [1]  0.47796652  0.45684969  0.37908885  0.31055869  0.27846235  0.20940000
 [7]  0.20330266  0.20070581  0.02639600 -0.02833537

Largest  eigenvalues:
 [1] 100304472  96987869  90575756  87251576  85419424  85179391  82857770
 [8]  82308672  80406475  79251323

Smallest eigenvalues:
 [1]  0.46403123  0.35692262  0.34718261  0.32525475  0.32240378  0.26540520
 [7]  0.23531617  0.15888102 -0.07622361 -0.74325361

Largest  eigenvalues:
 [1] 100874296  96869032  90512209  86478389  86361265  83590610  83435132
 [8]  81265617  80408758  78116568

Smallest eigenvalues:
 [1]  0.54342496  0.49489343  0.45629783  0.41508670  0.36114282  0.35119942
 [7]  0.27038261  0.24277144  0.20562848 -0.03024015

Largest  eigenvalues:
 [1] 101127527  96957381  90952912  86762119  85889780  83925428  83345599
 [8]  81498859  80118835  78466631

Smallest eigenvalues:
 [1]  0.42728072  0.33455752  0.32416050  0.32056341  0.31809632  0.29698017
 [7]  0.26466078  0.13199857 -0.01440903 -0.39626377

Largest  eigenvalues:
 [1] 100781381  97135407  91476641  86545224  85908812  83545136  83318852
 [8]  81217749  80464180  78242871

Smallest eigenvalues:
 [1]  0.41384263  0.39694174  0.32630602  0.31443622  0.27198068  0.26303314
 [7]  0.14563044  0.08390344 -0.05887081 -0.32927068

Largest  eigenvalues:
 [1] 99985856 96420730 89496861 86276708 85888583 83463933 82125367 80593602
 [9] 79556926 77284291

Smallest eigenvalues:
 [1]  0.48409846  0.46047950  0.33809180  0.32802802  0.30923408  0.30740876
 [7]  0.30633482  0.21646520  0.05395513 -0.26058177

Largest  eigenvalues:
 [1] 102086890  96633745  90799643  87215985  86681506  85125504  82646759
 [8]  82115853  80314791  79166057

Smallest eigenvalues:
 [1]  0.26115641  0.25706897  0.22502930  0.21352187  0.20397583  0.19166852
 [7]  0.15771685 -0.03954547 -0.21332860 -0.45011978

Largest  eigenvalues:
 [1] 103103219  96799581  91056879  87855379  86003186  85290215  82589807
 [8]  82353851  80264176  79434237

Smallest eigenvalues:
 [1]  0.35309845  0.35156979  0.32990841  0.31272979  0.23141193  0.17749904
 [7]  0.09621083 -0.36626742 -0.53864449 -0.58900444

Largest  eigenvalues:
 [1] 101060562  97105503  90689879  87663794  85832575  84416876  83287501
 [8]  81692048  80685160  78628708

Smallest eigenvalues:
 [1]  0.20550306  0.12757887  0.11987698  0.06587969  0.01296513 -0.03522072
 [7] -0.20410615 -0.39973943 -0.55665765 -1.15107614

Largest  eigenvalues:
 [1] 98746734 95848128 89338104 85889286 84553559 83485920 81930213 80373130
 [9] 79284084 76920870

Smallest eigenvalues:
 [1]  0.52594425  0.52459640  0.42908248  0.41049870  0.38887935  0.38005278
 [7]  0.30121354  0.22013713  0.04129827 -0.20977980

Largest  eigenvalues:
 [1] 100140965  96502505  89994264  86821378  84988537  83605599  82487290
 [8]  81068985  79908957  78266658

Smallest eigenvalues:
 [1]  0.25983446  0.23987920  0.21500647  0.18577541  0.13195431  0.12474848
 [7]  0.01810365 -0.24138122 -0.30334257 -0.61039975

Largest  eigenvalues:
 [1] 102005547  96229923  90290784  86780741  85736703  84329573  82784464
 [8]  81924336  79630278  78661342

Smallest eigenvalues:
 [1]  0.206061583  0.158825275  0.094685515  0.081105260  0.062276448
 [6] -0.006946356 -0.022011346 -0.200217184 -0.736750012 -3.023532963

Largest  eigenvalues:
 [1] 99954394 96932845 90266678 86752148 86025662 83543424 83425671 80857339
 [9] 80238196 77634283

Smallest eigenvalues:
 [1]  0.29338960  0.28336088  0.25608377  0.21405189  0.13789354  0.12774976
 [7]  0.02917010 -0.05477915 -0.14952020 -0.50239001

Largest  eigenvalues:
 [1] 99283271 97712234 90788034 87033988 85743062 84241021 83867345 81565549
 [9] 80480758 78539430

Smallest eigenvalues:
 [1]  0.41191743  0.38831819  0.37829724  0.37110462  0.36234026  0.24324395
 [7]  0.13000044 -0.02806658 -0.25825507 -0.29734829

Largest  eigenvalues:
 [1] 100227988  96605618  90159287  86664578  86016001  83667416  83126864
 [8]  80836934  80229073  77553358

Smallest eigenvalues:
 [1]  0.36683396  0.32329157  0.27255923  0.24039080  0.22197503  0.12106564
 [7]  0.07198629  0.06427798 -0.03542347 -0.25320037

Largest  eigenvalues:
 [1] 97437351 96474726 89269088 86407381 84627558 83091606 82622272 80078310
 [9] 79606860 76899444

Smallest eigenvalues:
 [1]  0.41900098  0.41552782  0.39187334  0.37908836  0.31411864  0.29556530
 [7]  0.24607098  0.15354364  0.13832788 -0.09514892

Largest  eigenvalues:
 [1] 99262601 96319546 90756712 86038776 83983571 83423710 82997385 81009837
 [9] 80113669 78014063

Smallest eigenvalues:
 [1]  0.13542078  0.10838830  0.06527687  0.05114663  0.01252765 -0.06218801
 [7] -0.11624063 -0.18233019 -0.53721818 -1.59057088

Largest  eigenvalues:
 [1] 101744806  96061144  90408327  86327842  85589343  82837228  82520269
 [8]  80629715  79519545  77581417

Smallest eigenvalues:
 [1]  0.26264187  0.25289521  0.23944124  0.14147780  0.07836688  0.04588163
 [7]  0.02809017 -0.08795779 -0.22751067 -0.96404681

Largest  eigenvalues:
 [1] 98672707 96043462 89456281 85892452 85052371 83244846 82845759 80602218
 [9] 79749573 77295342

Smallest eigenvalues:
 [1]  0.18224151  0.14056577  0.11811042  0.11541480  0.06551399 -0.01665821
 [7] -0.02569742 -0.17271294 -0.42953448 -0.86161600

Largest  eigenvalues:
 [1] 100000715  97335765  91457644  87027396  85387482  83896507  83542443
 [8]  81354508  80409750  77989654

Smallest eigenvalues:
 [1]  0.410941368  0.409940961  0.405765945  0.385677498  0.342102471
 [6]  0.313067301  0.312958457  0.075523265 -0.009503385 -0.201398076

Largest  eigenvalues:
 [1] 101150566  97406295  90944200  86609898  86173769  84395456  83151267
 [8]  81596691  80215055  78405763

Smallest eigenvalues:
 [1]  0.35954504  0.28806519  0.28761561  0.28271469  0.25442688  0.25098268
 [7]  0.20826564  0.09919214  0.07259341 -0.17158757

Largest  eigenvalues:
 [1] 98632646 96261604 90381823 85830639 84958640 83141248 82971083 80827585
 [9] 79754962 77800286

Smallest eigenvalues:
 [1]  0.315504265  0.274150049  0.268798153  0.209765688  0.209184680
 [6]  0.188387185  0.152342979  0.044360849  0.007999525 -0.525304287

Largest  eigenvalues:
 [1] 98106401 96467204 90396168 86345511 84421316 83625563 82728924 81555621
 [9] 79754767 78263900

Smallest eigenvalues:
 [1]  0.37551098  0.35717644  0.35277251  0.32769410  0.29684679  0.27673303
 [7]  0.22555497  0.06252272 -0.06303788 -0.07195551

Largest  eigenvalues:
 [1] 100010490  95942987  89527235  86555914  85229991  83526427  82277213
 [8]  80863939  79324185  77766156

Smallest eigenvalues:
 [1]  0.40153764  0.38666062  0.37916862  0.35086708  0.34914564  0.26515184
 [7]  0.25919527  0.01648512 -0.04849692 -0.39697202

Largest  eigenvalues:
 [1] 100757118  96270989  90264260  86087865  85795869  83069813  82889792
 [8]  80830857  79909826  77967908

Smallest eigenvalues:
 [1]  0.41332623  0.40486474  0.39324460  0.30204771  0.29149568  0.20254791
 [7]  0.18401483  0.17777057 -0.03826471 -0.05574242

Largest  eigenvalues:
 [1] 101410146  96193191  89909644  85880860  85735157  83811789  81995320
 [8]  81150716  79327795  78002431

Smallest eigenvalues:
 [1]  0.31893150  0.31403269  0.23936019  0.22614173  0.14741564  0.13344797
 [7]  0.05984539  0.05161561 -0.26951289 -0.38600859

Largest  eigenvalues:
 [1] 98660803 96840884 91246244 85828325 85202653 83691319 83420177 81310383
 [9] 80311052 78199052

Smallest eigenvalues:
 [1]  0.31598378  0.28386395  0.28300100  0.18478046  0.16167060  0.07340897
 [7]  0.06000512 -0.02818990 -0.14806082 -0.82313271

Largest  eigenvalues:
 [1] 98773590 96734859 90721688 86895328 84122017 83531472 82822036 80224378
 [9] 79975781 76877540

Smallest eigenvalues:
 [1]  0.45672443  0.45356768  0.39039613  0.34271179  0.25906281  0.23425985
 [7]  0.20916326  0.09867012  0.09498200 -0.10650875

Largest  eigenvalues:
 [1] 100265857  96006411  90012619  86101666  85801491  83050926  82870980
 [8]  80470182  79739230  77154832

Smallest eigenvalues:
 [1]  0.4349221  0.3508096  0.3462192  0.3059278  0.2991485  0.2473554
 [7]  0.2446368  0.2129678  0.1354859 -0.4905267

Largest  eigenvalues:
 [1] 99702994 96658287 90098762 86479827 85919310 84410845 82890449 81676708
 [9] 79925750 78589519

Smallest eigenvalues:
 [1]  0.4483314  0.4392232  0.4204877  0.3603856  0.3368610  0.2981903
 [7]  0.2778506  0.2059360 -0.1309537 -0.3970985

Largest  eigenvalues:
 [1] 101884490  97141146  90672508  86832776  86370776  84071061  83300409
 [8]  81545253  80460380  78464208

Smallest eigenvalues:
 [1]  0.17426344  0.17182520  0.06169208  0.04080552 -0.01846709 -0.03059209
 [7] -0.05756674 -0.06531979 -0.24535768 -0.31927827

Largest  eigenvalues:
 [1] 98164402 96834498 90215328 86760997 84854385 83763509 83457659 81138065
 [9] 80413185 78323703

Smallest eigenvalues:
 [1]  0.24773276  0.19715515  0.19417415  0.16131015  0.15673156  0.12630187
 [7]  0.11154260 -0.08043828 -0.13345107 -0.21355205

Largest  eigenvalues:
 [1] 98525865 97307835 90281369 87651881 84674919 83889058 83773781 81062503
 [9] 80430124 78176983

Smallest eigenvalues:
 [1]  0.383493163  0.305957818  0.296519640  0.252084573  0.207161299
 [6]  0.182602334  0.061461769  0.055282320  0.008604677 -0.393837281

Largest  eigenvalues:
 [1] 100214054  96641137  90655279  86611317  85789325  84284459  82997968
 [8]  81904539  80069893  78620632

Smallest eigenvalues:
 [1]  0.34880471  0.32342149  0.31956390  0.23700840  0.15967854  0.13329146
 [7]  0.10890479 -0.05317232 -0.19427275 -0.27206121

Largest  eigenvalues:
 [1] 99188999 96356940 89534720 86159698 85180630 83343807 83027984 80902550
 [9] 79612682 77756380

Smallest eigenvalues:
 [1]  0.155172861  0.072894172  0.070185773  0.042781184  0.007175571
 [6] -0.011342685 -0.055372512 -0.237398157 -0.278440018 -0.729851642

Largest  eigenvalues:
 [1] 98579765 97357353 90474112 86556469 86092710 84108259 83883713 81411180
 [9] 80326220 78455355

Smallest eigenvalues:
 [1]  0.35499943  0.30073602  0.29654105  0.28200510  0.28023086  0.21120569
 [7]  0.19460628  0.13342011  0.09231254 -0.28238577

Largest  eigenvalues:
 [1] 100071901  97915129  91381873  86890165  86032251  84372367  83601445
 [8]  82035776  80798180  79240387

Smallest eigenvalues:
 [1]  0.31370045  0.28063132  0.25919905  0.23262713  0.18478666  0.15085317
 [7]  0.06557096  0.01305432 -0.49264782 -1.30855319

Largest  eigenvalues:
 [1] 98890768 96930549 90867894 86413382 85427615 83619758 83285159 81172121
 [9] 80346484 78097818

Smallest eigenvalues:
 [1]  0.3341142  0.2732187  0.2540869  0.1814860  0.1404521  0.1303099
 [7]  0.1123285 -0.2187510 -0.2642946 -0.2714035

Largest  eigenvalues:
 [1] 101524689  96943838  91075925  86159889  86090680  84276758  82832115
 [8]  81712116  80008882  78851804

Smallest eigenvalues:
 [1]  0.16416788  0.11323524  0.11172799  0.08739572  0.08640761  0.03301722
 [7] -0.09981504 -0.46938898 -0.59052810 -0.97609004

Largest  eigenvalues:
 [1] 99538329 97036720 91197781 86703210 85755467 84034430 83918077 81716019
 [9] 80472962 78344259

Smallest eigenvalues:
 [1]  0.404661666  0.281517763  0.234899294  0.231735637  0.191571480
 [6]  0.186306537  0.070013474  0.005452714 -0.130371006 -0.300630757

Largest  eigenvalues:
 [1] 100297171  95820536  90053142  85548104  85337359  82927690  82630018
 [8]  80913319  79282005  77517226

Smallest eigenvalues:
 [1]  0.41817883  0.37422092  0.32052509  0.30414643  0.25334850  0.23362959
 [7]  0.19075144  0.12417547 -0.03599612 -0.11118505

Largest  eigenvalues:
 [1] 99195220 96853467 90133959 87282673 84243851 83731022 83448442 80571997
 [9] 80289891 77316377

Smallest eigenvalues:
 [1]  0.24381848  0.21576391  0.15856428  0.15297957  0.12383629  0.08160785
 [7] -0.02978785 -0.03411285 -0.49109867 -0.53033102

Largest  eigenvalues:
 [1] 97374265 96245480 89769362 86196965 83572612 83031385 82947342 80458351
 [9] 79745645 77130126

Smallest eigenvalues:
 [1]  0.37636672  0.34651860  0.31825845  0.29080076  0.25412362  0.20325746
 [7]  0.19303854  0.13944486 -0.06950515 -0.39647607

Largest  eigenvalues:
 [1] 99787091 96169701 90316717 85960516 84925264 84616436 82216521 81565751
 [9] 79570393 78408758

Smallest eigenvalues:
 [1]  0.38931753  0.37298295  0.32462657  0.30245460  0.27467859  0.21651127
 [7]  0.14413236 -0.09411993 -0.28685808 -0.50445883

Largest  eigenvalues:
 [1] 100861031  96338902  90484974  85901975  85816310  83892440  82976856
 [8]  81548980  80045823  78543482

Smallest eigenvalues:
 [1]  0.4887759  0.4815089  0.4502573  0.3780822  0.3772039  0.3284920
 [7]  0.3059593  0.2677716  0.2492140 -0.1546292

Largest  eigenvalues:
 [1] 103028995  95626709  90134434  85487588  84538959  83695095  82111537
 [8]  81347664  79726460  78018679

Smallest eigenvalues:
 [1]  0.3955029  0.3321981  0.2870831  0.2598618  0.2188692  0.1578309
 [7]  0.1182783  0.0156418 -0.1830077 -0.3999441

Largest  eigenvalues:
 [1] 99164822 96028027 89548319 86260963 84525203 82956121 82461608 79559365
 [9] 79319510 76464971

Smallest eigenvalues:
 [1]  0.4767262  0.4288105  0.4025991  0.3216745  0.3013755  0.2578659
 [7]  0.1778260  0.1586763  0.1203154 -0.1112833

Largest  eigenvalues:
 [1] 98826409 96164071 89843520 86252132 83782243 82941004 82571985 80084052
 [9] 79648614 76869632

Smallest eigenvalues:
 [1]  0.24572210  0.21248467  0.20320529  0.18133973  0.17477387  0.10298381
 [7]  0.04049493  0.02598455 -0.01957025 -0.37745505

Largest  eigenvalues:
 [1] 98807663 97636162 90802080 86811761 85667643 84833666 83392098 81894952
 [9] 80572539 79070644

Smallest eigenvalues:
 [1]  0.32494936  0.31935302  0.27318597  0.24954817  0.15855708  0.14960057
 [7]  0.02209010  0.01375357 -0.21325186 -0.31215670

Largest  eigenvalues:
 [1] 100028598  96441595  90465666  86321915  85438548  84163956  83130278
 [8]  81447596  79989596  78466583

Smallest eigenvalues:
 [1]  0.34567278  0.28676210  0.26351511  0.23673034  0.17568903  0.14907552
 [7]  0.10940699  0.05997607  0.03050480 -0.56494643

Largest  eigenvalues:
 [1] 97790513 97122436 90361271 87294246 84908647 84037562 83889604 81416654
 [9] 80701826 78579237

Smallest eigenvalues:
 [1]  0.225675692  0.224534885  0.223187572  0.192975157  0.177508897
 [6]  0.064045867  0.003930736 -0.029519605 -0.690876052 -0.807599075

Largest  eigenvalues:
 [1] 98214376 97297919 90913947 87104103 84276072 83953672 83659715 81491935
 [9] 80449460 77972423

Smallest eigenvalues:
 [1]  0.35635727  0.24931975  0.22581877  0.22029411  0.19380178  0.12955552
 [7]  0.09527798 -0.01053746 -0.18503495 -0.26920432

Largest  eigenvalues:
 [1] 98946111 97700658 90436022 87331809 85390543 83918246 83747778 81359762
 [9] 80122272 77835803

Smallest eigenvalues:
 [1]  0.352636399  0.309437125  0.188931288  0.152171506  0.123511249
 [6]  0.119057268  0.002721336 -0.033698373 -0.331834582 -0.601425136

Largest  eigenvalues:
 [1] 99220690 95404759 89111125 85728780 85124875 82477878 82367181 80113924
 [9] 79208241 77065560

Smallest eigenvalues:
 [1]  0.36444915  0.33907555  0.30108956  0.23492446  0.19642916  0.18340258
 [7]  0.15510708  0.07184936  0.06246827 -0.02636197

Largest  eigenvalues:
 [1] 97435793 97320473 90256545 86733478 84231669 83997244 82751496 81103309
 [9] 79900040 78104654

Smallest eigenvalues:
 [1]  0.35122388  0.34557985  0.30998011  0.28319674  0.20932128  0.15284063
 [7]  0.12640085  0.07735302  0.04032326 -0.36850674

Largest  eigenvalues:
 [1] 99089984 96571109 90448137 86144777 85195778 84020013 82728350 81384573
 [9] 79376220 77965833

Smallest eigenvalues:
 [1]  0.23413280  0.22593062  0.22097383  0.19490262  0.19345159  0.13760096
 [7]  0.09268230 -0.02113823 -0.22935054 -0.37182262

Largest  eigenvalues:
 [1] 99936841 97365938 90531516 87328719 86059545 84691220 83536088 82021526
 [9] 80724664 78982079

Smallest eigenvalues:
 [1]  0.35646864  0.35621668  0.29771233  0.29643406  0.27201901  0.13566842
 [7]  0.09330052 -0.02555616 -0.21489309 -0.22480430

Largest  eigenvalues:
 [1] 99167909 96541992 90049428 86443603 85420910 83276437 83129470 80720455
 [9] 79789533 77592789

Smallest eigenvalues:
 [1]  0.247444786  0.214292469  0.153425737  0.145757214  0.093414648
 [6] -0.009802122 -0.067461703 -0.108966820 -0.339967754 -0.396803033

Largest  eigenvalues:
 [1] 101424742  96537063  90979045  86264026  85760795  83647672  83273439
 [8]  81695723  80247054  78748891

Smallest eigenvalues:
 [1]  0.3995752  0.3861944  0.3075573  0.2533182  0.2446386  0.2191666
 [7]  0.1809214  0.1350172  0.1206828 -0.3011655

Largest  eigenvalues:
 [1] 100054099  96704878  89861304  87109115  85641628  84456229  82561769
 [8]  81570723  80013130  78485529

Smallest eigenvalues:
 [1]  0.4487522  0.3998189  0.3990713  0.3423149  0.2793767  0.2749401
 [7]  0.2258511  0.2122147  0.1636149 -0.5377268

Largest  eigenvalues:
 [1] 100832596  96332060  90310555  86132986  85122182  83965089  82844240
 [8]  81246800  80281138  78356070

Smallest eigenvalues:
 [1]  0.30606598  0.29634342  0.19580032  0.12110825  0.08078618  0.02462287
 [7] -0.07258641 -0.31355326 -0.63209106 -0.99620054

Largest  eigenvalues:
 [1] 101666791  95637852  90518568  85796548  85140430  82990903  82224391
 [8]  80700831  79326895  77669289

Smallest eigenvalues:
 [1]  0.23860159  0.23141815  0.21786662  0.19348013  0.17394407  0.10782237
 [7]  0.05769664  0.01355850 -0.11474222 -0.68447938

Largest  eigenvalues:
 [1] 99922061 96789637 90487505 85928853 85874345 83426514 82904950 80937600
 [9] 79999634 78006305

Smallest eigenvalues:
 [1]  0.40182759  0.39254129  0.36799233  0.32131141  0.30188519  0.27435449
 [7]  0.22546005  0.16863591 -0.02489685 -0.16173751

Largest  eigenvalues:
 [1] 99126871 96126802 89665415 85750911 85428668 83062713 82732692 80643224
 [9] 79386018 77206279

Smallest eigenvalues:
 [1]  0.46461053  0.43554796  0.42727741  0.33542841  0.33402817  0.30740964
 [7]  0.27541710  0.16406832  0.14915552 -0.05658413

Largest  eigenvalues:
 [1] 99971209 95848538 89354237 86126572 85143954 83353723 82113431 80570020
 [9] 79439388 77552732

Smallest eigenvalues:
 [1]  0.36784686  0.32877916  0.32689721  0.31985606  0.26491347  0.25552511
 [7]  0.14644696  0.10677458  0.05207215 -0.12488462

Largest  eigenvalues:
 [1] 99791474 96884615 90205769 86546904 85090598 83992796 83036552 81330975
 [9] 80009793 77866120

Smallest eigenvalues:
 [1]  0.31953712  0.31181272  0.28402580  0.26550021  0.23532333  0.23112261
 [7]  0.15466897  0.07155424 -0.31226557 -0.88993360

Largest  eigenvalues:
 [1] 101740918  96462602  90608158  87351928  85365844  83932442  82082490
 [8]  81287498  79475034  78420145

Smallest eigenvalues:
 [1]  0.4524914  0.4459416  0.4104251  0.3606343  0.3117717  0.2796908
 [7]  0.1669751  0.1528316  0.1308103 -0.1546491

Largest  eigenvalues:
 [1] 98983496 96770048 89958279 86900654 84912629 83189107 82689406 80057690
 [9] 79811730 76898757

Smallest eigenvalues:
 [1]  0.40133594  0.38063107  0.34122381  0.30931897  0.25246874  0.16867394
 [7]  0.10477144  0.05625151 -0.04545561 -0.15253094

Largest  eigenvalues:
 [1] 99502697 97137231 91167685 86344911 85381320 83962773 83728185 81488974
 [9] 80593049 78703830

Smallest eigenvalues:
 [1]  0.377478867  0.374785142  0.300490170  0.263067050  0.256155320
 [6]  0.255597417  0.156797013  0.054077637 -0.009283969 -0.646392121

Largest  eigenvalues:
 [1] 99879632 98554075 91819072 88012136 86231621 85670492 84088259 82913136
 [9] 80796756 79751815

Smallest eigenvalues:
 [1]  0.38684892  0.35256063  0.35027141  0.29815667  0.26069783  0.20290028
 [7]  0.12866846  0.10752501 -0.07398599 -0.20880520

Largest  eigenvalues:
 [1] 99381133 95450959 89098007 85677282 84647521 83208743 82526926 80909876
 [9] 79058676 77605546

Smallest eigenvalues:
 [1]  0.40017253  0.37063367  0.35164918  0.33259087  0.27451587  0.17724248
 [7]  0.13739204  0.11806899 -0.09707913 -0.33473433

Largest  eigenvalues:
 [1] 100919432  95591550  89262516  86531864  85420744  83464754  82003665
 [8]  80762835  79043355  77403950

Smallest eigenvalues:
 [1]  0.36476280  0.29011148  0.24984857  0.20427609  0.17491026  0.16963265
 [7]  0.16540353  0.12071118 -0.05522887 -0.41669961

Largest  eigenvalues:
 [1] 101310264  97055975  91110423  86605304  86584859  84950632  83128303
 [8]  82262817  80842449  79357356

Smallest eigenvalues:
 [1]  0.3296075  0.2728563  0.2615494  0.2492401  0.2311479  0.1625284
 [7]  0.1509390 -0.1630511 -0.4244158 -0.7234031

Largest  eigenvalues:
 [1] 100218216  96588281  90816829  86475103  86339803  84558363  83276740
 [8]  82111448  80008258  78705989

Smallest eigenvalues:
 [1]  0.27569481  0.26903723  0.24113019  0.19816557  0.14926897  0.11453316
 [7]  0.08413974  0.04647350 -0.19379624 -0.38530425

Largest  eigenvalues:
 [1] 101157073  96832411  90572813  86709485  85697109  84516436  83067507
 [8]  81764743  80606752  78465484

Smallest eigenvalues:
 [1]  0.38431598  0.36340146  0.30762859  0.29361553  0.27656759  0.26409070
 [7]  0.17356957  0.17311955 -0.01481429 -0.34806793

Largest  eigenvalues:
 [1] 99209191 97104441 90970782 86596695 85378808 83950158 83459398 81804383
 [9] 79953565 78377505

Smallest eigenvalues:
 [1]  0.24551377  0.23186245  0.22558035  0.20370132  0.14953925  0.08285052
 [7] -0.00369371 -0.09445282 -0.10480596 -0.22987720

Largest  eigenvalues:
 [1] 97155034 96372654 90731211 86074369 84373642 84027325 83538678 81370072
 [9] 80430557 78537128

Smallest eigenvalues:
 [1]  0.40600543  0.30358233  0.29694394  0.28271463  0.26384152  0.07228635
 [7]  0.01886570  0.01639374 -0.02469746 -0.28751733

Largest  eigenvalues:
 [1] 101695624  96223097  90643108  86366063  85793687  83603564  83103101
 [8]  81157538  80143913  78104443

Smallest eigenvalues:
 [1]  0.41391815  0.31796303  0.28691679  0.28262731  0.25734193  0.17927178
 [7]  0.16979021  0.05924129 -0.05302641 -0.15750450

Largest  eigenvalues:
 [1] 100364415  96408296  89974809  86373465  85643452  83526106  82471721
 [8]  80983524  79245995  77669790

Smallest eigenvalues:
 [1]  0.17432864  0.16916192  0.16035653  0.15674914  0.07422896 -0.13277239
 [7] -0.22666780 -0.39543984 -0.54018638 -0.86850116

Largest  eigenvalues:
 [1] 101688281  97517104  92062024  86738585  86452671  84380580  83988759
 [8]  82485602  81067288  79520143

Smallest eigenvalues:
 [1]  0.44329224  0.42913610  0.41652505  0.34661711  0.31057302  0.29445932
 [7]  0.28106263  0.08765684 -0.08221495 -0.65419945

Largest  eigenvalues:
 [1] 102397805  96824677  91415476  86573144  86433616  84236501  83170403
 [8]  81923231  80468675  78970242

Smallest eigenvalues:
 [1]  0.44850073  0.36970957  0.36374926  0.35857882  0.29862854  0.24408555
 [7]  0.14465521  0.04634988 -0.04085345 -0.19452264

Largest  eigenvalues:
 [1] 101642708  96098377  90673083  85995790  85909638  82964052  82671795
 [8]  80667869  80014578  77771767

Smallest eigenvalues:
 [1]  0.22625762  0.18733332  0.18073175  0.14164846  0.08719953  0.07226312
 [7] -0.06683011 -0.07138373 -0.27896282 -0.30504011

Largest  eigenvalues:
 [1] 98098374 96377253 90231038 85616629 84814079 84185687 83273781 82123934
 [9] 79688359 78424671

Smallest eigenvalues:
 [1]  0.26228933  0.25516369  0.20127234  0.19251817  0.18656578  0.13696064
 [7]  0.07152340 -0.04973992 -0.19924104 -0.53310386

Largest  eigenvalues:
 [1] 101144359  96572544  90895970  86566300  85322799  85023336  82885762
 [8]  82335552  80258291  78946044

Smallest eigenvalues:
 [1]  0.31425472  0.29232665  0.29075440  0.21315227  0.19541121  0.12096287
 [7]  0.10495014  0.03156166 -0.09900187 -0.56218498

Largest  eigenvalues:
 [1] 99622731 97436697 90892607 87405121 85757009 84020041 83803027 81371208
 [9] 80354054 77885160

Smallest eigenvalues:
 [1]  0.4465739  0.4193418  0.4051978  0.3187929  0.3119098  0.2671968
 [7]  0.1688253 -0.1336306 -0.1804687 -0.2749556

Largest  eigenvalues:
 [1] 100381539  96660805  90605672  86253895  86158424  83631946  83530252
 [8]  81099220  80189865  78040963

Smallest eigenvalues:
 [1]  0.39008753  0.38160474  0.36413128  0.34316733  0.30699135  0.28512160
 [7]  0.25444969 -0.01322824 -0.01544472 -0.16627302

Largest  eigenvalues:
 [1] 100162096  96473592  90180263  86733724  85540054  84059328  83101169
 [8]  81531313  80092393  78119442

Smallest eigenvalues:
 [1]  0.41861967  0.39262556  0.38049540  0.33515061  0.26838976  0.23596506
 [7]  0.12945188  0.09761897 -0.06329057 -0.23699486

Largest  eigenvalues:
 [1] 100374704  96103018  89791830  85923019  85266917  83171212  82136710
 [8]  80295545  79215579  77147460

Smallest eigenvalues:
 [1]  0.28738449  0.24913151  0.24652734  0.18475134  0.17914336  0.14902647
 [7]  0.12668149  0.07205256  0.03869582 -0.16388367

Largest  eigenvalues:
 [1] 99232217 96327823 89835456 85651361 85587322 83597217 82559834 81079558
 [9] 79303218 77895041

Smallest eigenvalues:
 [1]  0.48928234  0.46392669  0.42913993  0.40900368  0.31466784  0.31025645
 [7]  0.19904872  0.02996629 -0.10909826 -0.30305982

Largest  eigenvalues:
 [1] 101245356  96956479  90547754  86728756  86132677  84187650  83422985
 [8]  81614638  80404206  78615373

Smallest eigenvalues:
 [1]  0.48683616  0.40605442  0.39315705  0.38228399  0.30552375  0.26655492
 [7]  0.22389781  0.19634832  0.10197018 -0.01158128

Largest  eigenvalues:
 [1] 99989298 95692157 89377903 86219262 85180256 83889768 81867681 80859266
 [9] 79414338 77970261

Smallest eigenvalues:
 [1]  0.32579221  0.31422255  0.30954782  0.30603726  0.28792185  0.25651022
 [7]  0.25000196  0.16151739  0.08090955 -0.27462201

Largest  eigenvalues:
 [1] 98873143 96744610 90674457 85669109 84743710 83576046 82891876 80578961
 [9] 80070338 77711055

Smallest eigenvalues:
 [1]  0.22526279  0.17317759  0.10599801  0.05908499  0.03306539  0.02518277
 [7] -0.03273921 -0.07240640 -0.34068194 -1.21983101

Largest  eigenvalues:
 [1] 99112819 96381256 90515844 86556055 84394800 83413816 83269114 80998778
 [9] 80171892 77411919

Smallest eigenvalues:
 [1]  0.40259340  0.39362327  0.34444887  0.33384453  0.24983615  0.20863125
 [7]  0.09461222  0.07240370  0.01613215 -0.13904183

Largest  eigenvalues:
 [1] 98892184 96958354 90007214 87212967 84424141 83813097 82858974 80421131
 [9] 80061215 77213586

Smallest eigenvalues:
 [1]  0.43057434  0.36382332  0.30067717  0.29230871  0.27096904  0.23761812
 [7]  0.22916630  0.15295642 -0.01816134 -0.59872798

Largest  eigenvalues:
 [1] 99877461 97352596 90918817 86801097 85585995 84453827 83259039 82024081
 [9] 80310399 78913063

Smallest eigenvalues:
 [1]  0.34739348  0.30659360  0.29108482  0.23788418  0.16880245  0.15659054
 [7]  0.14583203  0.09183633 -0.01252479 -0.60626167

Largest  eigenvalues:
 [1] 99553497 97122614 91168791 86879778 85778748 84820483 83091831 82105560
 [9] 80151687 78942715

Smallest eigenvalues:
 [1]  0.450956053  0.442523383  0.427279110  0.412650720  0.338030639
 [6]  0.298041333  0.260460946  0.148424385  0.002344365 -0.271899040

Largest  eigenvalues:
 [1] 101520316  96516418  90605210  86880818  86064790  83535332  83123199
 [8]  81269675  79963993  78193027

Smallest eigenvalues:
 [1]  0.34018108  0.29864039  0.27460988  0.26176493  0.19859976  0.19573599
 [7]  0.14219140  0.09380002 -0.12350303 -0.42591160

Largest  eigenvalues:
 [1] 101278509  96487122  90574845  86014869  84022823  83781279  82470949
 [8]  80986426  79915223  77815519

Smallest eigenvalues:
 [1]  0.22495882  0.20455576  0.20245823  0.19698026  0.13884342  0.02618067
 [7] -0.12289622 -0.23587343 -0.27023480 -0.27352964

Largest  eigenvalues:
 [1] 100358750  95466105  90014201  85278854  84937147  83239576  82768721
 [8]  81162770  79677906  78053183

Smallest eigenvalues:
 [1]  0.38823012  0.38712569  0.37378028  0.36105341  0.32477152  0.30614659
 [7]  0.28048654  0.09945887 -0.06009152 -0.08498040

Largest  eigenvalues:
 [1] 100709733  97151207  90792849  86596243  85640497  84254894  83145570
 [8]  81462551  80292895  78331537

Smallest eigenvalues:
 [1]  0.45027281  0.44817929  0.43074911  0.37958881  0.33360187  0.24300297
 [7]  0.15577164  0.10935828 -0.01744099 -0.59285194

Largest  eigenvalues:
 [1] 98907222 95621812 90119568 85517997 84303424 83649226 82453253 81064251
 [9] 79473062 77934888

Smallest eigenvalues:
 [1]  0.21604247  0.16766568  0.14039010  0.09394209  0.09072088  0.08102785
 [7]  0.07933263 -0.06598817 -0.08301799 -0.66654315

Largest  eigenvalues:
 [1] 99648748 96213718 90744505 86177607 85513596 84631061 82664140 81893909
 [9] 80078251 79301089

Smallest eigenvalues:
 [1]  0.223231799  0.215173801  0.213164127  0.185839058  0.080812111
 [6]  0.032679906 -0.002710683 -0.195506878 -0.379178233 -0.407147630

Largest  eigenvalues:
 [1] 99285888 96369196 89730201 86284418 85154246 82719495 82594682 80097223
 [9] 79580125 77037997

Smallest eigenvalues:
 [1]  0.38210214  0.33330334  0.32887680  0.29342782  0.28370784  0.21505827
 [7]  0.19067972  0.10801247 -0.08479556 -0.24816456

Largest  eigenvalues:
 [1] 98035128 97140450 90120027 86959673 84674544 84008355 83053190 81279098
 [9] 79866359 78092984

Smallest eigenvalues:
 [1]  0.42095191  0.40586310  0.39196811  0.32951223  0.27188078  0.25067862
 [7]  0.24427800  0.22358717  0.12756453 -0.01524738

Largest  eigenvalues:
 [1] 100272784  95602079  89441475  85961379  84149784  83627979  81827737
 [8]  80735630  79391403  77237907

Smallest eigenvalues:
 [1]  0.337518850  0.313931226  0.310652171  0.293687131  0.232552235
 [6]  0.148557061  0.002684596 -0.039277516 -0.145194806 -0.397152129

Largest  eigenvalues:
 [1] 100543735  96721070  90651002  86316689  85461133  83968735  83146689
 [8]  81549110  80094928  78466743

Smallest eigenvalues:
 [1]  0.51708467  0.47575527  0.43004257  0.40503028  0.37028150  0.33466927
 [7]  0.28618749  0.24838679 -0.01219082 -0.22384564

Largest  eigenvalues:
 [1] 100908170  97928412  91218783  87472626  86591219  84754166  83816093
 [8]  82011116  80900929  79106800

Smallest eigenvalues:
 [1]  0.4170582  0.3849799  0.3615875  0.3249693  0.3052663  0.2800357
 [7]  0.2492211  0.1430776 -0.2622172 -0.5314545

Largest  eigenvalues:
 [1] 100529120  96762162  90523829  86396672  86019035  84130099  82613911
 [8]  81486187  80096608  78692339

Smallest eigenvalues:
 [1]  0.2882131581  0.2507007011  0.2461772948  0.2136708819  0.1739795803
 [6]  0.1320590895  0.0006083194 -0.0426102072 -0.3553098171 -0.8678625185

Largest  eigenvalues:
 [1] 100702551  96868425  90858529  87003845  84265959  84104150  83730697
 [8]  81669663  80483022  78280670

Smallest eigenvalues:
 [1]  0.389565927  0.382001945  0.343533618  0.334162226  0.333193126
 [6]  0.271996440  0.219229834 -0.008580813 -0.095131886 -0.307370850

Largest  eigenvalues:
 [1] 100996903  96197731  90071617  86640032  85248194  83804839  82419325
 [8]  80875394  79593832  77906293

Smallest eigenvalues:
 [1]  0.45406298  0.41596934  0.35874272  0.30455855  0.25275811  0.24717082
 [7]  0.21060864  0.07776984 -0.14985800 -0.63722932

Largest  eigenvalues:
 [1] 100712713  95027493  89219612  85556197  85017605  82228151  82021609
 [8]  79935306  79062798  76944379

Smallest eigenvalues:
 [1]  0.3567306  0.3235459  0.2525263  0.2378950  0.2295788  0.1737657
 [7]  0.1403549  0.1017452 -0.1588549 -0.2259587

Largest  eigenvalues:
 [1] 98520110 97389215 90984757 87058738 84481405 84054224 83694725 81143519
 [9] 80416261 78261546

Smallest eigenvalues:
 [1]  0.10512725  0.03501004  0.02448124  0.02104269 -0.25180588 -0.38267106
 [7] -0.45106993 -0.65973958 -0.68814195 -0.78222381

Largest  eigenvalues:
 [1] 98226777 97829734 91460341 86985686 84636698 84011445 83893764 81112292
 [9] 80458439 77848076

Smallest eigenvalues:
 [1]  0.42229072  0.41364868  0.38231237  0.31810273  0.26337545  0.23998662
 [7]  0.17490495  0.08922615  0.06088044 -0.25937998

Largest  eigenvalues:
 [1] 99180563 95629957 89445454 85908698 84553340 83003197 82523376 80558981
 [9] 79516431 77566614

Smallest eigenvalues:
 [1]  0.34633722  0.32758718  0.31749913  0.30171195  0.25463636  0.22123821
 [7]  0.15995147  0.08587602 -0.39927322 -0.59175271

Largest  eigenvalues:
 [1] 99451051 96628302 90729090 86307868 85890907 84149444 83659432 81668002
 [9] 80386894 78603134

Smallest eigenvalues:
 [1]  0.25140056  0.24398003  0.17889252  0.13288612  0.11690513  0.06701467
 [7] -0.01931691 -0.17686512 -0.40370415 -0.56734953

Largest  eigenvalues:
 [1] 100276625  96841263  90031187  86445723  86294272  84433987  82882410
 [8]  81557008  79874566  78323875

Smallest eigenvalues:
 [1]  0.4000925  0.3464329  0.3342947  0.3292621  0.2904134  0.2646720
 [7]  0.2529778  0.1890054  0.1072928 -0.2506938

Largest  eigenvalues:
 [1] 100185053  96984280  90562612  86741563  84868734  83791909  82769729
 [8]  80937645  79880551  78168111

Smallest eigenvalues:
 [1]  0.4655190  0.4286237  0.4004332  0.3814505  0.3480695  0.3312053
 [7]  0.1973777  0.1847620  0.1483448 -0.2754437

Largest  eigenvalues:
 [1] 99641537 95720650 89569075 86080477 85003635 83896115 82250269 81024622
 [9] 79673390 78140749

Smallest eigenvalues:
 [1]  0.28487984  0.25965614  0.25928171  0.25114519  0.20739786  0.14697560
 [7] -0.02552457 -0.03067389 -0.04248938 -0.21548912

Largest  eigenvalues:
 [1] 98360930 97956436 91609113 88006856 84966266 84043688 83448733 81147691
 [9] 80489249 77453931

Smallest eigenvalues:
 [1]  0.40348231  0.35871517  0.34439924  0.29462767  0.26835584  0.20248058
 [7]  0.12035211  0.04711807 -0.34253262 -0.40355534

Largest  eigenvalues:
 [1] 99081992 96498225 90036295 86414576 85165714 83608951 83022245 80754922
 [9] 79880628 77650349

Smallest eigenvalues:
 [1]  0.36973058  0.24558072  0.24354208  0.24295108  0.19838105  0.18505031
 [7]  0.11492212 -0.02736849 -0.06631418 -0.60687569

Largest  eigenvalues:
 [1] 101088625  97651330  91415090  87150853  86296308  84867018  83534621
 [8]  82075352  80577420  78873691

Smallest eigenvalues:
 [1]  0.4323251  0.4260857  0.4184527  0.3205421  0.2541329  0.1927956
 [7]  0.1756116  0.1575012 -0.1320411 -0.2270379

Largest  eigenvalues:
 [1] 100847129  96282092  89986380  86306721  84818229  83418770  82852103
 [8]  80960585  80119646  77782715

Smallest eigenvalues:
 [1]  0.41561646  0.38364172  0.32530082  0.30007041  0.26910228  0.23647945
 [7]  0.16373446 -0.02968727 -0.03596532 -0.33166659

Largest  eigenvalues:
 [1] 101109639  96199594  90185777  86434782  86163396  84327425  83227996
 [8]  82004246  80072649  78654393

Smallest eigenvalues:
 [1]  0.30779216  0.30414069  0.28797484  0.27439569  0.18072347  0.15884774
 [7]  0.06233294 -0.38741537 -0.74679006 -0.77220231

Largest  eigenvalues:
 [1] 100203915  96386324  89936975  86142450  86058216  83523760  83228908
 [8]  80938425  80043933  77885025

Smallest eigenvalues:
 [1]  0.3640130  0.3437144  0.3151329  0.2875822  0.2788707  0.2564149
 [7]  0.2229312  0.1026802 -0.3913795 -0.3935394

Largest  eigenvalues:
 [1] 100008977  97577321  91078401  87390210  85498138  83986670  83597054
 [8]  81080537  80661441  77915508

Smallest eigenvalues:
 [1]  0.38173382  0.35580841  0.31893826  0.28715904  0.25146163  0.09758433
 [7]  0.05960150 -0.03232801 -0.15323409 -0.25395670

Largest  eigenvalues:
 [1] 100994317  95801696  90178177  85603291  85241789  83495794  82012156
 [8]  80766914  79585798  77905954

Smallest eigenvalues:
 [1]  0.422539908  0.368664441  0.335734760  0.319807536  0.279513037
 [6]  0.271428306  0.242369693 -0.004495994 -0.014857761 -0.534931724

Largest  eigenvalues:
 [1] 101518806  96172589  90132744  86531284  85415544  83882602  82175895
 [8]  81147573  79861314  78120511

Smallest eigenvalues:
 [1]  0.4046639  0.3546784  0.3531929  0.3237723  0.2742388  0.1953243
 [7]  0.1188659  0.1017503 -0.1840807 -0.2361507

Largest  eigenvalues:
 [1] 100910634  95601076  89484175  85795414  85596304  83010294  82187040
 [8]  80373637  79364889  77456641

Smallest eigenvalues:
 [1]  0.37565698  0.30643723  0.29395285  0.26265620  0.23216807  0.20760756
 [7]  0.16162055  0.09730921 -0.05464493 -0.32412276

Largest  eigenvalues:
 [1] 98791412 95603540 89533656 85425404 84200588 83988961 81895810 81192265
 [9] 79105974 77852984

Smallest eigenvalues:
 [1]  0.35053932  0.31988756  0.30457879  0.28305635  0.23601211  0.22062125
 [7]  0.17952252  0.05293524 -0.01422083 -0.12139775

Largest  eigenvalues:
 [1] 98716373 97089248 90042200 86716488 84753165 83612065 82902253 80975747
 [9] 79591971 77440248

Smallest eigenvalues:
 [1]  0.4315482  0.3212320  0.2775270  0.2635595  0.2525289  0.2318917
 [7]  0.2225824  0.1866442  0.1580802 -0.1838012

Largest  eigenvalues:
 [1] 99867989 97783772 90737901 87262105 85916826 84599054 83539407 81861719
 [9] 80637532 79225262

Smallest eigenvalues:
 [1]  0.41778702  0.37188209  0.33111567  0.29305827  0.29200653  0.28780413
 [7]  0.26014597  0.19363434  0.14132096 -0.03054311

Largest  eigenvalues:
 [1] 98697255 96039709 89476168 85930693 85071462 83277755 82979098 80838213
 [9] 79802189 77856048

Smallest eigenvalues:
 [1]  0.31735061  0.31204173  0.29569054  0.28252792  0.26950029  0.19944601
 [7]  0.16057404  0.12080352  0.05726589 -0.16960427

Largest  eigenvalues:
 [1] 97089410 97018751 90793359 86874936 83828849 83081839 82701049 80444433
 [9] 80118783 77165167

Smallest eigenvalues:
 [1]  0.26672444  0.25123775  0.23719834  0.21283683  0.19948307  0.16346010
 [7]  0.08639443  0.03927285 -0.02403168 -0.40746805

Largest  eigenvalues:
 [1] 98627691 96571191 89636254 86587376 84739535 83371775 83161558 81119893
 [9] 79683786 77965882

Smallest eigenvalues:
 [1]  0.21531951  0.20729704  0.17897215  0.16221977  0.15645348  0.13183488
 [7]  0.07069141  0.05819838 -0.10136669 -0.81570001

Largest  eigenvalues:
 [1] 101462852  97445671  91591733  86918663  86721773  85216150  83597053
 [8]  82716586  80722430  79377115

Smallest eigenvalues:
 [1]  0.4138523  0.4124753  0.3941361  0.3765952  0.3673656  0.3013338
 [7]  0.2884123  0.2693577  0.2671783 -0.2159696

Largest  eigenvalues:
 [1] 100416910  95405210  89187089  85717638  84766989  83592314  82829357
 [8]  81264930  79519038  77868719

Smallest eigenvalues:
 [1]  0.4803736  0.4648956  0.4130571  0.4060590  0.3918486  0.3636475
 [7]  0.3342313  0.2763485  0.1966139 -0.2143531

Largest  eigenvalues:
 [1] 99591361 96294388 90208650 86173062 85513287 83634110 82663206 81076684
 [9] 79999366 78150311

Smallest eigenvalues:
 [1]  0.43162536  0.39235037  0.33362075  0.30794097  0.30098441  0.29714699
 [7]  0.10115827  0.07900846  0.05870488 -0.36593480

Largest  eigenvalues:
 [1] 99295479 96819116 90310691 86604233 85942191 83757742 83521595 81247519
 [9] 80259111 77994443

Smallest eigenvalues:
 [1]  0.26752533  0.25597285  0.24233937  0.23143638  0.15439079  0.06197901
 [7]  0.04931553  0.01421427 -0.07378400 -0.51012329

Largest  eigenvalues:
 [1] 99887657 96427297 90747635 86198826 85968456 84904778 82850402 82039778
 [9] 80146214 78997904

Smallest eigenvalues:
 [1]  0.280689378  0.249771292  0.247927707  0.203628403  0.193103932
 [6]  0.111617560  0.049305170  0.007692562  0.001829109 -0.477047265

Largest  eigenvalues:
 [1] 100975994  97875139  91711351  87148814  85853602  84821558  83387261
 [8]  82087265  80061380  78704714

Smallest eigenvalues:
 [1]  0.35031501  0.30057697  0.29749850  0.23742719  0.22917048  0.14593471
 [7]  0.13998219 -0.01573393 -0.02939857 -0.82813323

Largest  eigenvalues:
 [1] 102346028  96512219  91000331  86588224  86368776  83578359  82898729
 [8]  80976793  80155377  77808097

Smallest eigenvalues:
 [1]  0.23953005  0.18574767  0.15495206  0.12693522  0.10872901  0.10675879
 [7]  0.02511950 -0.05398068 -0.18715285 -0.19360303

Largest  eigenvalues:
 [1] 99176755 97227996 90114528 86530746 85707485 83190764 82920750 80482543
 [9] 79877246 77633915

Smallest eigenvalues:
 [1]  0.39586305  0.38929281  0.34561935  0.29629986  0.28342246  0.12108434
 [7]  0.04130694  0.03658649 -0.10510365 -0.48165769

Largest  eigenvalues:
 [1] 99847994 96329765 89809365 86621724 84554900 83644057 82313680 80706031
 [9] 79504729 77240011

Smallest eigenvalues:
 [1]  0.24959236  0.23573055  0.21193732  0.16333859  0.15469907  0.11834565
 [7]  0.11208011  0.07893102 -0.51020532 -1.01657483

Largest  eigenvalues:
 [1] 98756900 97588085 91229250 86935560 85423134 84837303 83834838 82014312
 [9] 80833715 78960086

Smallest eigenvalues:
 [1]  0.23049271  0.17259789  0.15795286  0.13370686  0.11952944  0.10526978
 [7]  0.09780656 -0.03463285 -0.43738020 -0.57699751

Largest  eigenvalues:
 [1] 99700823 98708148 91657957 88164539 86179600 85871006 84235209 82489902
 [9] 81433598 79722391

Smallest eigenvalues:
 [1]  0.1926638704  0.1886783332  0.1684652738  0.0820769670  0.0577678044
 [6]  0.0007470578 -0.0735877005 -0.0882565391 -0.3116061119 -0.5334949285

Largest  eigenvalues:
 [1] 98668223 97421074 90954417 86675651 84998913 84057689 83454829 81164469
 [9] 80379879 77965271

Smallest eigenvalues:
 [1]  0.38508090  0.37205729  0.36358650  0.27906184  0.19664225  0.14815868
 [7]  0.02223784 -0.03584776 -0.20877023 -0.34899210

Largest  eigenvalues:
 [1] 101059165  96041245  90435313  86129629  85847844  84144114  83149862
 [8]  81650237  79942263  78460162

Smallest eigenvalues:
 [1]  0.33306914  0.32589570  0.27336716  0.26575993  0.23635918  0.19886799
 [7]  0.17934528  0.12390215 -0.03895463 -0.45555546

Largest  eigenvalues:
 [1] 97763597 96975526 90323189 86804237 84631726 83883732 82781668 81750044
 [9] 79492959 78230699

Smallest eigenvalues:
 [1]  0.39937269  0.35969961  0.35222583  0.34500986  0.25150033  0.23377614
 [7]  0.18107403  0.03753776 -0.34911042 -0.38920895

Largest  eigenvalues:
 [1] 100021071  95952913  90002151  85974665  85512004  83270178  83152051
 [8]  80935016  79803354  77730536

Smallest eigenvalues:
 [1]  0.27011731  0.24859072  0.24796274  0.19995566  0.17175407  0.10208083
 [7] -0.01935700 -0.02458107 -0.13557538 -0.81492607

Largest  eigenvalues:
 [1] 101264022  96610525  91186401  86179287  86173355  84398976  83380485
 [8]  82201158  80321313  78890433

Smallest eigenvalues:
 [1]  0.44034696  0.36036845  0.32329327  0.31905050  0.31463437  0.29631225
 [7]  0.21948459  0.09859459 -0.04423912 -0.04614522

Largest  eigenvalues:
 [1] 100440536  96170997  90439181  86300042  84716190  83778400  82770122
 [8]  81048288  79994776  78133742

Smallest eigenvalues:
 [1]  0.37421110  0.32599877  0.31509411  0.28505454  0.24147991  0.20826107
 [7]  0.19516552  0.04896781  0.04807424 -0.02752855

Largest  eigenvalues:
 [1] 99485811 96744465 90006993 86261064 84845184 83167826 82890605 80369329
 [9] 79773275 77202238

Smallest eigenvalues:
 [1]  0.30151903  0.20625776  0.15434672  0.11963654  0.04986176 -0.04840008
 [7] -0.08866457 -0.14978759 -0.41278671 -0.81969876

Largest  eigenvalues:
 [1] 100792195  97025816  91052751  86886736  85770543  83508886  83310820
 [8]  81218164  80196053  78150179

Smallest eigenvalues:
 [1]  0.3938262  0.3835030  0.3444733  0.3411253  0.3067322  0.2080827
 [7]  0.1721212  0.1465819 -0.1001295 -0.1662654

Largest  eigenvalues:
 [1] 98976366 96230683 89700439 86337712 84710462 83362802 82981616 80898480
 [9] 79979825 77804298

Smallest eigenvalues:
 [1]  0.40418773  0.39475125  0.31551012  0.25216223  0.22927721  0.16817612
 [7]  0.09901924  0.09239385 -0.02714463 -0.10646846

Largest  eigenvalues:
 [1] 98985422 96639401 90708870 85759168 84828584 83674609 83109352 81056603
 [9] 80017481 78215784

Smallest eigenvalues:
 [1]  0.23550919  0.22882326  0.15052621  0.08568235  0.04739304  0.02480883
 [7] -0.02468985 -0.04299996 -0.15974593 -0.60927196

Largest  eigenvalues:
 [1] 99068265 96186320 90658330 85907951 84085032 83389443 82626820 80907600
 [9] 79856025 77478548

Smallest eigenvalues:
 [1]  0.27108994  0.24439420  0.20530583  0.17430710  0.14953447  0.09561237
 [7]  0.09486943  0.02209804 -0.15089026 -0.57755486

Largest  eigenvalues:
 [1] 99632845 95398855 89633377 85624057 84483144 83886155 82463862 81437498
 [9] 79505550 78295345

Smallest eigenvalues:
 [1]  0.449113802  0.448274072  0.420258724  0.385066194  0.358959415
 [6]  0.215238348  0.202719945  0.008369484 -0.002545651 -0.097033668

Largest  eigenvalues:
 [1] 99231445 96222466 90028811 86520658 84519227 83776852 83223562 81333433
 [9] 79880390 78015307

Smallest eigenvalues:
 [1]  0.22310133  0.18785070  0.13420682  0.12730033  0.08039525  0.06986402
 [7]  0.05962369 -0.13627781 -0.42258206 -0.62618678

Largest  eigenvalues:
 [1] 98113994 97355537 90524497 87172360 84680906 84144215 83458597 81307262
 [9] 80429975 77906986

Smallest eigenvalues:
 [1]  0.36070889  0.35466051  0.26676820  0.25474898  0.25318535  0.21290835
 [7]  0.18446632  0.18154968  0.02585697 -0.06153801

Largest  eigenvalues:
 [1] 97903130 96615910 89430511 86482607 84381989 83426775 82497828 80530382
 [9] 79669045 77122707

Smallest eigenvalues:
 [1]  0.3409468  0.3021379  0.2999484  0.2304528  0.2035924  0.1838266
 [7]  0.1702454  0.1604355 -0.2597936 -0.4075668

Largest  eigenvalues:
 [1] 99324699 98540922 91806746 87474548 85990939 84518205 84100426 81618580
 [9] 81099155 78675610

Smallest eigenvalues:
 [1]  0.37735259  0.31294602  0.24329095  0.14005362  0.13819981  0.02840671
 [7] -0.05518334 -0.07977283 -0.13087838 -0.38907929

Largest  eigenvalues:
 [1] 99513594 97056602 90214599 86546127 85633018 83697804 83263246 80798172
 [9] 80256301 77898612

Smallest eigenvalues:
 [1]  0.4542761  0.4138827  0.4075287  0.2999736  0.2009530  0.1558497
 [7]  0.1531053  0.1388860 -0.1646449 -0.3706835

Largest  eigenvalues:
 [1] 101135774  96617585  90338240  86791460  85724094  84494789  82876909
 [8]  81500129  80144316  78268364

Smallest eigenvalues:
 [1]  0.4376275229  0.4219747376  0.3913908038  0.2947092078  0.2862341011
 [6]  0.2703908297  0.2296939039  0.0839935492 -0.0003486296 -0.0994138395

Largest  eigenvalues:
 [1] 98989603 96615496 90788490 86067778 84646760 83460049 83274542 81099423
 [9] 80232567 78018947

Smallest eigenvalues:
 [1]  0.31125821  0.30756006  0.30001058  0.28426259  0.22086590  0.16831740
 [7]  0.13492852  0.13217185 -0.07676006 -0.30992984

Largest  eigenvalues:
 [1] 99752773 95835715 90006065 85722744 85382725 83267947 82363813 80566495
 [9] 79683650 77477526

Smallest eigenvalues:
 [1]  0.39018705  0.37096744  0.34210719  0.29877313  0.28561771  0.23928139
 [7]  0.22306082  0.03063135 -0.01285469 -0.19431874

Largest  eigenvalues:
 [1] 99876531 97622510 91157293 87292598 85513137 84238900 83503917 81701967
 [9] 80452736 78306467

Smallest eigenvalues:
 [1]  0.33373436  0.31788416  0.31095196  0.29292469  0.24197851  0.22653076
 [7]  0.11741449  0.07935776  0.01182836 -0.46686532

Largest  eigenvalues:
 [1] 99136468 96570847 90324217 87144056 84291429 84014020 83102242 81481736
 [9] 80249748 78075517

Smallest eigenvalues:
 [1]  0.3492333  0.3183674  0.2999183  0.2751889  0.2748991  0.2381646
 [7]  0.2198520  0.1731930  0.1133202 -0.2993485

Largest  eigenvalues:
 [1] 99964134 96006905 90738075 85711013 85335832 84775810 82444194 82113944
 [9] 79722442 78831376

Smallest eigenvalues:
 [1]  0.43907095  0.34541057  0.33726545  0.29386774  0.29145759  0.27812008
 [7]  0.15318857  0.12422081  0.08260224 -0.10733687

Largest  eigenvalues:
 [1] 100622931  97541656  91370427  86903309  85774861  85508313  83084135
 [8]  82253946  80571532  79629639

Smallest eigenvalues:
 [1]  0.3206931  0.3144289  0.3140894  0.2889132  0.2602198  0.2175505
 [7]  0.2028738  0.1096424 -0.2766387 -0.3634534

Largest  eigenvalues:
 [1] 101138909  96942098  91218154  86157699  85275534  83543985  83204662
 [8]  81130508  80508769  78041763

Smallest eigenvalues:
 [1]  0.42738273  0.41166329  0.39525201  0.27552693  0.26959841  0.24230490
 [7]  0.20538706  0.15522210 -0.09870404 -0.31463964

Largest  eigenvalues:
 [1] 101888679  96133533  90035557  87071150  85429035  83603039  82113817
 [8]  80958188  79715092  78146017

Smallest eigenvalues:
 [1]  0.39669429  0.37847748  0.37782070  0.27519668  0.26374311  0.21415789
 [7]  0.20797428  0.15556163  0.01250644 -0.11256888

Largest  eigenvalues:
 [1] 98548420 95384392 89245605 85337467 82990884 82731878 82343105 80381749
 [9] 79255826 76925433

Smallest eigenvalues:
 [1]  0.4689156166  0.4554242251  0.4320563565  0.3449777003  0.2625576859
 [6]  0.2120052072  0.2031850588  0.1483157421  0.0005732822 -0.0479211227

Largest  eigenvalues:
 [1] 100218560  96480542  90479396  86909834  85130397  84280259  82946339
 [8]  81350251  80554946  78585002

Smallest eigenvalues:
 [1]  0.22816545  0.17283149  0.15660339  0.14095849  0.11119365  0.04680411
 [7]  0.04017759 -0.27807809 -0.37721787 -0.44670587

Largest  eigenvalues:
 [1] 100296305  97186698  91196691  86915922  84940356  83904032  83658723
 [8]  80980332  80492975  77860742

Smallest eigenvalues:
 [1]  0.3578494  0.3318037  0.3162512  0.3105722  0.3089050  0.2521968
 [7]  0.2267988  0.1347732  0.1240214 -0.0144601

Largest  eigenvalues:
 [1] 99457311 98069142 91533684 87616419 84692653 84613349 83240662 81203132
 [9] 80634439 78131058

Smallest eigenvalues:
 [1]  0.44454474  0.38368426  0.35360068  0.30528310  0.27886134  0.26433023
 [7]  0.24853326  0.15108415  0.05328573 -0.29308998

Largest  eigenvalues:
 [1] 98802357 95386421 89339547 85520124 84181553 83010458 81738468 80442613
 [9] 78942457 77090234

Smallest eigenvalues:
 [1]  0.4634143  0.3941080  0.3496938  0.3015902  0.2704276  0.2588945
 [7]  0.2486256  0.2196774  0.0755789 -0.5539918

Largest  eigenvalues:
 [1] 100953149  97048901  90866016  86374013  86305230  84092679  82841758
 [8]  81497632  80257455  78503913

Smallest eigenvalues:
 [1]  0.304397732  0.261754626  0.253640653  0.222707844  0.197160573
 [6]  0.139352309  0.135077492  0.041905552  0.001260181 -0.365215168

Largest  eigenvalues:
 [1] 99179909 97134107 91029016 86824209 84608984 83880464 83068343 81308878
 [9] 80063611 78001902

Smallest eigenvalues:
 [1]  0.39036382  0.38814500  0.32118717  0.28249365  0.26706930  0.23092764
 [7]  0.15663242  0.07084688 -0.09617200 -0.48041005

Largest  eigenvalues:
 [1] 102831748  96588186  90609969  87578399  86207711  84675827  82558034
 [8]  81939453  79826894  78774727

Smallest eigenvalues:
 [1]  0.44533986  0.42877758  0.40946613  0.39609396  0.37742077  0.31375589
 [7]  0.24210320  0.15528385  0.05655215 -0.20191647

Largest  eigenvalues:
 [1] 99487182 96677476 90458017 87210612 84393553 83519497 82900985 80868716
 [9] 79890787 77546962

Smallest eigenvalues:
 [1]  0.118010818  0.076144054  0.057050369  0.014531861  0.007574394
 [6] -0.070783322 -0.173814969 -0.359602087 -0.551051105 -0.944043629

Largest  eigenvalues:
 [1] 98544517 96573762 90471337 86863437 84517827 83930449 83749691 81513812
 [9] 80177523 78328041

Smallest eigenvalues:
 [1]  0.3733985  0.3636938  0.3539554  0.3240115  0.3210622  0.2401722
 [7]  0.1522610  0.1407973  0.1331477 -0.5066377

Largest  eigenvalues:
 [1] 101144776  97357336  91101274  86640136  86113996  84975844  82970432
 [8]  82211823  80365497  79169163

Smallest eigenvalues:
 [1]  0.42194630  0.36643540  0.30849887  0.29495970  0.18556692  0.14946758
 [7]  0.08895793  0.07119086 -0.32794784 -0.36333182

Largest  eigenvalues:
 [1] 101290411  96570051  90344413  86498084  86264317  84975927  82205111
 [8]  81800160  79699262  78675675

Smallest eigenvalues:
 [1]  0.463517033  0.427795954  0.396663602  0.324266657  0.321517994
 [6]  0.294482232  0.177336549  0.045929547  0.005135486 -0.107882241

Largest  eigenvalues:
 [1] 99757105 96264813 89901609 86284396 84826118 83209415 82811075 80340764
 [9] 79813229 77158752

Smallest eigenvalues:
 [1]  0.13763711  0.11744402  0.03383973 -0.09361435 -0.17177170 -0.23744794
 [7] -0.30895757 -0.39655814 -0.88606288 -1.00357106

Largest  eigenvalues:
 [1] 101159724  94758652  88489718  85676057  85378605  82998513  81429547
 [8]  80128194  78605823  77110950

Smallest eigenvalues:
 [1]  0.39836413  0.38816964  0.35950824  0.35574254  0.34229493  0.25651961
 [7]  0.19019463  0.18419021  0.05260736 -0.35659083

Largest  eigenvalues:
 [1] 100085244  97735354  91472440  87104303  86051268  85127331  83499348
 [8]  82499517  80418803  79279001

Smallest eigenvalues:
 [1]  0.31754143  0.29906450  0.28651197  0.25754892  0.21770808  0.21063717
 [7]  0.14253485  0.10340743 -0.01625338 -0.11601395

Largest  eigenvalues:
 [1] 97601372 97230764 91004793 86860837 84169476 83746789 83640481 81654338
 [9] 80318818 78525039

Smallest eigenvalues:
 [1]  0.34445024  0.32043208  0.30597717  0.23314078  0.22107962  0.16928771
 [7]  0.08206912  0.05399807 -0.27254118 -0.99980294

Largest  eigenvalues:
 [1] 97983187 95012557 89382975 85404738 83510979 82521898 82260044 80093153
 [9] 79255467 77302231

Smallest eigenvalues:
 [1]  0.35640603  0.32531971  0.23836030  0.18078362  0.15318344  0.12505446
 [7]  0.10760883 -0.06218987 -0.18915834 -0.26120759

Largest  eigenvalues:
 [1] 102126616  96256080  90558052  86950230  85451714  84259059  82769964
 [8]  81598687  80334404  79002354

Smallest eigenvalues:
 [1]  0.34708835  0.34284117  0.26071459  0.24445478  0.21504923  0.19387273
 [7]  0.14720569 -0.05828855 -0.18398081 -0.35060766

Largest  eigenvalues:
 [1] 100090153  97319417  90522292  87302095  85661284  84423359  83743176
 [8]  81336722  80577103  78290675

Smallest eigenvalues:
 [1]  0.33243466  0.31689379  0.27451006  0.26389887  0.21991949  0.11776743
 [7]  0.07909847  0.05716138  0.05633957 -0.17631125

Largest  eigenvalues:
 [1] 98698435 96353425 90118551 85997130 85061451 83820509 82730846 80689341
 [9] 80106444 77694374

Smallest eigenvalues:
 [1]  0.27108158  0.25878729  0.25383143  0.22965802  0.14378848  0.08547422
 [7]  0.02281610  0.02165068 -0.07151370 -0.26469923

Largest  eigenvalues:
 [1] 98267799 96766553 90464609 85615434 85167333 83671075 83255380 81231873
 [9] 80027464 78412721

Smallest eigenvalues:
 [1]  0.40739037  0.40297082  0.37039658  0.34531499  0.28885457  0.23115028
 [7]  0.21801250  0.20091496  0.01010609 -0.20407532

Largest  eigenvalues:
 [1] 100859675  96140646  90010993  86636553  85396301  84632570  82225618
 [8]  81567740  79975414  78561177

Smallest eigenvalues:
 [1]  0.36153185  0.35263144  0.34359855  0.34176053  0.24570836  0.21139960
 [7]  0.19190760  0.12164975  0.07469133 -0.05388423

Largest  eigenvalues:
 [1] 97781326 96178115 89850755 85389126 84489496 82954034 82799225 80355126
 [9] 79614703 77560920

Smallest eigenvalues:
 [1]  0.370120289  0.364771342  0.346577410  0.304753132  0.296859094
 [6]  0.163146158  0.096873328  0.031080391  0.009492749 -0.625070383

Largest  eigenvalues:
 [1] 99342844 96076435 90367556 86383141 84528461 83335996 83110458 80729534
 [9] 80132964 77386873

Smallest eigenvalues:
 [1]  0.39181350  0.38373232  0.33429629  0.28292813  0.27653197  0.26483503
 [7]  0.18200635  0.17685264 -0.05443421 -0.13852630

Largest  eigenvalues:
 [1] 100953955  97211231  91011546  86769461  86223204  85066524  82953790
 [8]  81943442  80157711  78912494

Smallest eigenvalues:
 [1]  0.35549314  0.34385815  0.34203176  0.32588590  0.02205661  0.01722075
 [7] -0.01454430 -0.23008843 -0.31394841 -0.39610048

Largest  eigenvalues:
 [1] 99702420 96581917 90329176 86153787 85283814 84022335 83059505 81237630
 [9] 80148723 78088218

Smallest eigenvalues:
 [1]  0.39574475  0.38690746  0.37161963  0.35791519  0.32649832  0.32647130
 [7]  0.30877303  0.23639015 -0.04260909 -0.13348769

Largest  eigenvalues:
 [1] 99413493 97472799 90630126 86902027 85302150 83856854 83476993 81212258
 [9] 80347437 78286521

Smallest eigenvalues:
 [1]  0.43707474  0.37342799  0.35335179  0.33287168  0.28823153  0.22765054
 [7]  0.19577074  0.16938743  0.13989620 -0.03962136

Largest  eigenvalues:
 [1] 98856420 96852163 90350029 86601524 84550863 83978947 82702317 81112294
 [9] 80032112 77907788

Smallest eigenvalues:
 [1]  0.34429309  0.28980578  0.26433521  0.24939250  0.15785677  0.14481161
 [7]  0.06367226 -0.16941722 -0.29621078 -0.35527919

Largest  eigenvalues:
 [1] 101097984  97652515  91516624  86847647  86036786  84796862  83551164
 [8]  82100781  80939333  79433297

Smallest eigenvalues:
 [1]  0.38765615  0.33113480  0.32208901  0.29174656  0.28967414  0.26968406
 [7]  0.25091721  0.11253298  0.08109373 -0.06002116

Largest  eigenvalues:
 [1] 100964601  97208429  90662132  86907512  85818321  84285424  82425000
 [8]  81096460  80062632  78262584

Smallest eigenvalues:
 [1]  0.3676270  0.2664219  0.2479153  0.2466358  0.2283154  0.2155199
 [7]  0.1766076  0.1135760 -0.0178251 -0.5790804

Largest  eigenvalues:
 [1] 97747191 96058790 89718279 85797684 83807856 82929869 82454151 80385163
 [9] 79163229 76911361

Smallest eigenvalues:
 [1]  0.4166852  0.3694587  0.3627989  0.2695094  0.2666033  0.1207934
 [7] -0.2451575 -0.3191504 -0.4614576 -1.2888291

Largest  eigenvalues:
 [1] 101978532  96283555  90792960  86701656  86071691  84420093  82982429
 [8]  81824887  80305554  78978541

Smallest eigenvalues:
 [1]  0.34430764  0.30309128  0.24474618  0.22964111  0.12496146  0.09400842
 [7]  0.08674272  0.05373652 -0.17392909 -0.61076441

Largest  eigenvalues:
 [1] 100508186  95946811  89856940  86426764  85022283  83727163  82260063
 [8]  80867761  79806600  78205625

Smallest eigenvalues:
 [1]  0.3712703  0.3406365  0.3290207  0.3225666  0.2161522  0.1695865
 [7]  0.0734146 -0.2901562 -0.3214343 -0.4076146

Largest  eigenvalues:
 [1] 100937365  96746227  90461548  86710095  85157652  83798163  82888118
 [8]  80885111  79848012  77537719

Smallest eigenvalues:
 [1]  0.3878788  0.3801770  0.3214060  0.2949996  0.2694249  0.2398643
 [7]  0.2284926  0.1284223 -0.1234032 -0.3112984

Largest  eigenvalues:
 [1] 98636176 96682916 89806236 86601063 85098097 83922890 83500637 81097789
 [9] 79843689 77645868

Smallest eigenvalues:
 [1]  0.3241729733  0.3115427612  0.3014599295  0.2695526028  0.2231204055
 [6]  0.0308982248  0.0113911885  0.0003479822 -0.2314885175 -0.9148584589

Largest  eigenvalues:
 [1] 100740455  96258273  90864222  85974469  85687490  84241898  82916836
 [8]  81782719  80044210  78684461

Smallest eigenvalues:
 [1]  0.30007003  0.29104257  0.27013914  0.26686089  0.25958276  0.16606629
 [7]  0.12700005  0.10862977  0.05919622 -0.98114946

Largest  eigenvalues:
 [1] 98703080 96814323 90306020 86394761 85406938 83618090 83302743 81174032
 [9] 79996759 77857167

Smallest eigenvalues:
 [1]  0.40025262  0.36846199  0.36287890  0.34600333  0.31688411  0.31107306
 [7]  0.23995088  0.16284988  0.15259396 -0.09884837

Largest  eigenvalues:
 [1] 98633237 95623443 89457089 85562300 83976992 82556768 82398596 80188985
 [9] 79283667 76923215

Smallest eigenvalues:
 [1]  0.33388794  0.30209265  0.29591901  0.25304083  0.22680882  0.12645044
 [7]  0.11219459  0.10285303  0.00966683 -0.33590339

Largest  eigenvalues:
 [1] 98082746 96997856 90761132 86473092 84726099 83875588 83561247 81170043
 [9] 80431276 77811189

Smallest eigenvalues:
 [1]  0.31123053  0.26049558  0.25405609  0.25324440  0.18694500  0.13857176
 [7]  0.09704981 -0.10138859 -0.31468305 -0.53202822

Largest  eigenvalues:
 [1] 99411750 97441034 90315099 87152475 85774286 84309084 83222317 81309676
 [9] 80332733 78451171

Smallest eigenvalues:
 [1]  0.3753334  0.2634897  0.2588335  0.2410766  0.2332993  0.2246530
 [7]  0.2184609  0.1172257 -0.2176387 -0.2239272

Largest  eigenvalues:
 [1] 100399856  97555392  91191325  87347504  85571653  85058091  83595414
 [8]  82275814  81086629  79713132

Smallest eigenvalues:
 [1]  0.38741653  0.38370448  0.37525905  0.37318332  0.27706767  0.20593097
 [7]  0.05590575  0.02377025 -0.06203291 -0.13339107

Largest  eigenvalues:
 [1] 100663081  96981526  90548509  86338172  86284908  84156315  82937900
 [8]  81154449  80079177  78381154

Smallest eigenvalues:
 [1]  0.30879773  0.29781915  0.24994595  0.24066122  0.23308781  0.20513364
 [7]  0.16985581  0.15584044  0.09696983 -0.11819995

Largest  eigenvalues:
 [1] 101046211  96003885  89963409  85860551  85731885  83624311  81858372
 [8]  80948789  79732490  77756975

Smallest eigenvalues:
 [1]  0.4271959  0.4002332  0.3904296  0.3903091  0.3785927  0.2463006
 [7]  0.1798466  0.1640075  0.1218662 -0.3006366

Largest  eigenvalues:
 [1] 98590081 97057204 90208731 87370173 84370904 83480790 83201959 80696706
 [9] 80170677 77536368

Smallest eigenvalues:
 [1]  0.30296087  0.21429638  0.20016446  0.19828833  0.19465761  0.15978757
 [7]  0.15446267  0.03500772 -0.06108077 -0.42671351

Largest  eigenvalues:
 [1] 100510727  96503035  90688969  85990047  84868299  83615351  83157202
 [8]  81047763  80330202  78128504

Smallest eigenvalues:
 [1]  0.348695042  0.337564143  0.281479485  0.177135988  0.142988303
 [6]  0.029398012  0.011129277 -0.008415165 -0.743042352 -0.833540453

Largest  eigenvalues:
 [1] 101982494  95703977  90503058  85977231  85643654  83661654  82357253
 [8]  81357618  79868481  78403165

Smallest eigenvalues:
 [1]  0.45671648  0.41165927  0.40249679  0.33846605  0.22319678  0.21497284
 [7]  0.15765044  0.07886118  0.03730287 -0.08667760

Largest  eigenvalues:
 [1] 100285640  96718821  90148183  86447098  85417992  83564620  82507627
 [8]  80634430  79975668  77724542

Smallest eigenvalues:
 [1]  0.228541447  0.227063607  0.221173417  0.154167774  0.071543494
 [6] -0.001522917 -0.188033620 -0.194962143 -0.244090342 -0.590038148

Largest  eigenvalues:
 [1] 101528831  95719596  90556762  85764367  84838753  83934358  82125818
 [8]  81475583  79874321  78847358

Smallest eigenvalues:
 [1]  0.38392711  0.37686344  0.34237811  0.33672498  0.28698969  0.16325425
 [7]  0.03551562 -0.01511404 -0.02935671 -0.05721715

Largest  eigenvalues:
 [1] 99671282 95847824 90017591 85403772 85202862 83615256 82609529 80891207
 [9] 79699671 77883010

Smallest eigenvalues:
 [1]  0.36413909  0.36187706  0.32672426  0.27982996  0.25610037  0.19266826
 [7]  0.18818113  0.07963762  0.07320753 -0.45621319

Largest  eigenvalues:
 [1] 98956070 96295260 90274372 85726087 84916247 82907470 82773324 80569358
 [9] 79743566 77448320

Smallest eigenvalues:
 [1]  0.272452752  0.268093112  0.233269719  0.221057581  0.099897359
 [6]  0.077135881 -0.008974206 -0.152999573 -0.409153890 -0.786816028

Largest  eigenvalues:
 [1] 99835657 96930201 90290150 86547782 85571775 83981321 83303663 81425771
 [9] 80039813 78010161

Smallest eigenvalues:
 [1]  0.38470796  0.34961126  0.31197878  0.22413131  0.21462432  0.17429218
 [7]  0.16704220  0.05242967 -0.01362830 -0.51049669

Largest  eigenvalues:
 [1] 100575003  96798507  90488934  87109534  85388331  84524575  83476270
 [8]  81833050  80669382  78577768

Smallest eigenvalues:
 [1]  0.48168969  0.48063126  0.42853678  0.38863011  0.34302813  0.26067613
 [7]  0.22760373  0.03906630  0.01561523 -0.17975349

Largest  eigenvalues:
 [1] 101548885  95906017  89918625  85850754  85423537  83681532  82268306
 [8]  80950093  79617825  77881376

Smallest eigenvalues:
 [1]  0.36801243  0.31612583  0.30568380  0.30311802  0.27669096  0.18039616
 [7]  0.14550022  0.10414646 -0.05708747 -0.41127360

Largest  eigenvalues:
 [1] 99195211 95135297 89205131 85035639 83656068 83236589 82362740 80709965
 [9] 79407447 77568013

Smallest eigenvalues:
 [1]  0.3630558  0.3552533  0.2788957  0.2157778  0.2140177  0.1891380
 [7]  0.1706367  0.1163342  0.0427792 -0.8699088

Largest  eigenvalues:
 [1] 98132246 96452716 89997706 86088919 84177904 83288053 83053140 80971923
 [9] 79924560 78119995

Smallest eigenvalues:
 [1]  0.44210401  0.43596528  0.38314672  0.34376226  0.34208626  0.29392120
 [7]  0.25062822  0.23417909  0.14346429 -0.06698027

Largest  eigenvalues:
 [1] 100588362  96848137  90676689  86421278  85451337  83733043  83141376
 [8]  81303894  80472746  78474060

Smallest eigenvalues:
 [1]  0.24608415  0.12301252  0.11425315  0.08439212  0.02875445 -0.03239082
 [7] -0.13014552 -0.14691597 -0.24464442 -0.30533046

Largest  eigenvalues:
 [1] 96951152 96658835 89772218 86225000 84400714 83040963 82856794 80279190
 [9] 79196044 76986566

Smallest eigenvalues:
 [1]  0.30971552  0.26663164  0.25016579  0.22264682  0.19538359  0.15502151
 [7]  0.11417466  0.06639802  0.06342260 -0.77227511

Largest  eigenvalues:
 [1] 100521470  95542785  89887270  85125396  85032344  82663969  81733479
 [8]  80229544  79069333  77375327

Smallest eigenvalues:
 [1]  0.37261245  0.31810526  0.29554204  0.25251230  0.20639885  0.17947953
 [7]  0.05152177  0.01526193 -0.12796109 -0.19750224

Largest  eigenvalues:
 [1] 99478784 96441494 90163582 85793140 85161265 83797013 82439933 81009093
 [9] 79588749 77820312

Smallest eigenvalues:
 [1]  0.54628650  0.49356860  0.47864726  0.42718756  0.41245972  0.37671630
 [7]  0.32817865  0.17343919  0.07379411 -0.02165498

Largest  eigenvalues:
 [1] 100093914  96780531  90486255  87226384  85409093  83704813  83316878
 [8]  80914446  80263471  77726184

Smallest eigenvalues:
 [1]  0.37093775  0.36395958  0.32819322  0.29290160  0.19931767  0.18901128
 [7]  0.16802766  0.07071485 -0.03583926 -0.49426202

Largest  eigenvalues:
 [1] 101186816  96130766  90466651  85743035  85226720  83928363  82559008
 [8]  81470684  79656057  78205768

Smallest eigenvalues:
 [1]  0.28492384  0.21090119  0.19604934  0.18954266  0.14050079  0.13812079
 [7]  0.12776229 -0.06964428 -0.37194664 -0.46445000

Largest  eigenvalues:
 [1] 100025122  97352387  90222962  87153482  85470228  85025177  82822855
 [8]  81986114  80266759  79090436

Smallest eigenvalues:
 [1]  0.411993004  0.409709787  0.391715183  0.367397629  0.318052164
 [6]  0.304488174  0.248749069  0.226122460  0.006895722 -0.160416584

Largest  eigenvalues:
 [1] 101006864  96814507  91040875  86284502  85397228  84197222  82871980
 [8]  81301505  80273266  78635324

Smallest eigenvalues:
 [1]  0.4566624  0.4466032  0.4247940  0.4007810  0.3823345  0.3261750
 [7]  0.2313097  0.1291146 -0.1605673 -0.1820893

Largest  eigenvalues:
 [1] 100680907  96348762  89993856  86262287  85534866  83859967  83017513
 [8]  81328067  80044789  78181806

Smallest eigenvalues:
 [1]  0.34482383  0.29991965  0.29282460  0.24273262  0.18534238  0.15430959
 [7]  0.05373261  0.04469854 -0.07354668 -0.16024261

Largest  eigenvalues:
 [1] 99841020 96727836 90060725 86519018 85337827 83718913 83094694 81091010
 [9] 80371329 78055516

Smallest eigenvalues:
 [1]  0.354283470  0.294617263  0.260464994  0.245314008  0.216354223
 [6]  0.170487939  0.131768582  0.104071752 -0.006006261 -0.070503264

Largest  eigenvalues:
 [1] 99697980 98087148 91278574 87220021 86028957 84760132 83390133 81760204
 [9] 80382114 78795805

Smallest eigenvalues:
 [1]  0.26009382  0.25825686  0.23073219  0.14848904  0.11808849  0.11397764
 [7]  0.10083738  0.02216616  0.01815838 -0.85852118

Largest  eigenvalues:
 [1] 97645229 95758734 89720401 86525329 84453644 83602088 82737544 81084832
 [9] 79560621 77753369

Smallest eigenvalues:
 [1]  0.36215334  0.33200552  0.32354317  0.28822947  0.28443315  0.25354143
 [7]  0.16765527  0.01306040 -0.02126239 -0.24619437

Largest  eigenvalues:
 [1] 97817880 94978679 89086698 85477604 82523695 82021733 81468917 79380357
 [9] 78669947 76345007

Smallest eigenvalues:
 [1]  0.54287051  0.49056861  0.43077711  0.39718352  0.39610485  0.38419621
 [7]  0.31519397  0.27934390  0.07812666 -0.12855651

Largest  eigenvalues:
 [1] 102191832  95909261  90375557  86247877  85666205  84086668  82148600
 [8]  81463063  79758393  78434092

Smallest eigenvalues:
 [1]  0.29684947  0.26154647  0.25173220  0.24769201  0.23990333  0.21592635
 [7]  0.09245003  0.05114277 -0.00888879 -0.09204184

Largest  eigenvalues:
 [1] 100579681  97261462  90938698  86866813  85781427  84944154  83139873
 [8]  82377581  80063928  78966255

Smallest eigenvalues:
 [1]  0.48837812  0.46538074  0.39483984  0.36812518  0.36293155  0.36089380
 [7]  0.29982250  0.23608839  0.14942120 -0.08436834

Largest  eigenvalues:
 [1] 99783275 97211044 90207119 86764491 85692849 83288019 83071112 80632100
 [9] 80002648 77621999

Smallest eigenvalues:
 [1]  0.328762978  0.279383006  0.239245073  0.228611371  0.218796356
 [6]  0.216969040  0.066138058 -0.008804448 -0.101897702 -0.345301606

Largest  eigenvalues:
 [1] 99566549 96006192 90226234 86324257 84357264 83397317 83175515 80979997
 [9] 80360049 77609028

Smallest eigenvalues:
 [1]  0.42760836  0.39695539  0.37799744  0.37448479  0.35124914  0.22765205
 [7]  0.18707256  0.15156045 -0.09179962 -0.37689368

Largest  eigenvalues:
 [1] 100770756  97227655  91021203  86728108  85990028  84159791  83550042
 [8]  81948538  80446341  78912480

Smallest eigenvalues:
 [1]  0.33278368  0.33175610  0.22649417  0.19076022  0.17700991  0.11279682
 [7]  0.09700239  0.04099863 -0.23462927 -0.23610921

Largest  eigenvalues:
 [1] 98273947 97180455 90709358 86814452 84815039 83901773 82910927 80768144
 [9] 80199051 77855863

Smallest eigenvalues:
 [1]  0.42691156  0.38715787  0.37500290  0.37055189  0.35284878  0.23669577
 [7]  0.21510769  0.16668320 -0.02719969 -0.05248460

Largest  eigenvalues:
 [1] 99114594 96041449 89662641 86149405 85387719 84558115 82663378 81616155
 [9] 79833867 78434825

Smallest eigenvalues:
 [1]  0.42290109  0.38039727  0.33927692  0.31964401  0.30431695  0.20422458
 [7]  0.19405433  0.09168327  0.02855149 -0.17863149

Largest  eigenvalues:
 [1] 100172270  97788595  91608112  86802119  85909058  83969881  83669569
 [8]  81574411  80473886  78684329

Smallest eigenvalues:
 [1]  0.37791803  0.34551114  0.34166535  0.30159110  0.27940815  0.21942159
 [7]  0.14642246  0.07762277  0.06817518 -0.28825981

Largest  eigenvalues:
 [1] 97863998 96532893 89684855 86034569 84816578 83626743 82787056 80769365
 [9] 79728096 77838767

Smallest eigenvalues:
 [1]  0.43475421  0.42663472  0.42619223  0.34561639  0.32651875  0.31021487
 [7]  0.25307035  0.12156014  0.07994455 -0.06094652

Largest  eigenvalues:
 [1] 98423803 95139108 89158878 84706367 83648604 82339988 81853719 79891260
 [9] 78989200 76960403

Smallest eigenvalues:
 [1]  0.33792263  0.28148467  0.26673520  0.25492677  0.22208890  0.20700823
 [7]  0.15722524  0.07982529  0.04877991 -0.64969001

Largest  eigenvalues:
 [1] 98880222 96535454 90433446 86232730 85508353 83706478 83049555 81112742
 [9] 79705227 77837725

Smallest eigenvalues:
 [1]  0.34743019  0.33400505  0.27868723  0.20866929  0.20359728  0.18888553
 [7]  0.14531753  0.05805121  0.02947548 -0.12448300

Largest  eigenvalues:
 [1] 99757453 98065596 91994620 87161858 86035173 85570370 84044304 82403752
 [9] 80988756 79362791

Smallest eigenvalues:
 [1]  0.26697761  0.26664204  0.25371362  0.24444707  0.01305265 -0.17989474
 [7] -0.24634201 -0.46320660 -0.74346493 -0.93219520

Largest  eigenvalues:
 [1] 101189337  95929023  90244969  86814011  85326241  82956353  82810194
 [8]  80605059  79801258  77712274

Smallest eigenvalues:
 [1]  0.32697845  0.31177554  0.30709096  0.22379773  0.21125860  0.02467064
 [7] -0.03566370 -0.12183877 -0.31410091 -0.34614835

Largest  eigenvalues:
 [1] 97337540 94851179 88622049 85133697 83125050 82297215 81502706 79590325
 [9] 78595728 76357052

Smallest eigenvalues:
 [1]  0.23420983  0.22626169  0.21599331  0.20910381  0.16391971  0.09933557
 [7]  0.01949609 -0.05158341 -0.10881832 -0.49407252

Largest  eigenvalues:
 [1] 98166023 95009308 89036809 85125818 82721599 82268312 82091384 79730734
 [9] 79007585 76455425

Smallest eigenvalues:
 [1]  0.28286345  0.26949619  0.24007289  0.22154884  0.20570567  0.14487649
 [7]  0.07398656 -0.05284925 -0.35967355 -0.50310239

Largest  eigenvalues:
 [1] 101690482  97211345  91764085  87133390  86535925  85359389  83533148
 [8]  82632572  80680912  79497692

Smallest eigenvalues:
 [1]  0.393795338  0.385298235  0.369522021  0.334718406  0.329348797
 [6]  0.312995348  0.209513696  0.104409429 -0.008657202 -0.010730160

Largest  eigenvalues:
 [1] 100586027  97698195  91042561  86719949  86180074  83989552  83037952
 [8]  80818679  80417390  78278361

Smallest eigenvalues:
 [1]  0.44682124  0.42928444  0.38548750  0.32385364  0.30566305  0.29532295
 [7]  0.27387176  0.27097945  0.26918173 -0.06675064

Largest  eigenvalues:
 [1] 99156445 96301342 90227937 85720301 85345997 83463121 82943076 81004706
 [9] 79764650 77899106

Smallest eigenvalues:
 [1]  0.2869746  0.2707422  0.2591637  0.2569717  0.2203477  0.2191196
 [7]  0.1102222  0.1012788 -0.4479487 -0.7359944

Largest  eigenvalues:
 [1] 101082558  97469395  91774426  86844929  86557415  85016807  83327756
 [8]  82044638  80376471  78936290

Smallest eigenvalues:
 [1]  0.36154435  0.35528275  0.34745181  0.26154884  0.22116694  0.19556946
 [7]  0.11044037  0.08842001 -0.16344848 -0.17419351

Largest  eigenvalues:
 [1] 99924018 97152557 91031842 86080018 85692379 84078667 82779338 81246448
 [9] 80111426 78656759

Smallest eigenvalues:
 [1]  0.46645225  0.33452829  0.32861863  0.30407173  0.29472933  0.25607429
 [7]  0.20206810  0.19231033  0.07086878 -0.04548917

Largest  eigenvalues:
 [1] 101548791  96684790  90796081  86946336  85655549  85267532  82696523
 [8]  82220609  80324964  79244341

Smallest eigenvalues:
 [1]  0.154858576  0.105073449  0.088844204 -0.007575988 -0.175607434
 [6] -0.229360824 -0.290800719 -0.298618821 -0.416415107 -0.979371346

Largest  eigenvalues:
 [1] 101878771  95677861  89940214  86005765  85418313  83936187  82734301
 [8]  81629792  79542898  78329694

Smallest eigenvalues:
 [1]  0.37961553  0.34225829  0.27415639  0.23696539  0.17896868  0.11815653
 [7]  0.09066802  0.03963638 -0.07176412 -0.17937928

Largest  eigenvalues:
 [1] 97971950 95660599 89876090 85393122 84332558 83631724 82662159 80974591
 [9] 79491563 78058423

Smallest eigenvalues:
 [1]  0.29624273  0.28305774  0.26130040  0.23707974  0.22337609  0.17175739
 [7]  0.16179654  0.07259951 -0.02515440 -0.05012574

Largest  eigenvalues:
 [1] 98563368 96330194 89639280 86027206 85169767 82699435 82560795 80203400
 [9] 79481521 77224119

Smallest eigenvalues:
 [1]  0.38963566  0.38886048  0.33183788  0.29017331  0.26915344  0.24032852
 [7]  0.21138502  0.21111700  0.06538584 -0.02814864

Largest  eigenvalues:
 [1] 97739869 95506995 89293852 85084973 84346385 83391217 82341959 80975478
 [9] 79017813 77670699

Smallest eigenvalues:
 [1]  0.39340653  0.36962752  0.34932305  0.33285840  0.29052747  0.21464714
 [7]  0.18992228  0.11901901  0.08937024 -0.52085392

Largest  eigenvalues:
 [1] 99966174 95955485 89944989 86096419 84766547 83166533 82602511 80770613
 [9] 79758673 77686966

Smallest eigenvalues:
 [1]  0.3826192  0.3622961  0.3372793  0.3198039  0.2721926  0.1954268
 [7]  0.1704835 -0.1181644 -0.2327284 -0.4010284

Largest  eigenvalues:
 [1] 101633322  96742106  90421358  86601572  85801057  84145303  82665742
 [8]  81566379  80427781  78311276

Smallest eigenvalues:
 [1]  0.32710056  0.28571297  0.22112551  0.19843754  0.19092330  0.15505902
 [7]  0.11570371  0.07036709 -0.01677417 -0.08125318

Largest  eigenvalues:
 [1] 97047801 96570505 89996693 86243752 83613364 83454293 83121887 80804134
 [9] 80087335 77521134

Smallest eigenvalues:
 [1]  0.358422211  0.354652747  0.342115403  0.310069088  0.189125892
 [6]  0.167548832  0.081846922  0.009986815 -0.151345758 -0.280494041

Largest  eigenvalues:
 [1] 99199436 96950750 90026852 86426929 85187488 83782829 82490859 80613274
 [9] 79618461 77348242

Smallest eigenvalues:
 [1]  0.335086534  0.298815068  0.271147149  0.253947734  0.241306794
 [6]  0.183991248  0.158177142  0.087580542  0.079893715 -0.007231212

Largest  eigenvalues:
 [1] 100228624  97955122  91603622  86822549  85604723  84804199  83542040
 [8]  81807890  80627316  78844511

Smallest eigenvalues:
 [1]  0.3708371568  0.3653915566  0.3269298229  0.3205833194  0.2931298639
 [6]  0.2266393519  0.1844310085  0.0624871614 -0.0005274267 -0.4571866048

Largest  eigenvalues:
 [1] 97654679 95726247 89603926 86043276 83316912 82931962 82816333 80321103
 [9] 79589577 77248469

Smallest eigenvalues:
 [1]  0.41543063  0.32164773  0.24228880  0.21285122  0.20985308  0.13772626
 [7]  0.08647726 -0.14076971 -0.17953838 -0.51983491

Largest  eigenvalues:
 [1] 99525655 97638460 90475833 87488974 85952898 84215473 84059048 81750571
 [9] 80908513 78578469

Smallest eigenvalues:
 [1]  0.43131297  0.37442354  0.34046640  0.33561261  0.31970827  0.31955520
 [7]  0.29485693 -0.08118299 -0.17679021 -0.23402752

Largest  eigenvalues:
 [1] 98846701 97347317 90531035 87171144 85362951 83711789 83536715 81162234
 [9] 80409767 77991534

Smallest eigenvalues:
 [1]  0.30325982  0.29479733  0.28082512  0.26871949  0.19170329  0.10872022
 [7]  0.04443420 -0.07489060 -0.08698856 -0.31101186

Largest  eigenvalues:
 [1] 99040845 95757641 89389395 86158691 84625161 82792021 81911989 79490340
 [9] 79163782 76211277

Smallest eigenvalues:
 [1]  0.46666791  0.46358262  0.43353654  0.38437966  0.31903084  0.31256042
 [7]  0.20298092  0.01698847  0.01189491 -0.12225563

Largest  eigenvalues:
 [1] 99189783 95551189 89327909 86041551 83511165 82568855 82074468 79868670
 [9] 79231508 76633605

Smallest eigenvalues:
 [1]  0.39020227  0.34092285  0.33598386  0.31321449  0.29964486  0.25196604
 [7]  0.10743470 -0.09202008 -0.23172585 -0.28804027

Largest  eigenvalues:
 [1] 99830095 96586112 90626323 85991053 85643736 83472272 83231004 80910369
 [9] 80175591 77889234

Smallest eigenvalues:
 [1]  0.28320454  0.25958116  0.24378756  0.21870046  0.18277943  0.15390318
 [7]  0.04188932 -0.24710383 -0.28858293 -0.36889302

Largest  eigenvalues:
 [1] 101899157  98574697  92137381  87769714  86597328  84622061  84026574
 [8]  82082088  81075974  78993620

Smallest eigenvalues:
 [1]  0.26631089  0.26286016  0.25898521  0.17578746  0.11403746  0.10354723
 [7]  0.09354100  0.04253485  0.02346783 -0.17119786

Largest  eigenvalues:
 [1] 98973759 97381954 90351276 86779232 85723563 84366020 83195249 81591094
 [9] 80064656 78448919

Smallest eigenvalues:
 [1]  0.40071810  0.35422130  0.30762008  0.26855154  0.26194039  0.21403270
 [7]  0.20320264  0.19192062  0.16898296 -0.03978557

Largest  eigenvalues:
 [1] 99487606 97172688 90350023 86958578 85541470 84051364 83278495 81328406
 [9] 80445128 78359890

Smallest eigenvalues:
 [1]  0.37763075  0.34001618  0.28316890  0.23632699  0.19810442  0.19480682
 [7]  0.10493518  0.04993961  0.04031737 -0.38129538

Largest  eigenvalues:
 [1] 100290854  96205546  89940106  86521334  85425125  83376536  82163317
 [8]  80568292  79277241  77426745

Smallest eigenvalues:
 [1]  0.21571452  0.20970990  0.20097836  0.11149273  0.10433972  0.10234894
 [7]  0.06543447 -0.06218629 -0.23637317 -0.37511666

Largest  eigenvalues:
 [1] 100576103  97580992  90701826  86826562  85550576  83903146  82531801
 [8]  80895510  79608835  78168928

Smallest eigenvalues:
 [1]  0.35107306  0.34475681  0.27594283  0.21324193  0.17394462 -0.01265951
 [7] -0.05325034 -0.49364756 -0.59916208 -1.23622475

Largest  eigenvalues:
 [1] 100736836  96096396  90067013  86516393  86276193  83922357  83471951
 [8]  81481829  80119847  78470199

Smallest eigenvalues:
 [1]  0.31895155  0.30904963  0.29664551  0.25066719  0.23202901  0.21034124
 [7]  0.19445494  0.03857835 -0.37225559 -0.38495409

Largest  eigenvalues:
 [1] 99761822 96610921 90319999 85840125 85708797 83609452 83235783 81095857
 [9] 80061666 78087957

Smallest eigenvalues:
 [1]  0.18897963  0.18286349  0.17811690  0.16424739  0.10453966  0.05541427
 [7]  0.03618658 -0.18426589 -0.32394880 -0.32896853

Largest  eigenvalues:
 [1] 99150309 96482620 90156508 85906934 84737615 83667286 82719843 80988628
 [9] 79849181 77611173

Smallest eigenvalues:
 [1]  0.4650368  0.4189460  0.4117889  0.3849716  0.2966940  0.2152522
 [7]  0.2110367  0.1690589  0.1104567 -0.6699063

Largest  eigenvalues:
 [1] 98453176 97063541 90347654 87207103 85115244 83877910 83511672 81377239
 [9] 80131819 77766178

Smallest eigenvalues:
 [1]  0.390759166  0.375720334  0.296813812  0.255742485  0.251404776
 [6]  0.219734925  0.208227600 -0.006735731 -0.047181825 -0.267267814

Largest  eigenvalues:
 [1] 100769543  97989060  91102873  87505758  86260085  85101359  83957227
 [8]  82365189  81240584  79497117

Smallest eigenvalues:
 [1]  0.258215394  0.210897573  0.170801222  0.159052154  0.119704950
 [6]  0.088160921  0.008721204 -0.079877502 -0.158543241 -0.381340640

Largest  eigenvalues:
 [1] 100449376  96841399  90697012  86941380  85326661  85039637  83246693
 [8]  81970080  80678840  79232128

Smallest eigenvalues:
 [1]  0.1884011  0.1700106  0.1484323  0.1279615  0.1265200  0.1106676
 [7] -0.1065177 -0.1340896 -0.3502637 -0.3932765

Largest  eigenvalues:
 [1] 98254099 96307564 90137516 85943560 84685490 83692881 83318673 81019168
 [9] 80059348 77656369

Smallest eigenvalues:
 [1]  0.41833972  0.40632956  0.39214475  0.32056459  0.26185378  0.10531804
 [7] -0.07650263 -0.11396690 -0.39511743 -0.62749559

Largest  eigenvalues:
 [1] 100195719  96648284  90503245  86685696  86243520  84319094  83364073
 [8]  81433612  80262396  78094466

Smallest eigenvalues:
 [1]  0.28162721  0.26686780  0.20659324  0.16136058  0.08912136  0.07378089
 [7]  0.01215832 -0.19537132 -0.38042876 -0.75577945

Largest  eigenvalues:
 [1] 101016364  96971299  90202489  86785003  86781813  83554222  83023950
 [8]  80834995  80104615  77517945

Smallest eigenvalues:
 [1]  0.3686360  0.3676027  0.3422527  0.3045278  0.2608960  0.1700752
 [7]  0.1384833  0.0324884 -0.1374538 -0.3630848

Largest  eigenvalues:
 [1] 99539531 96670101 90344339 86589730 85151165 84254208 83245116 81567788
 [9] 80319398 77993292

Smallest eigenvalues:
 [1]  0.32741697  0.32279430  0.22375320  0.22352534  0.04608776  0.04078883
 [7]  0.01247902 -0.01979584 -0.06089093 -0.10959968

Largest  eigenvalues:
 [1] 97974152 97394416 90690320 87393482 83851608 83818091 83303394 80740865
 [9] 80168394 77393837

Smallest eigenvalues:
 [1]  0.46678422  0.42066312  0.41700106  0.37687560  0.30033924  0.17604920
 [7]  0.16054940  0.08964765  0.04675098 -0.08867313

Largest  eigenvalues:
 [1] 99913878 95913751 89858761 86041960 85328677 83478911 82944365 80811351
 [9] 79891956 77815040

Smallest eigenvalues:
 [1]  0.15966331  0.12270555  0.11976892  0.11798695  0.05763677  0.02585065
 [7]  0.01901152 -0.06469881 -0.11457037 -0.48985042

Largest  eigenvalues:
 [1] 97427824 96519589 90454526 86039843 84167560 83325984 82574734 80526596
 [9] 79872892 77558667

Smallest eigenvalues:
 [1]  0.3281647  0.2880198  0.2522436  0.2284610  0.2008078  0.1638020
 [7]  0.1162220  0.1088844 -0.4722262 -0.7772378

Largest  eigenvalues:
 [1] 98586712 96546355 90657682 86786894 84507911 83611350 83282389 81143462
 [9] 80248744 78076916

Smallest eigenvalues:
 [1]  0.46583470  0.44468708  0.41853264  0.41170238  0.36337790  0.27495904
 [7]  0.25240456 -0.00750709 -0.05576002 -0.09204529

Largest  eigenvalues:
 [1] 100858934  96215397  90181030  86492275  85695305  83519666  83219920
 [8]  81162417  79966928  77640696

Smallest eigenvalues:
 [1]  0.40871638  0.40178277  0.30449931  0.28230541  0.27699379  0.27692281
 [7]  0.23814933  0.18395907  0.04911989 -0.01962100

Largest  eigenvalues:
 [1] 98732994 96563135 89042577 85932266 85227431 83009885 81967803 79860631
 [9] 79094495 76713285

Smallest eigenvalues:
 [1]  0.27829057  0.22412160  0.20581549  0.18830344  0.18050499  0.14787885
 [7]  0.02589929 -0.08581674 -0.25400724 -0.34305644

Largest  eigenvalues:
 [1] 99569912 96217685 90299475 85671414 84571169 83276896 82205908 80335955
 [9] 79805224 76999603

Smallest eigenvalues:
 [1]  0.44707692  0.43711738  0.41458408  0.39973400  0.39854641  0.23795090
 [7]  0.16222320  0.11418480  0.08753536 -0.21234781

Largest  eigenvalues:
 [1] 99801853 95739061 89995376 85330387 84684245 82900277 82288655 80495238
 [9] 79524284 77430307

Smallest eigenvalues:
 [1]  0.413811209  0.394259562  0.333798583  0.307790140  0.277660551
 [6]  0.251070096  0.201726082  0.056909372  0.002845021 -0.169623783

Largest  eigenvalues:
 [1] 99793791 96027886 89825430 85730029 85360926 83621402 82485074 81069036
 [9] 79295451 77638993

Smallest eigenvalues:
 [1]  0.11995874  0.03919464 -0.07243507 -0.08412915 -0.11057988 -0.32456428
 [7] -0.36273331 -0.55924449 -0.80779483 -1.61712177

Largest  eigenvalues:
 [1] 101652519  96009699  89751050  87301471  85990450  84835964  82802743
 [8]  82470617  79598948  78771856

Smallest eigenvalues:
 [1]  0.44998631  0.38067714  0.38036905  0.35732227  0.30758059  0.19522543
 [7]  0.14394653  0.04264131 -0.16017647 -0.33033004

Largest  eigenvalues:
 [1] 100969084  95716841  90146154  85691965  85244704  83599701  82634517
 [8]  81105501  79871539  78310264

Smallest eigenvalues:
 [1]  0.469243955  0.428198488  0.422090069  0.421018415  0.408523360
 [6]  0.357623788  0.322640652  0.192963784  0.169908836 -0.002812238

Largest  eigenvalues:
 [1] 98556672 96118360 89565355 85664886 85257483 83062379 82770246 80565719
 [9] 79479977 77604551

Smallest eigenvalues:
 [1]  0.41860136  0.37029896  0.31801096  0.24897891  0.20796656  0.18052219
 [7]  0.08919671  0.07344524 -0.04600283 -0.69180783

Largest  eigenvalues:
 [1] 99457607 97448552 90480151 87226710 86155651 84073151 83899395 81516304
 [9] 80673796 78294809

Smallest eigenvalues:
 [1]  0.28362831  0.27983886  0.22630221  0.21591160  0.20072536  0.17158643
 [7]  0.08049235 -0.04447852 -0.18347106 -0.29191282

Largest  eigenvalues:
 [1] 99271150 97124508 90285176 86778725 85488007 84243654 83539255 81711264
 [9] 80343914 78407622

Smallest eigenvalues:
 [1]  0.40221550  0.36517080  0.33047893  0.29337977  0.27269660  0.23886325
 [7]  0.22303246  0.12265450 -0.02931478 -0.11411915

Largest  eigenvalues:
 [1] 98308881 97373500 91212837 87680922 84549016 84320257 84011142 81749694
 [9] 80588719 78313682

Smallest eigenvalues:
 [1]  0.39895763  0.37175341  0.30362410  0.26865365  0.25120102  0.23109612
 [7]  0.20973494  0.14286938  0.05734573 -0.05568522

Largest  eigenvalues:
 [1] 100556966  96505408  90521617  86599748  85025891  83399858  82985071
 [8]  80741879  80084031  77628075

Smallest eigenvalues:
 [1]  0.24787018  0.22293180  0.17273842  0.16346320  0.15246370  0.13319736
 [7]  0.04228685 -0.01485719 -0.07777430 -0.53297647

Largest  eigenvalues:
 [1] 96334844 96082126 89863532 86355295 83260722 83255156 82283971 80008003
 [9] 79548141 76773201

Smallest eigenvalues:
 [1]  0.3618484  0.2915707  0.2651846  0.2441289  0.2237961  0.2214666
 [7]  0.1345436  0.1077194 -0.2025304 -0.3289915

Largest  eigenvalues:
 [1] 100797820  97332170  90719504  86642098  86471455  84710706  82580986
 [8]  81678026  79981180  78732765

Smallest eigenvalues:
 [1]  0.3503480  0.3260445  0.3035851  0.3026767  0.2936594  0.1982876
 [7]  0.1776095  0.1578595  0.1473551 -0.3187226

Largest  eigenvalues:
 [1] 97951103 97775431 90789912 87454569 84764436 84427198 83901762 81338180
 [9] 80618620 77820694

Smallest eigenvalues:
 [1]  0.328628473  0.326765207  0.248949641  0.245435263  0.148692339
 [6]  0.057359369  0.056986789  0.003396798 -0.013635293 -0.215169570

Largest  eigenvalues:
 [1] 99183861 97128128 91012404 86338119 85465276 83605826 83168600 80959356
 [9] 80466445 77890839

Smallest eigenvalues:
 [1]  0.47939074  0.45914412  0.42490396  0.36786352  0.30914964  0.26874575
 [7]  0.26685334  0.21623590  0.09964064 -0.09219625

Largest  eigenvalues:
 [1] 99653232 96524501 90777916 86282607 85117981 83589651 83106185 81027820
 [9] 80050314 78171692

Smallest eigenvalues:
 [1]  0.4098949  0.3896041  0.3015959  0.2935863  0.2894355  0.2777673
 [7]  0.2637986  0.1581019  0.1345543 -0.3122339

Largest  eigenvalues:
 [1] 99873829 98023905 91067532 87884588 86044064 84914448 83469801 82017838
 [9] 80333634 78940175

Smallest eigenvalues:
 [1]  0.44653273  0.43131648  0.39904705  0.39088873  0.38143333  0.31887100
 [7]  0.21951130  0.20311545  0.04105688 -0.02464155

Largest  eigenvalues:
 [1] 99519101 95716967 89880498 85804448 84183529 82952541 82590511 80681774
 [9] 79697880 77546489

Smallest eigenvalues:
 [1]  0.38409100  0.35642755  0.35481662  0.34147760  0.34130559  0.31010757
 [7]  0.26311322 -0.07400601 -0.08813636 -0.62520030

Largest  eigenvalues:
 [1] 99111387 96020971 89638692 85729068 84520098 82873395 82765339 80617042
 [9] 79486791 77420003

Smallest eigenvalues:
 [1]  0.18644207  0.16785706  0.12970683  0.05168045  0.01943262  0.00919379
 [7] -0.03104875 -0.31121409 -0.38931875 -0.42857215

Largest  eigenvalues:
 [1] 99671953 97942890 90966245 87209799 86137985 84985181 83949626 82553353
 [9] 81031691 79671049

Smallest eigenvalues:
 [1]  0.41273150  0.40773405  0.37294028  0.36140985  0.34767676  0.29962898
 [7]  0.28639645  0.27853129  0.27105357 -0.02228512

Largest  eigenvalues:
 [1] 98952140 96972201 90423726 86533980 85035379 83903218 83578216 81212177
 [9] 80520281 78010510

Smallest eigenvalues:
 [1]  0.41297424  0.41061207  0.39001577  0.35779259  0.35570481  0.27470053
 [7]  0.22408587  0.14111807  0.01769003 -0.59496670

Largest  eigenvalues:
 [1] 100058669  96235937  90011682  85883275  85414252  83740733  82740005
 [8]  80908048  79853121  77825327

Smallest eigenvalues:
 [1]  0.4351055222  0.3926015555  0.3497409722  0.3335023264  0.2936171643
 [6]  0.2104956290  0.1769735200  0.1634078285  0.0006303139 -0.3215011954

Largest  eigenvalues:
 [1] 100745479  96884741  90078457  86466393  86296507  84674447  82430804
 [8]  81675155  79621302  78491697

Smallest eigenvalues:
 [1]  0.41200828  0.39806753  0.36857776  0.33593407  0.27815240  0.26919631
 [7]  0.20373225  0.02794539 -0.13077873 -0.44102054

Largest  eigenvalues:
 [1] 99988073 96219352 90182236 86099725 85193816 83465233 82878315 81066049
 [9] 79713255 77835209

Smallest eigenvalues:
 [1]  0.40071427  0.38451405  0.32828446  0.31009699  0.28877841  0.24107593
 [7]  0.14281846  0.12196693 -0.04961201 -0.10280425

Largest  eigenvalues:
 [1] 99305319 96357607 90087146 86082944 84742490 83115165 82999260 80706502
 [9] 79756895 77392064

Smallest eigenvalues:
 [1]  0.32157280  0.28438689  0.26418235  0.23064139  0.23039579  0.11899563
 [7]  0.01544149 -0.05733516 -0.16830966 -0.67765665

Largest  eigenvalues:
 [1] 100357762  96096191  90401907  85961377  84642925  83644533  82543021
 [8]  80948917  79815592  77679269

Smallest eigenvalues:
 [1]  0.4371261  0.3120702  0.2750353  0.2590111  0.2381815  0.1240182
 [7]  0.1238669  0.1161227 -0.1186057 -0.3717290

Largest  eigenvalues:
 [1] 100184234  97829350  91264660  87447525  86100902  84929635  83934665
 [8]  82054740  80888801  78984779

Smallest eigenvalues:
 [1]  0.34794391  0.34330033  0.31268796  0.22063082  0.21116366  0.12587686
 [7]  0.07884995  0.06437375 -0.02300992 -0.22594675

Largest  eigenvalues:
 [1] 99606735 97598903 90585185 86966271 85429962 83217316 83104608 80412144
 [9] 79887589 77060904

Smallest eigenvalues:
 [1]  0.4157508  0.3932418  0.3588528  0.3462015  0.3135687  0.2287778
 [7]  0.1920207  0.1831763  0.0811108 -0.2172652

Largest  eigenvalues:
 [1] 99549113 95426060 89884784 85003268 84960071 82663530 82247757 80477534
 [9] 79335161 77402876

Smallest eigenvalues:
 [1]  0.37946752  0.37172274  0.31859915  0.27792094  0.27648965  0.26314745
 [7]  0.22205832  0.20741180 -0.02925941 -0.40423012

Largest  eigenvalues:
 [1] 100137334  97114814  90566136  86209824  86206208  84474293  83032546
 [8]  81685085  80145636  78575101

Smallest eigenvalues:
 [1]  0.214524849  0.209667174  0.154280963  0.137810455  0.126889796
 [6]  0.107633910  0.073928279  0.008884107 -0.154450990 -0.349349998

Largest  eigenvalues:
 [1] 99982408 95964374 89634490 85792525 85505828 83198698 82695617 80759804
 [9] 79581141 77699081

Smallest eigenvalues:
 [1]  0.29444729  0.26323111  0.23640645  0.22904055  0.18474092  0.15958907
 [7]  0.12228186  0.08612822 -0.23710986 -1.27384046

Largest  eigenvalues:
 [1] 98574313 97959636 91766096 88034147 84859206 84820948 84115404 81701433
 [9] 81218354 78487362

Smallest eigenvalues:
 [1]  0.4599506  0.4514126  0.4463866  0.4001985  0.3389677  0.3248367
 [7]  0.2274095  0.2262217  0.1965150 -0.1191005

Largest  eigenvalues:
 [1] 99334340 96629775 90242238 86515861 84830660 84056419 82641022 81329606
 [9] 79727904 77942348

Smallest eigenvalues:
 [1]  0.335924592  0.335065124  0.331494287  0.300316411  0.286209628
 [6]  0.276442072  0.006766482 -0.113275006 -0.152435429 -0.286789171

Largest  eigenvalues:
 [1] 101934834  96627139  90833858  86591782  85598163  83655458  82586700
 [8]  81064613  79870608  78119439

Smallest eigenvalues:
 [1]  0.32574374  0.32171409  0.30992380  0.25755374  0.24781882  0.23511191
 [7]  0.16005718  0.10275583 -0.03278057 -0.46249065

Largest  eigenvalues:
 [1] 101253008  96048572  90207021  86047744  85693611  84012591  82760519
 [8]  81690900  80169985  78984582

Smallest eigenvalues:
 [1]  0.4857009  0.4110675  0.3825500  0.3383431  0.2787793  0.2636261
 [7]  0.2452745  0.2054012 -0.1736380 -0.2938922

Largest  eigenvalues:
 [1] 99952339 97156374 90424184 87169041 85341461 84011819 83531924 81440231
 [9] 80210364 78227056

Smallest eigenvalues:
 [1]  0.42333337  0.29813212  0.29264586  0.27994932  0.21052209  0.18326102
 [7]  0.07881272  0.06673573 -0.07370267 -0.56037379

Largest  eigenvalues:
 [1] 99683874 96794020 90449190 86826819 85128844 83493661 83138906 80801915
 [9] 80047548 77440253

Smallest eigenvalues:
 [1]  0.47905799  0.46046822  0.42756646  0.32161236  0.26047172  0.15406170
 [7]  0.10397924  0.06858076 -0.10662799 -0.22108296

Largest  eigenvalues:
 [1] 98685068 96318846 89678597 86211585 85078920 83609171 82250553 80791929
 [9] 79238734 77639610

Smallest eigenvalues:
 [1] -0.03590173 -0.11457988 -0.23278926 -0.24937634 -0.26483858 -0.27397646
 [7] -0.33962305 -0.38154724 -0.51329823 -0.76300245

Largest  eigenvalues:
 [1] 97631881 96622744 89425155 85612966 85486524 83806217 83126574 81357396
 [9] 79405689 77832771

Smallest eigenvalues:
 [1]  0.4533305  0.4297536  0.4201626  0.3814635  0.2831721  0.2826120
 [7]  0.2443980  0.1396527 -0.1626018 -0.4293091

Largest  eigenvalues:
 [1] 100237093  96056232  90073703  86067952  85752373  83646035  82658894
 [8]  81178187  79490601  77890454

Smallest eigenvalues:
 [1]  0.28916751  0.27512700  0.26575476  0.23124121 -0.02715027 -0.08137438
 [7] -0.08515129 -0.12878559 -0.26455862 -0.61549841

Largest  eigenvalues:
 [1] 100382808  97518847  90838070  87012495  86697504  85272715  83522276
 [8]  82385801  80255137  79051281

Smallest eigenvalues:
 [1]  0.33100635  0.29530680  0.29513579  0.26185482  0.25711152  0.19401975
 [7]  0.12769166  0.11880813  0.02088322 -0.32586642

Largest  eigenvalues:
 [1] 100040960  96583417  90487916  86355342  85186330  84961869  82826427
 [8]  81949653  80508212  79029515

Smallest eigenvalues:
 [1]  0.30526755  0.28313257  0.24632652  0.20657573  0.18327488  0.15211597
 [7]  0.06874121 -0.05516681 -0.14165578 -0.42727101

Largest  eigenvalues:
 [1] 98830094 96119589 89581998 86717612 83978205 83321860 82855384 80422625
 [9] 79891379 76917442

Smallest eigenvalues:
 [1]  0.26525632  0.22470979  0.19688889  0.17806636  0.10733989  0.08158045
 [7]  0.05977386 -0.02077177 -0.34689190 -0.39992598

Largest  eigenvalues:
 [1] 100048790  97349755  91100888  86769919  85708245  83976975  83652349
 [8]  81225002  80664457  77856030

Smallest eigenvalues:
 [1]  0.36910747  0.36412448  0.31408484  0.27878684  0.21115075  0.13463200
 [7]  0.12378193  0.07704030  0.01208162 -0.53785989

Largest  eigenvalues:
 [1] 99430598 96340614 90137236 86626746 84356942 82944329 82812844 80061215
 [9] 79597498 76825666

Smallest eigenvalues:
 [1]  0.37050021  0.34258409  0.33784094  0.32122007  0.25750004  0.23923273
 [7]  0.23502325  0.17198663 -0.05557334 -0.06063662

Largest  eigenvalues:
 [1] 98513256 96600482 89694569 86386383 84998999 84155038 82577246 81532620
 [9] 79800589 78546112

Smallest eigenvalues:
 [1]  0.45282561  0.41421463  0.30710189  0.30136572  0.29551314  0.18750389
 [7]  0.16591856  0.10110126  0.03084501 -0.25978644

Largest  eigenvalues:
 [1] 98925115 97032644 90724672 87328993 84756524 84604864 83602966 82223380
 [9] 80881434 79027953

Smallest eigenvalues:
 [1]  0.44385771  0.41353578  0.35820682  0.35222261  0.32569639  0.30147233
 [7]  0.26474657  0.26010906  0.09172766 -0.15328164

Largest  eigenvalues:
 [1] 99137807 97045167 90100732 86971108 84859528 83998254 82629475 81163659
 [9] 79948977 78216298

Smallest eigenvalues:
 [1]  0.308794766  0.307812530  0.256323747  0.219629923  0.214666521
 [6]  0.195143492  0.048318529  0.001454203 -0.002153526 -0.027453624

Largest  eigenvalues:
 [1] 99448259 97144021 90523897 86416046 85507958 84812399 83284488 81958704
 [9] 80365638 78563121

Smallest eigenvalues:
 [1]  0.3535440  0.3452995  0.3429877  0.3392241  0.3378901  0.2754374
 [7]  0.2489767  0.2108280  0.1211729 -0.1334780

Largest  eigenvalues:
 [1] 100588000  96598302  90336237  85818727  85654072  84222431  82500906
 [8]  81417949  79816854  78343092

Smallest eigenvalues:
 [1]  0.33931675  0.33519505  0.28395574  0.27051586  0.18284945  0.08224592
 [7]  0.06686479 -0.03790621 -0.26468082 -0.29959123

Largest  eigenvalues:
 [1] 99339225 95241356 89687057 85114818 85015087 83009507 82335006 80692608
 [9] 79247637 77683059

Smallest eigenvalues:
 [1]  0.37020018  0.33712496  0.32751211  0.24210929  0.21230647  0.09959205
 [7]  0.05482187 -0.26992859 -0.50441247 -0.71550576

Largest  eigenvalues:
 [1] 102154921  96191347  90776653  87214824  85402737  84168524  82539854
 [8]  81248851  80008383  78552512

Smallest eigenvalues:
 [1]  0.44297332  0.39596349  0.38209998  0.34205767  0.32397433  0.22301753
 [7]  0.01304074 -0.01600393 -0.01612155 -0.04727207

Largest  eigenvalues:
 [1] 101904204  96239462  90106460  86658129  86620686  84256124  82737000
 [8]  81563019  80119000  78517832

Smallest eigenvalues:
 [1]  0.4074380  0.3984621  0.2965099  0.2587612  0.2450089  0.1818042
 [7]  0.1623147  0.1331376 -0.1806240 -0.2465380

Largest  eigenvalues:
 [1] 101471223  96946978  90962823  86335969  86304951  83915367  83464833
 [8]  81789074  80429631  78632441

Smallest eigenvalues:
 [1]  0.41594618  0.40292830  0.39912891  0.35642104  0.34214715  0.27730808
 [7]  0.25263374  0.16892183  0.10103507 -0.02928523

Largest  eigenvalues:
 [1] 100132834  96970782  90193581  86602022  86025884  84607407  82566458
 [8]  81527585  79938777  78308097

Smallest eigenvalues:
 [1]  0.45741268  0.42523873  0.41780677  0.37227785  0.29100024  0.25260691
 [7]  0.19008345  0.14551790  0.04884313 -0.25648368

Largest  eigenvalues:
 [1] 101665818  96741537  91246745  86441670  86292573  84964711  83248846
 [8]  82298896  80739273  79161245

Smallest eigenvalues:
 [1]  0.378598402  0.361240460  0.300501811  0.290002184  0.270561871
 [6]  0.234869258  0.106716611 -0.008069957 -0.256619834 -0.468712989

Largest  eigenvalues:
 [1] 99525641 96799276 91042909 86543519 84891544 83613183 83113246 81069936
 [9] 80032432 78016522

Smallest eigenvalues:
 [1]  0.41169138  0.33717606  0.30021891  0.28790297  0.28380580  0.28221251
 [7]  0.21823274  0.15755762 -0.01927377 -0.04683377

Largest  eigenvalues:
 [1] 99167728 95996643 89655738 85828946 84356177 84115270 82108036 81428352
 [9] 79336643 78213326

Smallest eigenvalues:
 [1]  0.4087712  0.3682560  0.3178610  0.2716648  0.1769101  0.1692591
 [7] -0.1062793 -0.1347701 -0.3127829 -0.3326485

Largest  eigenvalues:
 [1] 100302481  95818034  90270789  86059077  84819437  83034242  82792789
 [8]  80565589  79768763  77293530

Smallest eigenvalues:
 [1]  0.32943264  0.30553848  0.29684109  0.25534367  0.22507157  0.13589005
 [7] -0.01301935 -0.08712144 -0.20448882 -0.24821395

Largest  eigenvalues:
 [1] 100534488  95979779  89829568  85838925  85631711  83842355  83079140
 [8]  81561566  79712801  78424088

Smallest eigenvalues:
 [1]  0.3530961  0.3253809  0.2736174  0.2409434  0.2360708  0.1660788
 [7]  0.1338282 -0.0333838 -0.1430207 -0.5858916

Largest  eigenvalues:
 [1] 100512593  95892927  89919173  86179336  85747566  83637314  82509235
 [8]  81253531  79476638  78034720

Smallest eigenvalues:
 [1]  0.3864776  0.3706377  0.3139742  0.3008183  0.2355772  0.2217630
 [7]  0.1893592  0.1630022  0.1159066 -0.2718316

Largest  eigenvalues:
 [1] 99693227 97502175 91801509 86956927 85445489 84933143 83436753 82311668
 [9] 80316033 79340757

Smallest eigenvalues:
 [1]  0.38374686  0.33831406  0.32297664  0.30275801  0.27410673  0.26178423
 [7]  0.18602216  0.01032676 -0.04964811 -0.16237160

Largest  eigenvalues:
 [1] 99323475 97425391 90989949 86871741 85423995 85222654 83314660 82294763
 [9] 80552144 79447805

Smallest eigenvalues:
 [1]  0.41387061  0.39088158  0.38532791  0.34992032  0.34016442  0.30571860
 [7]  0.28110070  0.22171181 -0.03541281 -0.86860895

Largest  eigenvalues:
 [1] 101301235  95923502  89978253  85524046  85449237  83678039  82683271
 [8]  81384965  79755647  78212598

Smallest eigenvalues:
 [1]  0.39241626  0.38615728  0.29179294  0.28278681  0.26761982  0.24147663
 [7]  0.14352167 -0.06275526 -0.11670627 -0.27009033

Largest  eigenvalues:
 [1] 99919744 97568305 90528271 87518107 86104294 84404360 83460198 81392131
 [9] 80773193 78470696

Smallest eigenvalues:
 [1]  0.38719490  0.38128697  0.37137300  0.29253625  0.23260258  0.19386983
 [7]  0.09723603  0.09028213 -0.20608594 -0.38754870

Largest  eigenvalues:
 [1] 101573675  97265975  91094229  86727869  86505302  84110706  83176442
 [8]  81433427  80312861  78373686

Smallest eigenvalues:
 [1]  0.36979053  0.36037104  0.35282089  0.30986048  0.29735694  0.18659920
 [7]  0.13799608  0.07989385 -0.21270289 -0.25359430

Largest  eigenvalues:
 [1] 99099338 96400206 90615684 86235203 85138808 84257163 83801906 81801626
 [9] 80550008 78467057

Smallest eigenvalues:
 [1]  0.36067447  0.33037590  0.32519103  0.28914632  0.27926988  0.25833699
 [7]  0.20620909  0.17348839  0.04308379 -0.08857343

Largest  eigenvalues:
 [1] 100109333  95779059  89793253  85959638  84429492  82324295  82113748
 [8]  79702619  79228068  76713738

Smallest eigenvalues:
 [1]  0.42304311  0.36042991  0.31271548  0.28791304  0.27684811  0.23723371
 [7]  0.21796849  0.07120660 -0.02237187 -0.63493388

Largest  eigenvalues:
 [1] 101722966  95994150  90287994  85947993  85251462  82820882  82309043
 [8]  80531250  79701594  77492205

Smallest eigenvalues:
 [1]  0.35159164  0.27469262  0.26731641  0.22975085  0.20200425  0.14574051
 [7]  0.10283339  0.03553057 -0.24223512 -0.29002538

Largest  eigenvalues:
 [1] 100104393  96679358  91377399  86677848  84295123  83974915  83402248
 [8]  81853921  80533243  78568519

Smallest eigenvalues:
 [1]  0.24541885  0.22921133  0.20942235  0.17306889  0.14471083  0.13181056
 [7]  0.12840794  0.06594180 -0.05268891 -0.13857291

Largest  eigenvalues:
 [1] 98347628 97715285 91119325 86792860 84982724 84058554 83806782 81522682
 [9] 80656158 78422707

Smallest eigenvalues:
 [1]  0.45043161  0.42815873  0.41127570  0.40312496  0.29111002  0.28456549
 [7]  0.16291775  0.12988396  0.07920708 -0.11304293

Largest  eigenvalues:
 [1] 98659812 97220020 90334387 87374829 84993913 84300274 83322906 81471387
 [9] 80318216 78307722

Smallest eigenvalues:
 [1]  0.414645561  0.405161356  0.391337232  0.309882720  0.281418801
 [6]  0.257629127  0.212674421 -0.009580257 -0.256228673 -0.269336426

Largest  eigenvalues:
 [1] 100545573  95690410  89410685  85947519  85509873  83344931  82584344
 [8]  80697921  79513686  77545403

Smallest eigenvalues:
 [1]  0.23581934  0.22796968  0.18294131  0.15828560  0.10241977  0.09736069
 [7]  0.04861629 -0.09036118 -0.10028776 -0.27017882

Largest  eigenvalues:
 [1] 97964961 97854617 91594218 86985569 84233435 84017202 83848501 81545500
 [9] 80785376 78225536

Smallest eigenvalues:
 [1]  0.40792442  0.40063651  0.34636946  0.30914291  0.26640944  0.26014813
 [7]  0.23482755  0.12047004 -0.04598855 -0.63290009

Largest  eigenvalues:
 [1] 100284057  97428356  91057740  86985165  86358178  84598565  83457028
 [8]  82094778  80498048  78984909

Smallest eigenvalues:
 [1]  0.360022975  0.350879660  0.331159082  0.306940003  0.167590046
 [6]  0.085092829  0.079089555  0.001253826 -0.138100988 -0.561401944

Largest  eigenvalues:
 [1] 99609677 97043304 90422612 87030629 85620908 83565551 83379717 80870558
 [9] 80119930 77504901

Smallest eigenvalues:
 [1]  0.3415913  0.3309569  0.3149134  0.2865829  0.2631073  0.2591825
 [7]  0.2083322 -0.1622128 -0.3029000 -0.5120033

Largest  eigenvalues:
 [1] 101076244  95846751  90372576  85468963  84829325  82587223  82310554
 [8]  80219609  79759623  77312261

Smallest eigenvalues:
 [1]  0.38710124  0.37010100  0.34765493  0.34716105  0.30501143  0.30040755
 [7]  0.17430119  0.07250678  0.02114434 -0.09409915

Largest  eigenvalues:
 [1] 101359247  96037799  90037897  85930293  85687172  83360660  82131275
 [8]  80823348  79752626  77730805

Smallest eigenvalues:
 [1]  0.36442324  0.26062399  0.24861432  0.24711362  0.21461070  0.18237713
 [7]  0.05285535 -0.38625953 -0.41595973 -0.49799320

Largest  eigenvalues:
 [1] 101146649  96782490  90859991  86105633  85955891  83720021  83004798
 [8]  81245029  80077986  78112681

Smallest eigenvalues:
 [1]  0.34406127  0.30603621  0.26345613  0.19493754  0.14651040  0.13084890
 [7] -0.03040242 -0.19287732 -0.40788037 -1.27105975

Largest  eigenvalues:
 [1] 99697647 97567490 91272965 86752775 86499952 84078647 83478288 81520268
 [9] 80449796 78311124

Smallest eigenvalues:
 [1]  0.28593112  0.26158130  0.25038029  0.23835768  0.21921678  0.17174015
 [7]  0.12009712  0.03804566 -0.31729980 -0.45209937

Largest  eigenvalues:
 [1] 99766203 96952479 90618998 86609463 85153245 83474773 83258585 81043328
 [9] 79926760 77841713

Smallest eigenvalues:
 [1]  0.31854883  0.31559296  0.29078055  0.25868532  0.22862717  0.15863644
 [7]  0.06076703 -0.12953862 -0.30356301 -0.33887356

Largest  eigenvalues:
 [1] 100667652  96504714  90790332  86454895  85798432  84038749  83748470
 [8]  81969629  80169274  78579118

Smallest eigenvalues:
 [1]  0.329206836  0.295314581  0.285474527  0.219552353  0.192551997
 [6]  0.164640646  0.155556805 -0.003948534 -0.029137318 -0.625787271

Largest  eigenvalues:
 [1] 98208591 96365324 90324737 85859108 84797160 84098703 82625706 81459100
 [9] 79575894 78379991

Smallest eigenvalues:
 [1]  0.35921361  0.33405873  0.32220054  0.31447523  0.30925022  0.26963646
 [7]  0.26081412 -0.04587507 -0.07890507 -0.36534894

Largest  eigenvalues:
 [1] 99920911 97105968 90748278 86550439 86221569 84040569 83631416 81672739
 [9] 80131570 78224111

Smallest eigenvalues:
 [1]  0.44059449  0.40085540  0.36749858  0.36224092  0.33859151  0.23099110
 [7]  0.10010755 -0.09364577 -0.41785746 -0.55836732

Largest  eigenvalues:
 [1] 101858683  96287530  90733113  87195431  86281906  84163096  83209403
 [8]  81761802  80287065  78603641

Smallest eigenvalues:
 [1]  0.387240987  0.385768354  0.262362390  0.262190307  0.218876142
 [6]  0.121571188  0.094767420  0.008501898 -0.104583847 -0.285813405

Largest  eigenvalues:
 [1] 100712525  95132380  88761982  85378495  85370680  82960006  82109194
 [8]  80440187  78998839  77268080

Smallest eigenvalues:
 [1]  0.26912992  0.26069417  0.25444648  0.23181594  0.05138118  0.03159496
 [7]  0.00938838 -0.29604102 -0.30825268 -0.36712438

Largest  eigenvalues:
 [1] 100658703  96273749  90304140  86404238  85518271  83998323  83044597
 [8]  81457908  79972726  78372514

Smallest eigenvalues:
 [1]  0.32407416  0.32114539  0.27748895  0.20810011  0.20258967  0.15805709
 [7]  0.06696131 -0.29603293 -0.39726876 -0.40579943

Largest  eigenvalues:
 [1] 102414373  96866761  91030424  86737956  86241733  83311155  83111241
 [8]  81099157  80055928  78039565

Smallest eigenvalues:
 [1]  0.3333415  0.3307614  0.2679452  0.2353896  0.2278405  0.1887978
 [7]  0.1863526  0.1000907 -0.1084047 -0.3222269

Largest  eigenvalues:
 [1] 98916897 98272143 91085356 87671540 85458981 84930253 84063181 82249181
 [9] 80542929 78842452

Smallest eigenvalues:
 [1]  0.3252432  0.3236702  0.2587936  0.2570901  0.2138200  0.1898233
 [7]  0.1823028 -0.1941736 -0.5080307 -0.5878257

Largest  eigenvalues:
 [1] 100534729  96270286  90312455  86447931  85916946  83876272  82927739
 [8]  81415808  79810049  78194514

Smallest eigenvalues:
 [1]  0.33978195  0.32450688  0.32304182  0.30291759  0.26746959  0.22356956
 [7]  0.19171474  0.06420481 -0.09361734 -0.40027207

Largest  eigenvalues:
 [1] 98945519 96535586 90251214 86846749 83963327 83509976 82363560 79988630
 [9] 79744645 76677797

Smallest eigenvalues:
 [1]  0.45524621  0.37080956  0.34075105  0.30435148  0.30271412  0.23148284
 [7]  0.20631440  0.10943952 -0.06066836 -0.33361190

Largest  eigenvalues:
 [1] 100989164  97190809  91151960  86878468  86686303  85313047  83146892
 [8]  82387827  80567068  79197596

Smallest eigenvalues:
 [1]  0.3892958  0.3470475  0.3399532  0.3319880  0.2516991  0.2427675
 [7]  0.2335483  0.1406213 -0.1165941 -0.4440134

Largest  eigenvalues:
 [1] 100304475  96621454  90436083  86267121  84252811  83359025  82988258
 [8]  80567454  80171649  77548091

Smallest eigenvalues:
 [1]  0.269288253  0.250293868  0.220366559  0.196425584  0.178630889
 [6]  0.062653629 -0.005917483 -0.203564171 -0.355100577 -0.646384177

Largest  eigenvalues:
 [1] 99015534 96684774 90474022 86083428 85458611 83101851 82657322 80460969
 [9] 79591096 77254873

Smallest eigenvalues:
 [1]  0.36290943  0.34703396  0.33644038  0.33398851  0.29401877  0.27648343
 [7]  0.17385559  0.10716651  0.04718870 -0.04219012

Largest  eigenvalues:
 [1] 100962054  96221876  90325982  85848614  85510701  83740432  82137177
 [8]  80795176  79751739  77817228

Smallest eigenvalues:
 [1]  0.37829220  0.35311905  0.33909192  0.31716540  0.30581494  0.25547262
 [7]  0.15061953 -0.01193091 -0.09586587 -0.29030324

Largest  eigenvalues:
 [1] 100002542  95813457  89908710  85616428  84842557  82955173  82268649
 [8]  80359788  79633119  77446573

Smallest eigenvalues:
 [1]  0.47754787  0.43981971  0.37899259  0.33518024  0.31973254  0.31118224
 [7]  0.21432213  0.19998290  0.08201302 -0.03258115

Largest  eigenvalues:
 [1] 99440940 97895066 91436862 87745685 85154047 84298587 83359671 81226742
 [9] 80817557 78268165

Smallest eigenvalues:
 [1]  0.27101616  0.25588935  0.19517155  0.15755007  0.14420408  0.11234196
 [7]  0.09332968 -0.05251366 -0.22909777 -0.41137410

Largest  eigenvalues:
 [1] 98308238 97132015 90012293 86531408 85850984 84161356 83048449 81068236
 [9] 79892954 77995240

Smallest eigenvalues:
 [1]  0.25891842  0.20286471  0.17648655  0.08692107  0.07540490  0.07400722
 [7]  0.04513013  0.03796385 -0.19277212 -0.82219494

Largest  eigenvalues:
 [1] 98395293 95491996 89541130 85747771 83885151 82472547 81754538 79630633
 [9] 78855486 76777922

Smallest eigenvalues:
 [1]  0.265034117  0.263216770  0.200060769  0.144824518  0.135951402
 [6]  0.094062813  0.002719668 -0.089333358 -0.128194444 -0.378709045

Largest  eigenvalues:
 [1] 100802974  96898953  89779128  86965323  86297769  83536123  83378850
 [8]  80990625  80249987  77933634

Smallest eigenvalues:
 [1]  0.44423223  0.43057468  0.41141786  0.32293411  0.32022882  0.30047708
 [7]  0.07015480 -0.02047790 -0.07635961 -0.11637907

Largest  eigenvalues:
 [1] 99719997 96606527 90319375 86291306 85699906 83641316 83518529 81218185
 [9] 80007646 78114742

Smallest eigenvalues:
 [1]  0.30648148  0.30177833  0.28353165  0.26055169  0.19746398  0.12267941
 [7]  0.09542178  0.08065466  0.05374874 -0.06527863

Largest  eigenvalues:
 [1] 98588148 96346058 90370063 85724436 84300938 83214285 82635419 80551794
 [9] 79680096 77495749

Smallest eigenvalues:
 [1]  0.46611392  0.42809735  0.38164417  0.37014454  0.32838964  0.28033429
 [7]  0.17073663  0.07292024 -0.09220727 -0.23463554

Largest  eigenvalues:
 [1] 101294813  96030655  90574643  86036519  84917832  83871287  82887272
 [8]  81548618  80122583  78511230

Smallest eigenvalues:
 [1]  0.14164692  0.13048144  0.12009368  0.11884011  0.05088143 -0.03386325
 [7] -0.06549473 -0.49987929 -0.58595928 -0.98003778

Largest  eigenvalues:
 [1] 99174427 96849984 90964309 87009184 85277483 84101003 83063713 80734758
 [9] 80186701 77339438

Smallest eigenvalues:
 [1]  0.35522881  0.33391898  0.29018010  0.22665490  0.22489750  0.19816241
 [7]  0.15149107  0.06507401  0.01013361 -0.10566087

Largest  eigenvalues:
 [1] 97200604 95901273 89607947 85539639 83936670 83484729 82416416 80698852
 [9] 79293464 77501731

Smallest eigenvalues:
 [1]  0.51736894  0.43903965  0.37079657  0.36382610  0.36316506  0.33474014
 [7]  0.19095110  0.09643754  0.06758517 -0.18097689

Largest  eigenvalues:
 [1] 100936465  97124387  90753727  86737058  86442390  84014544  83472842
 [8]  81521887  80311551  78597793

Smallest eigenvalues:
 [1]  0.318307310  0.301670750  0.278214607  0.269367713  0.174941153
 [6]  0.169132420  0.033620267  0.006543355 -0.006508230 -0.055428566

Largest  eigenvalues:
 [1] 100244369  97214126  90199603  87074347  85975058  83849172  83054874
 [8]  80901051  80337398  78221677

Smallest eigenvalues:
 [1]  0.32679061  0.30489287  0.30441204  0.24104726  0.22965224  0.18448882
 [7]  0.18358250  0.16968781 -0.06203376 -0.82547669

Largest  eigenvalues:
 [1] 103665366  97141944  91610786  87576172  86630814  84820978  83185698
 [8]  82510992  80823785  79767710

Smallest eigenvalues:
 [1]  0.38101368  0.36948409  0.28139799  0.27135121  0.24256993  0.14743772
 [7]  0.10809945 -0.01741811 -0.50122570 -0.61658680

Largest  eigenvalues:
 [1] 100888608  96120543  90450930  86333026  85707894  83322707  82858889
 [8]  80856460  79919502  77616693

Smallest eigenvalues:
 [1]  0.21387365  0.18062358  0.17254018  0.15777111  0.12167394 -0.09450063
 [7] -0.17962922 -0.22851672 -0.27521279 -0.55376973

Largest  eigenvalues:
 [1] 100763222  96275385  90546819  86250284  84847821  83707330  83397208
 [8]  81611896  80042645  78293932

Smallest eigenvalues:
 [1]  0.2769779693  0.2749239376  0.2419440858  0.2331986929  0.2137693792
 [6]  0.1503627679  0.0621359785 -0.0002230965 -0.0205912358 -0.1211693698

Largest  eigenvalues:
 [1] 98918204 96958873 90387079 87079185 84074003 83653882 83320904 80522168
 [9] 80219359 77195632

Smallest eigenvalues:
 [1]  0.15289437  0.14447446  0.10667951  0.09756873  0.06910796  0.02391637
 [7] -0.08199393 -0.13848079 -0.97552196 -1.16078334

Largest  eigenvalues:
 [1] 100946034  98203215  91632302  87502976  86311216  84351735  83885678
 [8]  82017208  81008746  78868439

Smallest eigenvalues:
 [1]  0.42175493  0.41310529  0.35287356  0.33863731  0.27437949  0.21571342
 [7]  0.18168980  0.16464877  0.02214248 -0.31607842

Largest  eigenvalues:
 [1] 97726547 95821281 89436304 85873586 84010214 82824036 82060915 80087201
 [9] 79240600 77205563

Smallest eigenvalues:
 [1]  0.45530619  0.40657997  0.40343068  0.35507777  0.27414260  0.26171305
 [7]  0.23582644  0.12773550  0.07895893 -0.02662757

Largest  eigenvalues:
 [1] 99501572 96108529 89886463 86232160 84735244 83089361 82524225 80357233
 [9] 79486635 77412799

Smallest eigenvalues:
 [1]  0.37546576  0.36217346  0.33612685  0.27188506  0.25536395  0.22506505
 [7]  0.07722396  0.06542981 -0.03454740 -0.38038333

Largest  eigenvalues:
 [1] 101888207  96687900  90557291  86534274  86087605  84249645  82657748
 [8]  81489801  80241120  78657434

Smallest eigenvalues:
 [1]  0.3829663  0.3576730  0.3179348  0.2904865  0.2726574  0.1814798
 [7]  0.1340488  0.1246567  0.1002205 -0.7081133

Largest  eigenvalues:
 [1] 100781688  96162057  90305828  86307933  85730517  84313254  82584914
 [8]  81579365  80155495  78392114

Smallest eigenvalues:
 [1]  0.25720185  0.18441927  0.18036709  0.16851042  0.16516973  0.10176839
 [7] -0.01023039 -0.03232582 -0.21278562 -0.70305152

Largest  eigenvalues:
 [1] 99682244 97225307 90212783 87040243 86139362 84252145 83938661 81806961
 [9] 80311342 78343625

Smallest eigenvalues:
 [1]  0.4427047  0.4049815  0.3925852  0.3780030  0.3215626  0.3124073
 [7]  0.2027723  0.1571198  0.1049125 -0.3180428

Largest  eigenvalues:
 [1] 100183480  96962421  90331201  86332950  86245620  84384667  82499721
 [8]  81396873  79970492  78628466

Smallest eigenvalues:
 [1]  0.3428997  0.3125843  0.2793097  0.1889007  0.1762229  0.1567958
 [7]  0.1406190 -0.1067381 -0.5360240 -1.2386752

Largest  eigenvalues:
 [1] 101439994  99196613  92461994  88214410  87205290  85133520  84912125
 [8]  82482582  81685771  79730755

Smallest eigenvalues:
 [1]  0.22330734  0.15532996  0.12645531  0.11513909  0.11454979  0.09818996
 [7]  0.07608425 -0.24173806 -0.29513137 -0.39955572

Largest  eigenvalues:
 [1] 100981529  97675053  90907080  86988525  86401914  84981329  83076282
 [8]  82100043  80425333  79342156

Smallest eigenvalues:
 [1]  0.375467012  0.314186094  0.298370076  0.243743570  0.227951687
 [6]  0.221269875  0.152860590  0.001978762 -0.087691693 -0.205439193

Largest  eigenvalues:
 [1] 98822775 96789331 90454575 86732671 84462378 84026242 83007030 80811443
 [9] 80352580 77642301

Smallest eigenvalues:
 [1]  0.34395981  0.32282129  0.31898461  0.30593223  0.19170489  0.15521998
 [7]  0.15206199  0.07796181  0.02909169 -0.09118520

Largest  eigenvalues:
 [1] 100431246  96485226  90277635  86816354  84523858  83869449  83298993
 [8]  80820301  80313929  77669780

Smallest eigenvalues:
 [1]  0.31570595  0.31261599  0.27705103  0.24795505  0.24509980  0.21083553
 [7]  0.09374186  0.08078667 -0.03057652 -0.37628683

Largest  eigenvalues:
 [1] 98315310 96914895 90686815 86727557 83795096 83667986 83330736 81420720
 [9] 80220792 78280765

Smallest eigenvalues:
 [1]  0.42315833  0.41228060  0.33859392  0.32698765  0.31095940  0.21625435
 [7]  0.18027965  0.07734574  0.07627199 -0.27090047

Largest  eigenvalues:
 [1] 98310324 96337950 89568266 85889820 84968454 82737517 82137430 79741747
 [9] 79385288 76757215

Smallest eigenvalues:
 [1]  0.32874101  0.32329138  0.28301205  0.25990655  0.20710777  0.07916048
 [7]  0.05360883  0.03074685 -0.12304220 -0.39724004

Largest  eigenvalues:
 [1] 101742329  96161868  90214280  86082323  85946858  84139315  82504125
 [8]  81524842  79737845  78334147

Smallest eigenvalues:
 [1]  0.33902812  0.25588174  0.17073009  0.09768705  0.08358784  0.07925768
 [7]  0.04610301 -0.02036309 -0.06923355 -0.52023621

Largest  eigenvalues:
 [1] 99377946 96227507 89932661 85832248 85750447 83340534 82723554 80388273
 [9] 79592430 77126032

Smallest eigenvalues:
 [1]  0.37370135  0.35292936  0.34376954  0.32726138  0.32332720  0.20673636
 [7]  0.15508779 -0.01555319 -0.08432910 -0.24511262

Largest  eigenvalues:
 [1] 101660122  96579303  90659656  86381006  85903692  83663435  82505088
 [8]  80963760  79759318  78122160

Smallest eigenvalues:
 [1]  0.40698124  0.39746455  0.39392774  0.38482903  0.34322729  0.30728987
 [7]  0.23443709  0.17958136  0.12850855 -0.02104188

Largest  eigenvalues:
 [1] 100893912  95701430  89691623  85403276  84983109  83930661  81967629
 [8]  81253545  79286682  78109945

Smallest eigenvalues:
 [1]  0.28058589  0.27557005  0.26785546  0.16717104  0.14404553  0.13562624
 [7]  0.04387775 -0.16510617 -0.22027758 -0.23868236

Largest  eigenvalues:
 [1] 100833855  95686900  89407919  85637824  85183376  83578922  81894249
 [8]  80601992  79355152  77321316

Smallest eigenvalues:
 [1]  0.30856184  0.29498890  0.24870723  0.22521840  0.17845647  0.13930659
 [7]  0.13073043  0.11074970  0.04135221 -0.58631023

Largest  eigenvalues:
 [1] 98925226 97225131 90958200 86527590 85330656 83819258 83430344 81500425
 [9] 80064969 78455089

Smallest eigenvalues:
 [1]  0.435408496  0.426051207  0.370830420  0.365491524  0.363332338
 [6]  0.325505455  0.289726870  0.120512469  0.009152599 -0.016328755

Largest  eigenvalues:
 [1] 101491481  97786222  91109919  87077604  86258623  84899958  83224649
 [8]  81984571  80559872  79213474

Smallest eigenvalues:
 [1]  0.26949642  0.25064022  0.23805653  0.22387735  0.17247543  0.11357622
 [7]  0.06407078  0.03800658 -0.14528434 -0.50267908

Largest  eigenvalues:
 [1] 98579488 97288599 90601787 86566712 85395685 84207791 83360711 81621257
 [9] 79990749 78148388

Smallest eigenvalues:
 [1]  0.24630152  0.21286801  0.19139528  0.12797883  0.10520245  0.07003822
 [7]  0.06932143  0.05127862 -0.20322455 -0.45219757

Largest  eigenvalues:
 [1] 99788504 96781095 90323029 86288802 85447151 83499151 83054511 80790721
 [9] 79825934 77999628

Smallest eigenvalues:
 [1]  0.28233847  0.27332421  0.24255549  0.19223129  0.17509779  0.16892407
 [7]  0.13634097 -0.04575108 -0.07619969 -0.62832893

Largest  eigenvalues:
 [1] 102070975  96958974  91032466  86551815  85698721  84401152  82687724
 [8]  81811097  80251122  78846673

Smallest eigenvalues:
 [1]  0.367992592  0.354952071  0.277123911  0.264630827  0.248221722
 [6]  0.216616993  0.004580147 -0.026011828 -0.032745576 -0.335493320

Largest  eigenvalues:
 [1] 99692373 95593283 89967695 85487108 85040278 83482774 82833556 81205149
 [9] 79490604 77931499

Smallest eigenvalues:
 [1]  0.4373976  0.3934819  0.3720379  0.3267914  0.2967690  0.2916497
 [7]  0.2151919  0.1217187 -0.1927631 -0.5144548

Largest  eigenvalues:
 [1] 100185529  96235469  90477765  85865236  85778839  83593597  82983255
 [8]  81200962  79617963  77829308

Smallest eigenvalues:
 [1]  0.193964713  0.173858068  0.145228973  0.108851648 -0.001530533
 [6] -0.021580024 -0.043332081 -0.116365992 -0.153404170 -0.835777802

Largest  eigenvalues:
 [1] 100802551  95578919  90012157  86001004  85697013  84074191  83009300
 [8]  82009325  79261955  78352545

Smallest eigenvalues:
 [1]  0.25350959  0.23266529  0.22954026  0.19772753  0.18457490  0.14639718
 [7]  0.13458830  0.06311683  0.05870040 -1.03453013

Largest  eigenvalues:
 [1] 97361770 96457179 89753151 86851004 84125034 83674723 82366893 79922875
 [9] 79691922 76462850

Smallest eigenvalues:
 [1]  0.49098702  0.47429287  0.41323306  0.40573073  0.26364523  0.21980028
 [7]  0.17063921  0.02151618 -0.01661733 -0.02147081

Largest  eigenvalues:
 [1] 100022185  97312183  90266161  86879663  85779451  83981762  82966927
 [8]  80922784  79861088  77645428

Smallest eigenvalues:
 [1]  0.393929726  0.379628970  0.348769947  0.298077084  0.294498408
 [6]  0.171287650  0.067825543 -0.006327819 -0.497079525 -0.977199512

Largest  eigenvalues:
 [1] 101372680  96965911  90831603  86849883  86441207  84213463  84106152
 [8]  81777948  80744674  78691573

Smallest eigenvalues:
 [1]  0.23379998  0.22478629  0.21326304  0.16991607  0.10952807  0.09163568
 [7] -0.04791301 -0.05687094 -0.08480244 -0.71676801

Largest  eigenvalues:
 [1] 99470854 96600709 91073089 86419683 84576439 83599188 83325904 81356330
 [9] 80266527 78037531

Smallest eigenvalues:
 [1]  0.35868647  0.30046439  0.28978962  0.24332217  0.23071174  0.22867006
 [7]  0.22038347  0.09394980  0.08676295 -0.35854221

Largest  eigenvalues:
 [1] 100447321  96125988  90691290  86066397  85655981  84163810  82437309
 [8]  81510642  79615706  78343649

Smallest eigenvalues:
 [1]  0.4989216  0.4526539  0.4414517  0.3820443  0.3325915  0.2464236
 [7]  0.1788345  0.1579513 -0.2706808 -0.3568685

Largest  eigenvalues:
 [1] 100442674  95887200  90404768  85704093  85393585  83179683  82575634
 [8]  80765677  79827911  77887586

Smallest eigenvalues:
 [1]  0.49987368  0.48355347  0.38170439  0.28558072  0.28056123  0.24441594
 [7]  0.23474553  0.08672474  0.02762622 -0.09416828

Largest  eigenvalues:
 [1] 100044102  96904455  90751792  86012106  85719400  84449730  83177800
 [8]  81680852  80226444  78923793

Smallest eigenvalues:
 [1]  0.26570293  0.21788362  0.19856372  0.19441752  0.18930588  0.16594464
 [7] -0.06969678 -0.16173829 -0.37795123 -0.38770709

Largest  eigenvalues:
 [1] 99540389 96801706 90545219 87039358 84644766 84020759 83837644 81644190
 [9] 80743756 78095750

Smallest eigenvalues:
 [1]  0.28533745  0.27285097  0.26439308  0.17680395  0.14750726  0.12236675
 [7]  0.12025387  0.01609772 -0.31863381 -0.46615717

Largest  eigenvalues:
 [1] 98756030 96260343 89626714 85869366 84112312 83533849 81823022 80673171
 [9] 79167506 77430289

Smallest eigenvalues:
 [1]  0.497556737  0.495172261  0.454786979  0.407647662  0.404733371
 [6]  0.351111730  0.303168744  0.295739882 -0.004874979 -0.081850305

Largest  eigenvalues:
 [1] 100001593  96811445  90443219  86781841  84871065  83371787  83088770
 [8]  80697214  80193685  77717951

Smallest eigenvalues:
 [1]  0.27024888  0.25228953  0.24906585  0.20699573  0.09297569  0.04605862
 [7]  0.02870689 -0.12258123 -0.12616889 -1.75371013

Largest  eigenvalues:
 [1] 101681597  96852039  90262326  86596967  86592030  85585003  81924257
 [8]  81640207  79715809  79079677

Smallest eigenvalues:
 [1]  0.42669423  0.37619827  0.36227879  0.35485227  0.33659022  0.31194881
 [7]  0.24630984  0.21527855  0.04338562 -0.13760546

Largest  eigenvalues:
 [1] 100209101  95784757  90113499  85595258  84192749  83019598  82347334
 [8]  80583952  79906829  77679194

Smallest eigenvalues:
 [1]  0.21364505  0.19610150  0.18307508  0.16729730  0.12284053  0.11405841
 [7]  0.05020886  0.02771747 -0.15077623 -0.40034629

Largest  eigenvalues:
 [1] 97885161 96990916 90435021 86145726 84984294 83532149 83221923 80997211
 [9] 80090705 77825558

Smallest eigenvalues:
 [1]  0.3736230  0.3374071  0.3067095  0.2522343  0.2263458  0.2020081
 [7]  0.1282889  0.1108718 -0.1697477 -0.3468982

Largest  eigenvalues:
 [1] 99792901 97049188 90499093 86578980 85587743 85201281 83368518 82706389
 [9] 80240701 79320293

Smallest eigenvalues:
 [1]  0.23983745  0.16937519  0.14493286  0.12064042  0.03046395 -0.12404895
 [7] -0.22804957 -0.26109377 -0.40687424 -0.43243059

Largest  eigenvalues:
 [1] 98663221 96184836 90206755 86439200 84275766 82709888 82577236 80233181
 [9] 79406053 76959661

Smallest eigenvalues:
 [1]  0.4451699  0.4431561  0.3947587  0.3713716  0.3136438  0.2597714
 [7]  0.2557163  0.1972763  0.1755912 -0.3928913

Largest  eigenvalues:
 [1] 100227114  96001951  90487612  85755312  84843863  83588693  82290334
 [8]  80968861  79644563  78360316

Smallest eigenvalues:
 [1]  0.410919202  0.307611160  0.299616485  0.234345693  0.189199443
 [6]  0.176813484  0.066231980 -0.006448311 -0.118182795 -0.602259108

Largest  eigenvalues:
 [1] 102053617  95728577  90355837  86643866  85137664  83299393  82201737
 [8]  81101762  79636955  78313268

Smallest eigenvalues:
 [1]  0.486125659  0.462965181  0.459883153  0.434099116  0.384306000
 [6]  0.271925116  0.214930852  0.208859088 -0.003055272 -0.078360690

Largest  eigenvalues:
 [1] 99359780 95574364 89192463 85598319 85008420 82913472 81878901 80293010
 [9] 79259568 77481033

Smallest eigenvalues:
 [1]  0.36708383  0.34148077  0.30836965  0.29042021  0.28701400  0.26216188
 [7]  0.20728511  0.15805510 -0.03650854 -0.04990305

Largest  eigenvalues:
 [1] 100905529  96010188  90135306  86022233  85319383  83609551  82578319
 [8]  81422949  79897572  78583589

Smallest eigenvalues:
 [1]  0.2676233  0.2613640  0.2535789  0.2405641  0.1499121  0.1167343
 [7] -0.1251079 -0.1319817 -0.5378806 -1.2653246

Largest  eigenvalues:
 [1] 102480994  96922635  90456361  87227572  85749218  83918850  82009016
 [8]  80981080  79575975  78067282

Smallest eigenvalues:
 [1]  0.37307124  0.36002937  0.26492682  0.25421795  0.19016202  0.17794390
 [7]  0.12851989  0.08671662 -0.12206186 -0.33635941

Largest  eigenvalues:
 [1] 101253708  96630967  90319504  86442156  86119368  84615128  82805730
 [8]  81754687  80189235  78845408

Smallest eigenvalues:
 [1]  0.19353523  0.18695231  0.18301145  0.12087163  0.05417411  0.04874524
 [7] -0.07298045 -0.22430083 -1.00062071 -1.07746785

Largest  eigenvalues:
 [1] 99220169 96459103 90764410 86440524 85109591 84000907 83141039 81651755
 [9] 80264644 78165685

Smallest eigenvalues:
 [1]  0.34473549  0.33805133  0.31608425  0.30257462  0.27864723  0.27376822
 [7]  0.26083911  0.21872766  0.15576333 -0.02846172

Largest  eigenvalues:
 [1] 99215541 96925455 90335002 86217316 85649208 83289874 83072192 80935185
 [9] 79716165 77669572

Smallest eigenvalues:
 [1]  0.422062726  0.365105044  0.361541424  0.303638691  0.259016320
 [6]  0.214095283  0.192809534  0.118222199  0.009957487 -0.163335701

Largest  eigenvalues:
 [1] 99177312 96264953 89897189 85962893 85213247 83119823 82925459 80590512
 [9] 79726333 77359286

Smallest eigenvalues:
 [1]  0.31748023  0.28010689  0.24958676  0.21534981  0.19876165  0.09469529
 [7]  0.03420157 -0.03116153 -0.15281649 -0.62831360

Largest  eigenvalues:
 [1] 101330400  96871011  90645525  86900087  86836824  84445946  83190552
 [8]  81956624  80114943  78717887

Smallest eigenvalues:
 [1]  0.42182003  0.37321893  0.36559867  0.33599278  0.33403131  0.27628590
 [7]  0.20453144  0.07251892  0.01448049 -0.08169950

Largest  eigenvalues:
 [1] 101234354  96465352  90016593  86792321  86096229  83612975  82844564
 [8]  80836623  80094273  77879991

Smallest eigenvalues:
 [1]  0.28502165  0.28159563  0.22076535  0.19000304  0.09163479  0.04482758
 [7]  0.02011410 -0.21463395 -0.36370739 -0.86907074

Largest  eigenvalues:
 [1] 98163290 96429949 90566274 85523478 84916286 83346669 82556011 80477976
 [9] 79921517 77690084

Smallest eigenvalues:
 [1]  0.413034634  0.357226641  0.333035459  0.313837245  0.257118456
 [6]  0.253594618  0.130557493  0.009496544 -0.138486543 -0.198375630

Largest  eigenvalues:
 [1] 101215833  96028439  89631163  86527916  85422348  83023537  82324586
 [8]  80534470  79481975  77594865

Smallest eigenvalues:
 [1]  0.36057929  0.32146896  0.29908777  0.26386354  0.23132451  0.19775808
 [7]  0.17241370  0.13260063  0.07459158 -0.10803125

Largest  eigenvalues:
 [1] 99376317 97184722 90442253 86784157 84800762 83849830 83444424 81289139
 [9] 80409697 78260669

Smallest eigenvalues:
 [1]  0.45093523  0.38375617  0.35825271  0.35012618  0.33568940  0.31060216
 [7]  0.29666262  0.14716025  0.12556358 -0.09481176

Largest  eigenvalues:
 [1] 101980191  96206299  90831338  85940800  85783007  85085476  82397328
 [8]  82011499  80149349  79132190

Smallest eigenvalues:
 [1]  0.3740530  0.3039464  0.2805691  0.2709624  0.2694180  0.2439939
 [7]  0.2059426  0.1340264 -0.1184669 -0.2225059

Largest  eigenvalues:
 [1] 98648677 97075359 90251792 87204225 84167032 83955898 82377871 80322949
 [9] 79992359 76953498

Smallest eigenvalues:
 [1]  0.3117263  0.3092279  0.3082531  0.2673207  0.2572633  0.2421880
 [7]  0.2332364  0.1088713 -0.2652469 -0.7921246

Largest  eigenvalues:
 [1] 100637291  97663155  91600432  87250839  84906391  84033935  83790281
 [8]  81630410  80520051  78204892

Smallest eigenvalues:
 [1]  0.3157915  0.3105208  0.3082454  0.2919145  0.2196778  0.2187327
 [7]  0.2039208  0.2018314 -0.3792878 -0.5097217

Largest  eigenvalues:
 [1] 101033333  96817430  90996261  86819957  86157753  83907712  83380270
 [8]  81360411  80435152  78555220

Smallest eigenvalues:
 [1]  0.33536689  0.31122465  0.26599466  0.26344337  0.13415317  0.07480666
 [7]  0.02879741 -0.06689987 -0.29059358 -1.27806633

Largest  eigenvalues:
 [1] 100439353  96335858  91029684  85996570  85515142  83614326  82638087
 [8]  80738874  80168594  77694829

Smallest eigenvalues:
 [1]  0.3701886  0.3474071  0.3370041  0.3316635  0.3249870  0.2999766
 [7]  0.2607384  0.1335747  0.1105421 -0.0654896

Largest  eigenvalues:
 [1] 99504253 98056766 90921346 87582338 85392336 84069003 83785429 81299277
 [9] 80504347 78085088

Smallest eigenvalues:
 [1]  0.4252150  0.3165391  0.2465866  0.2359261  0.2105595  0.1898413
 [7]  0.1357968  0.1347607 -0.1606183 -0.9055855

Largest  eigenvalues:
 [1] 98257049 96441349 90446250 86421283 84383851 83330517 83129535 80835803
 [9] 79838166 77554343

Smallest eigenvalues:
 [1]  0.367314405  0.352603458  0.308061400  0.297493166  0.163974263
 [6]  0.141354236 -0.002717346 -0.004521682 -0.248289443 -0.595272185

Largest  eigenvalues:
 [1] 100906724  95213698  89765312  85708252  85344429  82988737  82547424
 [8]  80739200  79522527  77559180

Smallest eigenvalues:
 [1]  0.393009763  0.378530213  0.324461601  0.302548215  0.241551709
 [6]  0.234259919  0.168916531  0.004956604 -0.115822843 -0.489686327

Largest  eigenvalues:
 [1] 101709030  96455109  90694697  86307157  85146624  83591293  82835652
 [8]  81225314  80108428  78107648

Smallest eigenvalues:
 [1]  0.35924798  0.32192219  0.27615622  0.24254617  0.20674056  0.20018933
 [7]  0.14136990  0.12057195 -0.07844178 -0.36648820

Largest  eigenvalues:
 [1] 101047268  97146837  91464966  86183610  85932396  83866939  83325563
 [8]  81746621  80473233  78979450

Smallest eigenvalues:
 [1]  0.41432250  0.41208545  0.38470291  0.36856348  0.28672240  0.25119610
 [7]  0.24546984  0.13816861  0.08463546 -0.06641738

Largest  eigenvalues:
 [1] 98339014 97060796 90331726 86398801 85231788 83542340 83318184 80935956
 [9] 80130436 78173536

Smallest eigenvalues:
 [1]  0.22786452  0.17739314  0.17048518  0.12784292  0.07301168 -0.01564448
 [7] -0.06232523 -0.12448032 -0.14011643 -0.52728264

Largest  eigenvalues:
 [1] 99407923 97677023 91448515 87075277 84967459 84014943 83426744 81236343
 [9] 80535389 77794700

Smallest eigenvalues:
 [1]  0.2820138228  0.2780053945  0.2638150379  0.2284649713  0.1867169368
 [6]  0.1042612267  0.0003991635 -0.0143361306 -0.1345914961 -0.6845269066

Largest  eigenvalues:
 [1] 102642127  96328627  91046735  87054249  85290591  84378978  82529313
 [8]  81812072  80362220  79259705

Smallest eigenvalues:
 [1]  0.26857557  0.25274310  0.24237258  0.19933513  0.11992270  0.08692335
 [7] -0.09039050 -0.18979159 -0.46425347 -0.53226819

Largest  eigenvalues:
 [1] 100536333  95697564  90566787  85582419  84716885  84104030  82268116
 [8]  81585512  79762008  78785993

Smallest eigenvalues:
 [1]  0.3016737  0.2956429  0.2274541  0.2234153  0.2223100  0.2106710
 [7]  0.1682070  0.1412075 -0.2994679 -0.3766576

Largest  eigenvalues:
 [1] 100094327  96835449  90255828  87078302  85315128  84641113  82775165
 [8]  81751115  80472503  79091788

Smallest eigenvalues:
 [1]  0.09782941  0.09120725  0.07632415  0.04633846 -0.01714826 -0.04149802
 [7] -0.09844518 -0.10613495 -0.26293153 -0.59201036

Largest  eigenvalues:
 [1] 98674990 96711708 90168630 85702560 85294522 84019255 82902394 81174221
 [9] 79888084 77820834

Smallest eigenvalues:
 [1]  0.25390550  0.18468622  0.15901635  0.07189273  0.03538747  0.01936834
 [7] -0.04194306 -0.08051520 -0.49222738 -0.53984591

Largest  eigenvalues:
 [1] 99175993 96649196 89925313 86253973 86101869 84000552 83755032 81721742
 [9] 79862414 78194303

Smallest eigenvalues:
 [1]  0.24267871  0.24088851  0.17119081  0.16683323  0.10931059  0.10693634
 [7]  0.04144335  0.01269298 -0.04081666 -0.38048138

Largest  eigenvalues:
 [1] 98934673 97181600 90305099 86085000 85741660 83165856 83032314 80392633
 [9] 79906505 77289383

Smallest eigenvalues:
 [1]  0.3781959  0.3543007  0.3539110  0.3079073  0.2268129  0.1736289
 [7]  0.1718044  0.1321291 -0.1225458 -0.1894113

Largest  eigenvalues:
 [1] 98684280 96221883 89833537 85734345 85170175 82998426 82903153 80813628
 [9] 79377888 77464617

Smallest eigenvalues:
 [1]  0.31729163  0.28393247  0.27828721  0.26678566  0.21702361  0.17935646
 [7]  0.11290860  0.08813261  0.06397922 -0.10362615

Largest  eigenvalues:
 [1] 101164957  97533564  91142876  86842767  86022148  85339588  83056556
 [8]  81873315  80903182  79243170

Smallest eigenvalues:
 [1]  0.24847780  0.24646271  0.24385713  0.21807976  0.21541971  0.19307716
 [7]  0.18976281  0.05842689 -0.14285929 -0.16916444

Largest  eigenvalues:
 [1] 97610850 96159742 90082255 85717357 84648842 83825354 83080373 81225083
 [9] 79932941 77848776

Smallest eigenvalues:
 [1]  0.18130475  0.15441579  0.13750425  0.06814803  0.06230960  0.03145429
 [7] -0.02237198 -0.13409704 -0.14146857 -0.61639628

Largest  eigenvalues:
 [1] 99991771 96470641 90822747 85909133 85508230 84417820 82826756 81562519
 [9] 79987602 78454738

Smallest eigenvalues:
 [1]  0.39190286  0.36999360  0.36725042  0.33784954  0.31260116  0.28227761
 [7]  0.19034259  0.02615499 -0.08496859 -0.66139602

Largest  eigenvalues:
 [1] 101170933  95860523  90164961  86120116  85242302  83528208  82850945
 [8]  81229091  79872702  77867409

Smallest eigenvalues:
 [1]  0.3018918  0.2916068  0.2690303  0.2573570  0.2059022  0.1788958
 [7]  0.1604716  0.1112276 -0.1276134 -0.3260372

Largest  eigenvalues:
 [1] 100348802  95383948  89115177  85543579  84787836  83865916  82284820
 [8]  81144793  79522613  77939634

Smallest eigenvalues:
 [1]  0.21806243  0.20097464  0.17019440  0.09983011  0.07671475  0.04034179
 [7] -0.13874662 -0.14632229 -0.42843390 -1.12865011

Largest  eigenvalues:
 [1] 100446891  96752064  90624076  86526833  85815778  84110916  83093020
 [8]  81450180  80031898  78344085

Smallest eigenvalues:
 [1]  0.34347912  0.33771385  0.30388027  0.26068041  0.22429142  0.12533827
 [7]  0.05406321 -0.16790513 -0.34473263 -0.67226335

Largest  eigenvalues:
 [1] 100954020  96530919  90644338  86510091  86166157  84572986  82896129
 [8]  81887376  80043080  78783008

Smallest eigenvalues:
 [1]  0.32976304  0.32817440  0.29558574  0.19935133  0.06820648  0.03141085
 [7]  0.01616753 -0.16307514 -0.37224911 -0.91049903

Largest  eigenvalues:
 [1] 100073644  96974452  91277944  86140647  86019630  83777852  83449228
 [8]  81577300  80206511  78471908

Smallest eigenvalues:
 [1]  0.4859582  0.4778705  0.3907490  0.3769227  0.3325242  0.2431768
 [7]  0.1475656  0.1063857 -0.1099742 -0.2387493

Largest  eigenvalues:
 [1] 100843574  97657236  91224040  86872348  86578842  84189771  83887339
 [8]  81908675  80531393  78774095

Smallest eigenvalues:
 [1]  0.41091831  0.37959180  0.36609571  0.30828534  0.30820319  0.29566864
 [7]  0.23653728  0.23617240 -0.03778251 -0.07781687

Largest  eigenvalues:
 [1] 98849756 95883902 89641143 85977425 84329514 83834821 82138007 80976035
 [9] 79453437 77901773

Smallest eigenvalues:
 [1]  0.3597069  0.3426749  0.3176368  0.3066898  0.3008171  0.2362749
 [7]  0.2255470  0.1266001  0.0215460 -0.3858261

Largest  eigenvalues:
 [1] 99685992 96083623 89974822 85781833 85086431 83154277 82496939 80687315
 [9] 79559764 77496596

Smallest eigenvalues:
 [1]  0.34401435  0.32443904  0.31272906  0.30271971  0.25868588  0.19641356
 [7]  0.19347415  0.04161880  0.01143266 -0.01861231

Largest  eigenvalues:
 [1] 99526737 97599324 90739713 86851354 84768870 83933782 83288217 81059766
 [9] 80239519 77968785

Smallest eigenvalues:
 [1]  0.31958511  0.24201136  0.24045561  0.20323544  0.19925910  0.16504003
 [7]  0.06541139  0.01959612 -0.22043898 -0.49159819

Largest  eigenvalues:
 [1] 99389963 97077459 90241400 86256408 85395784 83688590 83460306 81001723
 [9] 79921756 77555647

Smallest eigenvalues:
 [1]  0.4019783  0.3851504  0.3728061  0.3665693  0.2722349  0.2492861
 [7]  0.2387072  0.1566864  0.1494581 -0.2031747

Largest  eigenvalues:
 [1] 100250819  97554856  91451339  86923529  86370624  85303230  83389507
 [8]  82392815  80458509  79204142

Smallest eigenvalues:
 [1]  0.4174715  0.3964313  0.3753994  0.3532460  0.3337285  0.3157935
 [7]  0.2328301  0.0538846 -0.1664282 -0.6054575

Largest  eigenvalues:
 [1] 101218859  95451407  89119243  85773390  85330127  83351268  82143931
 [8]  80631644  79413157  77627363

Smallest eigenvalues:
 [1]  0.247810414  0.203461416  0.172893552  0.131337930  0.099074611
 [6]  0.041276482  0.033758348  0.002250354 -0.099130422 -0.579543265

Largest  eigenvalues:
 [1] 100127740  97125677  90568981  87083268  86531624  84981164  83416024
 [8]  82330022  80437442  78884262

Smallest eigenvalues:
 [1]  0.3261207  0.3131559  0.2912936  0.2673997  0.2652748  0.1410470
 [7]  0.1131774 -0.1064315 -0.1227680 -0.4471696

Largest  eigenvalues:
 [1] 99803615 95916262 89859432 85844871 83964593 83282382 82882476 80819039
 [9] 79869351 77600178

Smallest eigenvalues:
 [1]  0.22086688  0.20527194  0.20484562  0.19209282  0.14680942  0.12868537
 [7]  0.05852761 -0.17623479 -0.30502828 -0.35009102

Largest  eigenvalues:
 [1] 100773414  97440254  90462421  87053710  86544023  84653914  83347248
 [8]  81711713  80404946  78731973

Smallest eigenvalues:
 [1]  0.43178468  0.40362088  0.34779946  0.27933677  0.24824041  0.19570727
 [7]  0.18820812  0.15917898 -0.01524716 -0.05846435

Largest  eigenvalues:
 [1] 98705859 95258465 88951857 85295467 84632320 82496491 82014205 80147669
 [9] 79011301 76861834

Smallest eigenvalues:
 [1]  0.4298952  0.3298005  0.3181860  0.3139809  0.2805922  0.2355021
 [7]  0.2087183  0.1169353 -0.3322489 -0.5148637

Largest  eigenvalues:
 [1] 99740042 97098475 90821440 86668124 85420287 83640597 83520211 80888302
 [9] 80460971 77860036

Smallest eigenvalues:
 [1]  0.4133652  0.3894668  0.3580659  0.3536213  0.3262899  0.2934145
 [7]  0.2265833  0.1346292  0.1014016 -0.1088358

Largest  eigenvalues:
 [1] 101042206  95733767  89403257  86406096  85510865  84336353  82026821
 [8]  81374630  79411243  78341398

Smallest eigenvalues:
 [1]  0.38987647  0.30183137  0.29022469  0.28771409  0.27436498  0.26862774
 [7]  0.20945322  0.08533152 -0.14396644 -0.54787710

Largest  eigenvalues:
 [1] 100181949  97346029  91153469  86891362  85474813  84293709  83082966
 [8]  81494852  79792988  78460229

Smallest eigenvalues:
 [1]  0.35898569  0.26377683  0.22188948  0.21136922  0.08472485 -0.01356438
 [7] -0.03667985 -0.07921603 -0.16598165 -0.81080051

Largest  eigenvalues:
 [1] 100807757  96517035  91007425  86558814  86001376  84142841  82944098
 [8]  82040829  80131488  79099517

Smallest eigenvalues:
 [1]  0.46184799  0.41285785  0.37399167  0.30409468  0.28056764  0.26628987
 [7]  0.25465284  0.23195175  0.14651147 -0.03860563

Largest  eigenvalues:
 [1] 99857962 96986364 90463621 86629042 85754393 83527884 83332071 81022403
 [9] 79974752 77694400

Smallest eigenvalues:
 [1]  0.36466491  0.33555811  0.31252402  0.30098028  0.29458908  0.21853265
 [7]  0.15170526  0.11998501  0.09915988 -0.07292839

Largest  eigenvalues:
 [1] 100811004  96670618  90920318  86678218  85721395  84719400  83242146
 [8]  81851574  80753979  78987519

Smallest eigenvalues:
 [1]  0.44598612  0.44013086  0.41854185  0.31997958  0.30250959  0.29829036
 [7]  0.24781988  0.20233861 -0.04654796 -0.39349475

Largest  eigenvalues:
 [1] 98313810 95636098 89221450 85726450 84483585 83137141 82759818 80821819
 [9] 79294555 77421350

Smallest eigenvalues:
 [1]  0.23989531  0.22090523  0.21455050  0.16486679  0.15884446  0.15840597
 [7]  0.05598711 -0.04339037 -0.38878132 -0.49868785

Largest  eigenvalues:
 [1] 98789330 96737489 90634120 86462586 84912757 83648484 83415411 81118730
 [9] 80207245 77965196

Smallest eigenvalues:
 [1]  0.31168222  0.25353680  0.24949300  0.24021093  0.10174613  0.09481438
 [7]  0.04240132  0.02840958 -0.22619922 -0.51343839

Largest  eigenvalues:
 [1] 98571227 95006935 89206289 85122555 84330635 83028969 82022366 80452708
 [9] 79145343 77415463

Smallest eigenvalues:
 [1]  0.4356259  0.2943868  0.2841524  0.2626148  0.2459918  0.2028113
 [7]  0.2014719  0.1960665  0.1558654 -0.3909477

Largest  eigenvalues:
 [1] 98645618 96999844 89988999 86642169 85932831 83894257 83644449 81331765
 [9] 80073997 78042546

Smallest eigenvalues:
 [1]  0.29604328  0.29275349  0.25501350  0.22155154  0.12901531  0.12792562
 [7] -0.01038097 -0.14064843 -0.19711501 -0.27851100

Largest  eigenvalues:
 [1] 99826191 96638642 90782386 86355378 85632277 83680330 82911629 81234733
 [9] 79988670 78337364

Smallest eigenvalues:
 [1]  0.3905256  0.3512474  0.3503530  0.3019063  0.2872718  0.2746599
 [7]  0.1325682 -0.1414563 -0.3217902 -0.5096902

Largest  eigenvalues:
 [1] 99439559 96099265 89657085 85914612 85023736 83216149 82045496 80202562
 [9] 79314430 77136311

Smallest eigenvalues:
 [1]  0.35512886  0.33572438  0.27205764  0.26343692  0.24087203  0.19521688
 [7]  0.14989329  0.11865864  0.09634692 -0.20818026

Largest  eigenvalues:
 [1] 99313115 98943551 91672512 87995046 86206852 84658099 84550148 81772491
 [9] 81090329 78590846

Smallest eigenvalues:
 [1]  0.4176510  0.4123693  0.3740232  0.3533558  0.3501120  0.2910960
 [7]  0.2196074  0.1644901 -0.2416777 -0.4304060

Largest  eigenvalues:
 [1] 99300748 97008419 91005478 86882992 85305778 83810269 83641137 81392641
 [9] 80519647 78570503

Smallest eigenvalues:
 [1]  0.42783581  0.33525190  0.32505385  0.31782397  0.25703251  0.05261268
 [7]  0.03851447 -0.12354776 -0.12645968 -0.14051009

Largest  eigenvalues:
 [1] 100872972  96462069  90884476  86305128  85628522  83283524  82956559
 [8]  80836011  80182261  77942612

Smallest eigenvalues:
 [1]  0.3654109  0.3503852  0.2750677  0.2730756  0.2332120  0.1445943
 [7]  0.1171699  0.1128073 -0.5573580 -0.5791528

Largest  eigenvalues:
 [1] 102041803  96745366  91211167  87049489  86529897  85507986  83164655
 [8]  82638721  80661069  79663244

Smallest eigenvalues:
 [1]  0.15036286  0.11633921  0.11612360  0.07169196  0.06805087  0.01348978
 [7] -0.07297831 -0.15168004 -0.45481533 -1.08288060

Largest  eigenvalues:
 [1] 100481178  95598998  90225580  86193010  85105276  84420073  82055738
 [8]  81742213  79332865  78432874

Smallest eigenvalues:
 [1]  0.413418226  0.410581623  0.375521935  0.350286370  0.295574365
 [6]  0.257760878  0.196999313  0.195384777 -0.005708832 -0.146178692

Largest  eigenvalues:
 [1] 98659506 97336137 90470268 87226046 85277366 84101153 83722740 81443367
 [9] 80460739 78368846

Smallest eigenvalues:
 [1]  0.3493328  0.3210295  0.2938926  0.2633207  0.2515230  0.2184117
 [7]  0.1234785 -0.3392918 -0.4321458 -0.7186832

Largest  eigenvalues:
 [1] 103000364  96991662  91290069  87558242  86065316  84245699  82719487
 [8]  81803102  80020080  78775299

Smallest eigenvalues:
 [1]  0.38873555  0.38228775  0.35190385  0.30146636  0.22268057  0.19337000
 [7]  0.15367902  0.03586512 -0.28537440 -0.36822807

Largest  eigenvalues:
 [1] 99807124 97462112 90549676 87122542 86024576 84727028 83737617 81978660
 [9] 80667245 78896223

Smallest eigenvalues:
 [1]  0.45802985  0.40430872  0.37328945  0.30458125  0.27351608  0.17827483
 [7]  0.15988937  0.07150365 -0.13564795 -0.98566650

Largest  eigenvalues:
 [1] 98565510 96356127 89377955 86021926 85209589 83355612 82422409 80715630
 [9] 79285456 77553673

Smallest eigenvalues:
 [1]  0.36198986  0.29722165  0.27378697  0.24281578  0.20708917  0.20637064
 [7] -0.05774765 -0.28746609 -0.35010056 -0.41462727

Largest  eigenvalues:
 [1] 100443291  97370005  91576859  86871494  85576274  84474251  83476583
 [8]  81881762  80614884  78902166

Smallest eigenvalues:
 [1]  0.412420724  0.397234631  0.372601233  0.343982289  0.276425600
 [6]  0.073605785  0.066395119  0.006211796 -0.092384215 -0.412626624

Largest  eigenvalues:
 [1] 101592904  96468565  90930067  86662332  85826233  84073104  83167226
 [8]  81931662  80245909  78873855

Smallest eigenvalues:
 [1]  0.31766340  0.28555370  0.26657389  0.25207415  0.12964632  0.05470906
 [7]  0.05138081  0.01219506 -0.11888441 -0.24786382

Largest  eigenvalues:
 [1] 97513489 97459606 89847751 87170016 85034123 83898672 83241974 80669351
 [9] 79915457 77321076

Smallest eigenvalues:
 [1]  0.36259016  0.32510649  0.31104789  0.31054227  0.22494381  0.12830367
 [7]  0.10534501 -0.01811261 -0.11267499 -0.19945695

Largest  eigenvalues:
 [1] 101581557  97371933  90752795  86642617  86593811  84478237  82929531
 [8]  81555534  80134920  78638303

Smallest eigenvalues:
 [1]  0.34852809  0.30154705  0.28182805  0.27422679  0.21324471  0.20509612
 [7]  0.11915295  0.05850887 -0.15246653 -0.17324254

Largest  eigenvalues:
 [1] 100959225  96947317  90632515  86595530  86200845  84030255  82914741
 [8]  81191769  80237991  78319704

Smallest eigenvalues:
 [1]  0.3306743  0.3267151  0.3260201  0.2644086  0.2437870  0.2324932
 [7]  0.2275857  0.1547772  0.1322022 -0.2226303

Largest  eigenvalues:
 [1] 99427851 96842193 90335725 86651494 85398602 84666975 82748954 81481666
 [9] 80312199 78823051

Smallest eigenvalues:
 [1]  0.28036522  0.20974969  0.19924252  0.19535833  0.07686242 -0.06838964
 [7] -0.09790813 -0.20138624 -0.27076025 -0.59267703

Largest  eigenvalues:
 [1] 100186486  95192459  89605903  85899692  84925204  82748408  81483289
 [8]  80133167  78641730  76729541

Smallest eigenvalues:
 [1]  0.39567951  0.37255765  0.33091148  0.32920575  0.24986001  0.22078849
 [7]  0.10474609  0.09977335 -0.01451989 -0.07664195

Largest  eigenvalues:
 [1] 97576027 96634922 90277359 86515204 84403290 84059790 83063013 81005403
 [9] 80241211 77894234

Smallest eigenvalues:
 [1]  0.46196283  0.44702071  0.42106215  0.38881487  0.34270979  0.28966687
 [7]  0.12610041  0.08757987  0.07175879 -0.17344314

Largest  eigenvalues:
 [1] 99446021 97876793 91056313 87805679 85616386 84230947 83275239 80918587
 [9] 80630147 77457093

Smallest eigenvalues:
 [1]  0.38013011  0.32168334  0.28323011  0.26469973  0.16896389  0.14120495
 [7]  0.04221954 -0.02844278 -0.09389949 -0.69687334

Largest  eigenvalues:
 [1] 100938869  97327282  90984649  87075130  86867850  84631827  83084530
 [8]  81742345  80281937  78608471

Smallest eigenvalues:
 [1]  0.32451366  0.29226107  0.26930681  0.21650710  0.15242247  0.14996509
 [7]  0.03492967 -0.08650536 -0.14121931 -0.52673655

Largest  eigenvalues:
 [1] 98207381 96015909 90220533 86779395 84299597 83799183 82474227 81130599
 [9] 79560418 78160258

Smallest eigenvalues:
 [1]  0.38247182  0.33960666  0.33632712  0.33614558  0.33448039  0.31918940
 [7]  0.06603729 -0.21687199 -0.48108407 -0.53153690

Largest  eigenvalues:
 [1] 100506121  97324269  91087321  86971520  86522545  84543591  83887817
 [8]  81907949  80645708  78448382

Smallest eigenvalues:
 [1]  0.40966937  0.40552871  0.40461496  0.31634271  0.28671932  0.25735547
 [7]  0.24254003  0.21292655  0.19136091 -0.03800068

Largest  eigenvalues:
 [1] 100366602  96299516  90081679  86061161  85693226  85215718  82329827
 [8]  82039059  79801765  78833439

Smallest eigenvalues:
 [1]  0.367481885  0.325608474  0.312482113  0.301844344  0.286118792
 [6]  0.178648339  0.140210187  0.105325389  0.006689325 -0.140624904

Largest  eigenvalues:
 [1] 101152795  96340251  89994067  86137877  86072559  84462059  82157791
 [8]  81366706  79756736  78634466

Smallest eigenvalues:
 [1]  0.26433533  0.24645939  0.22258122  0.20439770  0.19219744  0.17692440
 [7]  0.01654297 -0.03861417 -0.16754769 -0.53568710

Largest  eigenvalues:
 [1] 100385612  97370908  90605723  86866913  85775265  84338632  83168766
 [8]  81816590  79804868  78564805

Smallest eigenvalues:
 [1]  0.31470725  0.29454019  0.26824987  0.25385231  0.25300604  0.21998877
 [7]  0.20568504  0.11972803 -0.08919151 -0.55488497

Largest  eigenvalues:
 [1] 99531000 96757245 90677520 85743029 84545139 83436285 82677411 80579039
 [9] 80017944 77596081

Smallest eigenvalues:
 [1]  0.33153485  0.31889949  0.29358724  0.27698368  0.27496241  0.21402571
 [7]  0.18882513  0.07641162 -0.01237906 -0.20276627

Largest  eigenvalues:
 [1] 98358100 97587822 91101491 87478398 84519448 84278432 83985561 81668966
 [9] 80899400 78731260

Smallest eigenvalues:
 [1]  0.47636692  0.46264344  0.40341899  0.39259755  0.28619891  0.27660441
 [7]  0.26615804  0.25970389  0.24814522 -0.03421058

Largest  eigenvalues:
 [1] 99516066 97817099 91433870 87241328 85441102 84250136 83740582 81595518
 [9] 80499757 78705907

Smallest eigenvalues:
 [1]  0.3130544  0.2721272  0.2647464  0.1678493  0.1634615  0.1501569
 [7]  0.1170997 -0.1026341 -0.3805293 -0.5620523

Largest  eigenvalues:
 [1] 101038478  95999075  90631344  85919896  84544183  83873621  82729992
 [8]  81517372  80007967  78202866

Smallest eigenvalues:
 [1]  0.4930289  0.4266294  0.3881942  0.3764321  0.3678763  0.3052265
 [7]  0.2951427  0.1868237  0.1046018 -0.1401305

Largest  eigenvalues:
 [1] 100142376  96471243  90057896  86034674  85826868  83496529  82257378
 [8]  81035687  79433736  78069602

Smallest eigenvalues:
 [1]  0.4417768  0.3938884  0.3816582  0.3635002  0.3356939  0.2253713
 [7]  0.1907556  0.1902335  0.1620243 -0.3335311

Largest  eigenvalues:
 [1] 100510442  96648144  90819797  86268962  85648605  84744178  83043526
 [8]  82259391  79972448  78940390

Smallest eigenvalues:
 [1]  0.49576138  0.48729719  0.43282818  0.41013811  0.32650665  0.29477459
 [7]  0.15968936  0.05172536 -0.01414389 -0.07858247

Largest  eigenvalues:
 [1] 99399366 96981827 90457232 87214965 85410754 83983908 83807348 81353989
 [9] 80540737 78239019

Smallest eigenvalues:
 [1]  0.30888447  0.30242531  0.28613162  0.21658071  0.21546123  0.21271676
 [7]  0.15560434  0.12327398 -0.05126137 -0.06203630

Largest  eigenvalues:
 [1] 97769589 96085284 89105479 86175243 84071642 83671538 82392293 80606501
 [9] 79304595 77622715

Smallest eigenvalues:
 [1]  0.29759824  0.29147718  0.28363514  0.20669748  0.12468125  0.09164781
 [7]  0.07364580 -0.09970118 -0.29555256 -1.07550728

Largest  eigenvalues:
 [1] 100963119  96944552  91797519  86566994  85065406  84129288  83301730
 [8]  81853250  80259993  78550399

Smallest eigenvalues:
 [1]  0.3872525  0.3368564  0.3157052  0.2706642  0.2641446  0.2269352
 [7]  0.1953448  0.1298331 -0.1255989 -0.3009752

Largest  eigenvalues:
 [1] 100710071  96900710  90770975  86403134  86384578  85041336  82780290
 [8]  82264861  80028037  79038059

Smallest eigenvalues:
 [1]  0.27527613  0.27137581  0.25914801  0.25656747  0.18461267 -0.07290681
 [7] -0.22345898 -0.30605851 -0.37479661 -0.66340140

Largest  eigenvalues:
 [1] 102341349  97296731  91632741  87176338  86239546  84193230  83462415
 [8]  81879646  80564525  78812216

Smallest eigenvalues:
 [1]  0.18093415  0.16889585  0.16401746  0.12027430  0.11921471  0.02689398
 [7] -0.05238253 -0.08571017 -0.21302257 -0.78366284

Largest  eigenvalues:
 [1] 99273908 96703045 90691733 85924890 85183323 83474669 83282159 81211530
 [9] 79906412 78023656

Smallest eigenvalues:
 [1]  0.40504477  0.38761633  0.36105110  0.31586540  0.27253369  0.27170056
 [7]  0.17905399  0.16897847  0.04275914 -0.31065256

Largest  eigenvalues:
 [1] 99181698 96337933 90693090 85942945 85549255 84301171 82891302 81839458
 [9] 79912227 78530318

Smallest eigenvalues:
 [1]  0.32497730  0.31502244  0.31166086  0.24544025  0.15936889  0.01772494
 [7] -0.18640595 -0.25401010 -0.75985697 -1.06714046

Largest  eigenvalues:
 [1] 100692647  96124679  90141395  86941286  84984543  83897592  83584307
 [8]  81554695  80684697  78010335

Smallest eigenvalues:
 [1]  0.42801832  0.42539177  0.38526550  0.37777895  0.32664254  0.19038603
 [7]  0.13137168 -0.06903234 -0.12470086 -0.19110222

Largest  eigenvalues:
 [1] 100802700  95469561  89269078  86234024  85305939  83013523  82030838
 [8]  80378974  79238458  77538546

Smallest eigenvalues:
 [1]  0.389360340  0.307090100  0.275553361  0.190172059  0.167413842
 [6]  0.142664031  0.034919390  0.002410147 -0.187142511 -0.524603582

Largest  eigenvalues:
 [1] 99882346 96742565 90319643 86810194 85668244 84921044 83670895 82163323
 [9] 80655221 79207638

Smallest eigenvalues:
 [1]  0.4444926  0.3876377  0.3421871  0.2715840  0.2691509  0.2576597
 [7]  0.2287924  0.1353497  0.1300004 -0.4540134

Largest  eigenvalues:
 [1] 99247085 97300266 90772171 86359388 86203535 84036542 83389326 81440103
 [9] 80121510 78255658

Smallest eigenvalues:
 [1]  0.3367188  0.3363577  0.3163925  0.3077456  0.2520839  0.1984519
 [7]  0.1654329  0.1511559  0.1218176 -0.6849484

Largest  eigenvalues:
 [1] 98103629 96808812 89824855 87433487 84193380 83302332 82831640 80372829
 [9] 79986354 77263103

Smallest eigenvalues:
 [1]  0.35844824  0.32557692  0.32028014  0.27086770  0.24328510  0.23321196
 [7]  0.16191931  0.08792023  0.08357682 -0.41716542

Largest  eigenvalues:
 [1] 100064707  97117938  91043256  86667965  85307498  84400614  83384408
 [8]  81951674  80233113  78321996

Smallest eigenvalues:
 [1]  0.31235982  0.28653734  0.26557183  0.21289238  0.18735190  0.13647567
 [7] -0.02043652 -0.08609886 -0.39657922 -0.42953845

Largest  eigenvalues:
 [1] 101497705  96558429  90989372  86085057  85672474  84128802  82489598
 [8]  81342491  79805539  78182649

Smallest eigenvalues:
 [1]  0.4434507  0.4402761  0.4272075  0.4084900  0.3901887  0.2774006
 [7]  0.2319455  0.1820148 -0.1699446 -0.2283848

Largest  eigenvalues:
 [1] 101230361  97505289  91292684  86916883  86370348  84471908  83559688
 [8]  81883329  80778357  78737330

Smallest eigenvalues:
 [1]  0.47443623  0.33366809  0.32528364  0.30299483  0.28556437  0.23937332
 [7]  0.15941807  0.15485803  0.03977466 -0.76673232

Largest  eigenvalues:
 [1] 101064732  95934326  90388999  86225516  86127291  84366754  82548097
 [8]  81989279  79670604  78618232

Smallest eigenvalues:
 [1]  0.3763945  0.3703879  0.2971830  0.2949618  0.2809408  0.1497314
 [7]  0.1345459  0.1339935  0.1173175 -0.1741223

Largest  eigenvalues:
 [1] 99324338 95980869 89475536 85664404 84681862 82978472 82534680 80315564
 [9] 79327386 77113054

Smallest eigenvalues:
 [1]  0.32014156  0.27355147  0.26006149  0.23813363  0.16395446  0.14456900
 [7]  0.12797590  0.10187202  0.02259674 -0.18304101

Largest  eigenvalues:
 [1] 98239583 96522651 89671222 86831295 84096990 83702641 83327060 80711535
 [9] 80091839 77628541

Smallest eigenvalues:
 [1]  0.51832589  0.50853354  0.46171003  0.36713185  0.35744094  0.31503639
 [7]  0.23356697  0.14202624 -0.02140405 -0.47520121

Largest  eigenvalues:
 [1] 100826841  97186879  90642394  86932673  86306226  84271884  83405009
 [8]  81716878  80259589  78492801

Smallest eigenvalues:
 [1]  0.33055003  0.26887783  0.23941970  0.22154527  0.21153702  0.16444013
 [7]  0.05541203  0.02172149 -0.07982424 -0.59516971

Largest  eigenvalues:
 [1] 99860388 96375843 90051865 86101020 85026663 82761676 82531838 80174690
 [9] 79740935 77199788

Smallest eigenvalues:
 [1]  0.40094796  0.39698628  0.36372813  0.30916698  0.26878533  0.23061996
 [7]  0.15816240  0.08863852 -0.16325574 -0.41367608

Largest  eigenvalues:
 [1] 99339572 96177885 89119526 86128071 85178866 83250724 82181430 80228139
 [9] 79206758 77206148

Smallest eigenvalues:
 [1]  0.27022034  0.25738389  0.24325426  0.18231782  0.16899300  0.15882719
 [7]  0.05213702  0.00232125 -0.08915689 -0.55623809

Largest  eigenvalues:
 [1] 101154560  97359458  90439775  86940477  86327440  85379846  83484008
 [8]  82588059  80668174  79556214

Smallest eigenvalues:
 [1]  0.26476612  0.25453524  0.24074930  0.19302081  0.15186811  0.09148297
 [7]  0.02960722 -0.05878278 -0.22715014 -0.47184486

Largest  eigenvalues:
 [1] 99374674 96143651 90020105 86004860 84711374 83310391 83169945 80608895
 [9] 79894433 77226321

Smallest eigenvalues:
 [1]  0.2555768  0.2437922  0.1855864  0.1835593  0.1677392  0.1359722
 [7] -0.1626289 -0.3879118 -0.4752315 -0.5627773

Largest  eigenvalues:
 [1] 99603949 97714900 90945085 87474762 85535671 85097065 84118697 82102221
 [9] 81212835 79386653

Smallest eigenvalues:
 [1]  0.42103244  0.36843288  0.35070493  0.30339784  0.26206657  0.24816267
 [7]  0.11020235 -0.03674066 -0.08479632 -0.11568730

Largest  eigenvalues:
 [1] 99966369 97238194 90968452 87089423 86045335 85159104 83716747 82058895
 [9] 80886408 79007651

Smallest eigenvalues:
 [1]  0.41964079  0.39708324  0.36798591  0.32837872  0.28816739  0.24332365
 [7]  0.20902962  0.07001906 -0.28917419 -0.34205088

Largest  eigenvalues:
 [1] 100274123  95590151  89807011  85429433  85277995  83539786  82549506
 [8]  81004468  79672496  78180012

Smallest eigenvalues:
 [1]  0.238578507  0.204091551  0.163361071  0.097138253 -0.003480877
 [6] -0.011437154 -0.084189455 -0.222451568 -0.450870889 -0.459885916

Largest  eigenvalues:
 [1] 98631208 98502639 91682619 87527928 85997843 84834210 84658397 82144352
 [9] 81322062 79615434

Smallest eigenvalues:
 [1]  0.31775003  0.31259503  0.29501773  0.28488925  0.25772885  0.22963215
 [7]  0.15138230  0.06356559 -0.35227936 -0.37865105

Largest  eigenvalues:
 [1] 100835779  96614215  91052843  86178704  85978099  83477858  82950042
 [8]  81197642  79849336  78130332

Smallest eigenvalues:
 [1]  0.30700013  0.30382554  0.22228123  0.22120591  0.20781446  0.16799861
 [7]  0.09631524  0.04219502 -0.38080375 -1.01285960

Largest  eigenvalues:
 [1] 99852021 97804180 91033134 87381280 85618725 84090058 83788899 81601724
 [9] 80423487 78332127

Smallest eigenvalues:
 [1]  0.3556360  0.3469958  0.3372829  0.3291750  0.2365599  0.2196748
 [7]  0.1652917 -0.1564478 -0.2888138 -1.0287194

Largest  eigenvalues:
 [1] 100934143  96516788  90460779  86612506  86080385  83588681  82883591
 [8]  80999062  80124093  78214540

Smallest eigenvalues:
 [1]  0.41521572  0.39352013  0.28040467  0.27938557  0.27487905  0.19901880
 [7]  0.16677045  0.10998470 -0.07011668 -0.24481959

Largest  eigenvalues:
 [1] 100232367  96664166  90607881  86391789  85775096  85234793  82572038
 [8]  81961799  79907160  78883343

Smallest eigenvalues:
 [1]  0.456757452  0.409897708  0.364451849  0.341830965  0.298728278
 [6]  0.264774395  0.179002052  0.002590262 -0.014032614 -0.097905251

Largest  eigenvalues:
 [1] 100398340  96152118  89812650  86022307  85404940  83667160  82603318
 [8]  80968069  79875938  77775304

Smallest eigenvalues:
 [1]  0.22910671  0.18627107  0.12889673  0.11385283  0.09121772  0.04640370
 [7] -0.03224603 -0.05696002 -0.13875573 -0.45451063

Largest  eigenvalues:
 [1] 98401990 96132936 90046505 85392589 85258346 83158323 82688916 80911795
 [9] 79371969 77908138

Smallest eigenvalues:
 [1]  0.200857702  0.171291083  0.150766148  0.133182230  0.073107500
 [6]  0.022559550  0.019792492 -0.009079662 -0.096222206 -0.517303959

Largest  eigenvalues:
 [1] 100496639  97913830  90973567  87288930  85943361  83984851  83318784
 [8]  81539834  80135231  78334055

Smallest eigenvalues:
 [1]  0.325403210  0.322213689  0.239763807  0.158657945  0.142719925
 [6]  0.120036090  0.098669925  0.085226741  0.002312567 -0.129679458

Largest  eigenvalues:
 [1] 98468892 97023170 90062160 86234456 85318479 84454984 83049998 81659863
 [9] 80166136 79058901

Smallest eigenvalues:
 [1]  0.47093306  0.46537889  0.42278739  0.40808225  0.34524350  0.23265912
 [7]  0.18663709  0.15769439 -0.03348797 -0.09378785

Largest  eigenvalues:
 [1] 101412363  96733528  90795682  86751817  86161238  85037972  83173419
 [8]  82310430  80517471  79197617

Smallest eigenvalues:
 [1]  0.37746889  0.36906160  0.35372689  0.33227728  0.27779715  0.22030154
 [7]  0.11112100  0.09159873 -0.01520428 -0.15226064

Largest  eigenvalues:
 [1] 98507840 96049962 89685590 86030609 84114950 83071707 82351260 80424932
 [9] 79398183 77186555

Smallest eigenvalues:
 [1]  0.4510728  0.4166553  0.3955503  0.3911207  0.3901021  0.3390220
 [7]  0.2454311  0.2192114  0.1066379 -0.1003724

Largest  eigenvalues:
 [1] 99385739 95877045 89926437 85626417 84428922 83769044 82406760 80842115
 [9] 79892017 78052860

Smallest eigenvalues:
 [1]  0.45917983  0.43705319  0.39917284  0.32644766  0.32244990  0.25560739
 [7]  0.20754910  0.17152837  0.02960772 -0.30649185

Largest  eigenvalues:
 [1] 97593758 96797793 90412581 86843835 83763077 83657085 83503416 81252114
 [9] 80393664 78365015

Smallest eigenvalues:
 [1]  0.5577591  0.5422413  0.4550689  0.3970801  0.3969024  0.2743381
 [7]  0.2419286  0.1838882  0.1512396 -0.2603315

Largest  eigenvalues:
 [1] 99749981 95985642 90152596 85829393 84716477 83634117 82692199 81117954
 [9] 79968939 78322475

Smallest eigenvalues:
 [1]  0.225602554  0.214581145  0.145728807  0.137412819  0.009044246
 [6] -0.025110306 -0.071930109 -0.078152355 -0.818993267 -1.079613921

Largest  eigenvalues:
 [1] 99145018 98039822 92026200 87580033 84741617 84724122 83885947 81650270
 [9] 81202669 78199522

Smallest eigenvalues:
 [1]  0.27295827  0.27126668  0.25338751  0.20571338  0.19921919  0.14020680
 [7]  0.07485622 -0.00696153 -0.08793807 -0.30348721

Largest  eigenvalues:
 [1] 98714579 95510878 89163120 85375294 85003878 82879972 82100894 79885885
 [9] 79218544 76802091

Smallest eigenvalues:
 [1]  0.39016713  0.34351609  0.31708102  0.28833646  0.19754479  0.16785071
 [7]  0.15538290 -0.01928409 -0.21052918 -0.63022140

Largest  eigenvalues:
 [1] 98952563 96259597 90249322 86635513 84666844 83189106 82699595 80565157
 [9] 79948541 77542668

Smallest eigenvalues:
 [1]  0.3110508  0.3071504  0.2833117  0.2313054  0.2177674  0.1944799
 [7]  0.1605563 -0.1197110 -0.5500344 -0.5923815

Largest  eigenvalues:
 [1] 99952098 97206664 91280644 86848216 85243148 84561371 83422386 81941578
 [9] 80416363 78916156

Smallest eigenvalues:
 [1]  0.3058200  0.2953359  0.2774179  0.2463047  0.2106506  0.1819372
 [7]  0.1802838 -0.2475356 -0.4367461 -1.1228400

Largest  eigenvalues:
 [1] 99782269 98246863 92254381 87741042 85344211 84510955 84218629 81875595
 [9] 80746008 78916457

Smallest eigenvalues:
 [1]  0.35097233  0.33685414  0.27344704  0.23838261  0.22604015  0.20232826
 [7]  0.16410251  0.13838710 -0.01559964 -0.08264279

Largest  eigenvalues:
 [1] 98494382 96327689 89393280 85694590 85087190 83780496 82577073 80876820
 [9] 79653915 77757428

Smallest eigenvalues:
 [1]  0.37937807  0.36589304  0.35130278  0.32011392  0.28659130  0.24159562
 [7]  0.12639446  0.12224412  0.10368273 -0.07252465

Largest  eigenvalues:
 [1] 99531731 96082083 90444344 85923944 84600149 83404067 82337174 80584053
 [9] 79712198 77530214

Smallest eigenvalues:
 [1]  0.238748482  0.202007249  0.164039169  0.070645165  0.030505432
 [6] -0.003217926 -0.039184376 -0.183825122 -0.305765444 -0.468407192

Largest  eigenvalues:
 [1] 99803943 95824833 89523787 86292236 84991522 83002839 82704141 81046391
 [9] 79261750 77864668

Smallest eigenvalues:
 [1]  0.076232917  0.064960254  0.042619159 -0.002496888 -0.009726674
 [6] -0.056054187 -0.057546895 -0.126693962 -0.560913727 -0.631223870

Largest  eigenvalues:
 [1] 100906869  96438701  89636458  86996065  85945626  83634729  82832010
 [8]  80971638  79665932  77660396

Smallest eigenvalues:
 [1]  0.23007883  0.18217963  0.14480795  0.12472199  0.09424502  0.04590686
 [7]  0.01098493 -0.04388355 -0.32845037 -0.34599752

Largest  eigenvalues:
 [1] 99644240 97125114 90488781 86214707 85921969 83448268 83191621 81032966
 [9] 79975993 78067678

Smallest eigenvalues:
 [1]  0.36686289  0.35672981  0.35636914  0.32576554  0.31711246  0.27608313
 [7]  0.21698663  0.15408451 -0.01159193 -0.09183335

Largest  eigenvalues:
 [1] 100676934  98294168  91737070  88109327  85598193  84297736  84139066
 [8]  81350700  80891018  78184995

Smallest eigenvalues:
 [1]  0.297019246  0.234955405  0.223689486  0.197098203  0.159538660
 [6]  0.107199518  0.031883553 -0.005987563 -0.185209530 -0.464716667

Largest  eigenvalues:
 [1] 99403028 96995729 91271197 86334470 84845225 83720711 83141619 81051248
 [9] 80386006 78016618

Smallest eigenvalues:
 [1]  0.30125163  0.29857364  0.27697696  0.23653599  0.22493355  0.15931825
 [7]  0.15719980  0.09585035 -0.07523587 -0.24563079

Largest  eigenvalues:
 [1] 99255187 97601232 91540697 86557384 85320456 84259688 83430092 81740052
 [9] 80300100 78699978

Smallest eigenvalues:
 [1]  0.14770509  0.14703493  0.12877017  0.11995217  0.03044798  0.02842931
 [7] -0.02385802 -0.22328690 -0.41613392 -1.18032548

Largest  eigenvalues:
 [1] 98523226 96848887 90449028 87557021 84132674 83955483 82982210 81412613
 [9] 79877588 78084687

Smallest eigenvalues:
 [1]  0.51960806  0.45499548  0.39923555  0.36355990  0.34626187  0.30379534
 [7]  0.15830414  0.13624363  0.02287153 -0.01837780

Largest  eigenvalues:
 [1] 98580204 97143162 90240635 87044613 84973194 83060980 82671844 80219489
 [9] 79639565 77305825

Smallest eigenvalues:
 [1]  0.3735375  0.3124046  0.2955252  0.2661430  0.2339361  0.2322620
 [7]  0.2296551  0.2208476  0.1665363 -0.2014518

Largest  eigenvalues:
 [1] 100069852  97987902  90857389  87173121  86355576  85114828  82925917
 [8]  81785590  80064235  78549562

Smallest eigenvalues:
 [1]  0.18897226  0.13418871  0.13403572  0.11794544  0.08530734  0.03570521
 [7]  0.02717942 -0.02845286 -0.09525021 -1.09938105

Largest  eigenvalues:
 [1] 101445426  97239157  91464509  86942210  86539359  84450507  83229824
 [8]  82084077  80216620  78918983

Smallest eigenvalues:
 [1]  0.32187388  0.30941506  0.28040408  0.27005253  0.07063967  0.01791296
 [7] -0.04974077 -0.05007339 -0.07754903 -0.61300587

Largest  eigenvalues:
 [1] 99279205 96481973 90430966 86730510 84266721 83878917 83135030 81054785
 [9] 80265359 77496367

Smallest eigenvalues:
 [1]  0.266249936  0.183439818  0.183122112  0.165237483  0.133126026
 [6]  0.086028761  0.080281040  0.002261466 -0.065886258 -0.682818857

Largest  eigenvalues:
 [1] 98104025 96020905 90039357 85819099 84552218 84009847 83176366 81622894
 [9] 79703024 78143730

Smallest eigenvalues:
 [1]  0.4731831  0.4379850  0.3678234  0.3396353  0.3154924  0.1786980
 [7]  0.1424094 -0.0735300 -0.2596949 -0.3355862

Largest  eigenvalues:
 [1] 101695333  97016709  90753799  87111137  86413236  84559990  83148366
 [8]  81478659  80491103  78825166

Smallest eigenvalues:
 [1]  0.370881259  0.308468843  0.306375518  0.253293109  0.151681071
 [6]  0.064906167  0.034308609 -0.007546741 -0.103995517 -0.303814423

Largest  eigenvalues:
 [1] 100407792  97222775  90887078  86377793  86157911  84855368  83127518
 [8]  82177321  80286075  78988394

Smallest eigenvalues:
 [1]  0.36215672  0.32055746  0.29270195  0.22599062  0.20541405  0.07966848
 [7] -0.07010469 -0.08651217 -0.14687652 -0.17682493

Largest  eigenvalues:
 [1] 99742306 96457600 89932801 86458562 85660891 83215673 82796997 80335254
 [9] 79862019 77302228

Smallest eigenvalues:
 [1]  0.4069725  0.3789921  0.3720539  0.3493058  0.2786115  0.2763314
 [7]  0.1597281  0.1374649 -0.1555157 -0.3548150

Largest  eigenvalues:
 [1] 99430282 97382075 90744799 86780563 85729494 84453522 83125864 81558582
 [9] 80266725 78751869

Smallest eigenvalues:
 [1]  0.34660680  0.33242825  0.33024667  0.26505687  0.25308096  0.19190169
 [7]  0.18440978 -0.02657977 -0.07899601 -0.35406515

Largest  eigenvalues:
 [1] 100092330  97109606  90659208  87013364  85163538  83748493  83105247
 [8]  80868731  80483208  77660021

Smallest eigenvalues:
 [1]  0.315380299  0.300790229  0.298210052  0.240074360  0.216812909
 [6]  0.211242548  0.142964705  0.127009591 -0.006673591 -0.619316170

Largest  eigenvalues:
 [1] 98786252 96176105 89886380 85575809 84606864 83246926 82868686 81027626
 [9] 79678226 77911568

Smallest eigenvalues:
 [1]  0.3555102  0.3216519  0.2202893  0.1849291  0.1818633  0.1749043
 [7]  0.1500867 -0.1619119 -0.1768534 -0.3630047

Largest  eigenvalues:
 [1] 100026770  96430653  90588311  86126141  85693465  83939133  83177361
 [8]  81440171  80301745  78474493

Smallest eigenvalues:
 [1]  0.42323015  0.38460351  0.38354034  0.33435045  0.29748921  0.28011144
 [7]  0.19644361  0.05767292  0.03809383 -0.30141804

Largest  eigenvalues:
 [1] 99632097 96498508 90114598 86605080 84677056 83388952 83273005 80930241
 [9] 79913067 77464610

Smallest eigenvalues:
 [1]  0.34880830  0.32753423  0.31371720  0.31293268  0.29225905  0.24612374
 [7]  0.19394336  0.08634842 -0.14975843 -0.45819139

Largest  eigenvalues:
 [1] 100969016  97162852  90589520  86474617  86435663  84540020  83035146
 [8]  81850919  79764231  78534592

Smallest eigenvalues:
 [1]  0.121584650  0.099073605  0.083206678  0.030346252 -0.005349244
 [6] -0.030517717 -0.258229769 -0.315619402 -0.662853289 -0.976832846

Largest  eigenvalues:
 [1] 97769125 97727404 90306862 86323686 85593366 84314941 83002220 81440773
 [9] 79593279 78106522

Smallest eigenvalues:
 [1]  0.41539659  0.34861896  0.34535995  0.30761337  0.26335302  0.24672555
 [7]  0.19167796  0.07149844 -0.30944370 -0.35463270

Largest  eigenvalues:
 [1] 100925112  95104191  89451130  85567798  85047948  82231602  82103613
 [8]  79772505  79301558  76766044

Smallest eigenvalues:
 [1]  0.42645093  0.38110620  0.34579000  0.26418143  0.23611077  0.22212262
 [7]  0.18020006  0.14611503  0.04597814 -0.04967715

Largest  eigenvalues:
 [1] 98230818 96771523 89915329 86314222 84417574 83164438 82590980 80513474
 [9] 79235205 77431813

Smallest eigenvalues:
 [1]  0.33928706  0.30253223  0.29286834  0.27012046  0.24627677  0.20236523
 [7]  0.14500627  0.07341435 -0.04890873 -0.46030103

Largest  eigenvalues:
 [1] 99970209 95627966 89812444 85079576 85072865 82827664 82680085 80482524
 [9] 79731110 77673679

Smallest eigenvalues:
 [1]  0.4073399  0.3380502  0.3310765  0.2541292  0.2529722  0.2344397
 [7]  0.1328268  0.1247015  0.0222587 -0.1692082

Largest  eigenvalues:
 [1] 99808506 97446505 90799481 86933910 85895421 84754937 83017950 81574556
 [9] 80420369 78939377

Smallest eigenvalues:
 [1]  0.3792166  0.3641544  0.3128769  0.3043855  0.2261739  0.1949854
 [7]  0.1394099  0.1139854 -0.0909399 -0.3048475

Largest  eigenvalues:
 [1] 99353343 97031118 90188031 86791455 85242182 83316632 83166375 80456864
 [9] 79826073 77194419

Smallest eigenvalues:
 [1]  0.3207312  0.3084391  0.2566871  0.1728499  0.1347761  0.1288469
 [7]  0.1277789 -0.2828261 -0.3376426 -0.5095712

Largest  eigenvalues:
 [1] 101002692  98022261  91173223  87293577  87066456  85253229  83781613
 [8]  82125988  81099365  79246043

Smallest eigenvalues:
 [1]  0.25273977  0.23785645  0.23491200  0.17636359  0.14387486  0.10261795
 [7]  0.02288784 -0.04382888 -0.07816426 -0.36475216

Largest  eigenvalues:
 [1] 99865756 97139252 90869065 86204257 85755360 83635046 83462409 81354082
 [9] 80279024 78279106

Smallest eigenvalues:
 [1]  0.4629906  0.4420775  0.4155700  0.3524799  0.2971138  0.2928448
 [7]  0.2769946  0.1430292  0.1401606 -0.1545259

Largest  eigenvalues:
 [1] 99735377 96289980 89786104 86217632 84844589 83795729 82774334 81161230
 [9] 79908452 78089620

Smallest eigenvalues:
 [1]  0.40751238  0.34767727  0.33619892  0.31519661  0.27251762  0.26250855
 [7]  0.19233978  0.13649158 -0.01791136 -0.19899712

Largest  eigenvalues:
 [1] 99710815 96169856 89743849 85912101 85762431 83777472 82373537 81120251
 [9] 79769936 78348070

Smallest eigenvalues:
 [1]  0.298771596  0.277230016  0.139848803  0.139039924 -0.005230866
 [6] -0.036355574 -0.109102942 -0.116315323 -0.397277362 -0.540578190

Largest  eigenvalues:
 [1] 101025774  96513528  90371682  86102986  85864377  83321749  82947449
 [8]  80868528  79715410  77632146

Smallest eigenvalues:
 [1]  0.5131164  0.4907560  0.4739998  0.4694242  0.3360640  0.2722105
 [7]  0.2369400  0.2194937  0.1483563 -0.2358872

Largest  eigenvalues:
 [1] 100365683  96070086  89558984  86068350  85825333  82846514  82488891
 [8]  80314590  79431942  77418722

Smallest eigenvalues:
 [1]  0.30105502  0.26894437  0.23960410  0.23295230  0.19304696  0.18578099
 [7]  0.13973900  0.09517504  0.04515997 -0.35253910

Largest  eigenvalues:
 [1] 99319558 96716112 89687031 86609810 85574482 84140793 82580873 81109268
 [9] 80006296 77732149

Smallest eigenvalues:
 [1]  0.36358367  0.28819267  0.27403224  0.24161817  0.15204419  0.09333758
 [7]  0.07896315 -0.06422971 -0.30831007 -0.64741605

Largest  eigenvalues:
 [1] 101349599  97477660  90545677  87334685  86906170  84328733  83640155
 [8]  81839669  80264345  78561610

Smallest eigenvalues:
 [1]  0.459466185  0.407495612  0.377703889  0.328678514  0.325866528
 [6]  0.288111009  0.284745483  0.262835847  0.004364766 -0.082383562

Largest  eigenvalues:
 [1] 99435937 96649412 90044309 86108726 84943872 83928831 82553003 81169786
 [9] 79794549 78488240

Smallest eigenvalues:
 [1]  0.41537497  0.40535374  0.34421274  0.32700339  0.27610709  0.22002078
 [7]  0.19710006  0.09897471 -0.00771023 -0.28407823

Largest  eigenvalues:
 [1] 99653965 97224762 91543366 86435375 85683668 84547294 83766634 82106276
 [9] 80641352 78901691

Smallest eigenvalues:
 [1]  0.34030310  0.32689111  0.30790816  0.28885470  0.28430259  0.26379195
 [7]  0.22430123  0.08202055 -0.10218147 -0.31692941

Largest  eigenvalues:
 [1] 101903233  96420607  90562588  86831735  85989481  85315131  82582775
 [8]  82333614  80284166  79175720

Smallest eigenvalues:
 [1]  0.29037359  0.25700743  0.25349925  0.22795981  0.15675371  0.08572705
 [7]  0.07557650 -0.08264840 -0.15083149 -0.32028752

Largest  eigenvalues:
 [1] 99568059 96461940 89980655 86374277 83802878 83260333 82337601 80554634
 [9] 79295001 77231216

Smallest eigenvalues:
 [1]  0.37759119  0.29231589  0.28884124  0.19587054  0.17960990  0.11485089
 [7]  0.10701840  0.09736901  0.06116874 -0.34647536

Largest  eigenvalues:
 [1] 97588541 96680633 90064099 86955767 84209163 83152051 82868282 80732594
 [9] 80061395 77592326

Smallest eigenvalues:
 [1]  0.34686258  0.34583415  0.31361906  0.29654174  0.28332705  0.24200484
 [7]  0.21040720  0.04473258 -0.28758198 -0.53082289

Largest  eigenvalues:
 [1] 99641944 95702811 89590167 85920692 85298072 83165041 82682277 80940473
 [9] 79586337 77643459

Smallest eigenvalues:
 [1]  0.29271046  0.29118264  0.26699837  0.25924126  0.19462124  0.13784858
 [7]  0.12139078  0.00745901 -0.05622134 -0.13179928

Largest  eigenvalues:
 [1] 100375036  97811815  91231699  87669828  85935423  85551910  83474230
 [8]  82490834  81079099  79688696

Smallest eigenvalues:
 [1]  0.339738667  0.315040093  0.270685844  0.243474820  0.166553139
 [6] -0.001948778 -0.059927188 -0.092267569 -0.176340377 -0.529420838

Largest  eigenvalues:
 [1] 101381500  95939084  90410328  85657643  85431468  82834413  82475109
 [8]  80436580  79640427  77462497

Smallest eigenvalues:
 [1] -0.003938976 -0.035704192 -0.047703562 -0.075615587 -0.091875849
 [6] -0.106104269 -0.290740082 -0.337407321 -0.454290643 -0.820779699

Largest  eigenvalues:
 [1] 98779695 97112493 91222797 85940889 85936712 84428306 83450079 81575926
 [9] 80509973 78521844

Smallest eigenvalues:
 [1]  0.3762816  0.3382842  0.3103464  0.3021440  0.2777414  0.2718768
 [7]  0.2010620  0.1509750 -0.1365034 -0.2849609

Largest  eigenvalues:
 [1] 100009912  95622139  89383683  85082553  85034675  82877415  81973931
 [8]  80378962  79035693  77379378

Smallest eigenvalues:
 [1]  0.390401162  0.372220910  0.367856530  0.342678217  0.337739898
 [6]  0.258057348  0.227085397  0.207053595  0.185383695 -0.004998382

Largest  eigenvalues:
 [1] 99742136 95835713 89814745 85492454 85487902 83886129 82161729 80801793
 [9] 79627024 77744500

Smallest eigenvalues:
 [1]  0.42295849  0.38414668  0.32862636  0.30663701  0.28572025  0.23655167
 [7]  0.21902998  0.12850101  0.03747723 -0.04931241

Largest  eigenvalues:
 [1] 99163163 95983154 89742544 86374615 84960457 84210958 82121386 81243802
 [9] 79487460 78106613

Smallest eigenvalues:
 [1]  0.45928749  0.43885756  0.34611468  0.31469607  0.29921342  0.25451120
 [7]  0.21915914  0.12635405  0.11375772 -0.03626665

Largest  eigenvalues:
 [1] 98549912 97040216 90470396 86830900 84733535 84561694 83279185 81817033
 [9] 80136486 78590071

Smallest eigenvalues:
 [1]  0.21306716  0.20009471  0.18682018  0.14647698  0.11787026  0.05000114
 [7] -0.14125761 -0.21322068 -0.46372173 -0.86120880

Largest  eigenvalues:
 [1] 100269835  98786005  92116482  87573609  86744010  85041439  84023523
 [8]  82318287  80705836  79046902

Smallest eigenvalues:
 [1]  0.385178112  0.348892800  0.282647040  0.241740663  0.164744225
 [6]  0.088619098  0.061885102  0.026970585  0.002819512 -0.167604845

Largest  eigenvalues:
 [1] 100055869  97106544  90609896  87086111  84957765  84813716  82736560
 [8]  81692216  80467524  78745724

Smallest eigenvalues:
 [1]  0.33164411  0.32916894  0.30685450  0.30008293  0.26250964  0.21092857
 [7]  0.18231502  0.06657026 -0.03114995 -0.16383813

Largest  eigenvalues:
 [1] 98384155 95271270 89092485 85945027 83897194 83140667 81942109 80531137
 [9] 79245055 77600122

Smallest eigenvalues:
 [1]  0.265079219  0.257228032  0.229848256  0.210170685  0.204741606
 [6]  0.154336346  0.046422343  0.045166559  0.006347771 -0.141326789

Largest  eigenvalues:
 [1] 98578147 96161275 90399797 86264384 84010640 83466480 82965174 80852491
 [9] 80078958 77874336

Smallest eigenvalues:
 [1]  0.34606804  0.32028727  0.29796067  0.27689720  0.17631718  0.15690097
 [7]  0.14462176 -0.06529434 -0.10882231 -0.36449220

Largest  eigenvalues:
 [1] 100864270  95669008  89881292  85293074  85068746  83946463  82376830
 [8]  81515995  79530016  78273042

Smallest eigenvalues:
 [1]  0.3883854  0.3671962  0.3368524  0.3034305  0.3008313  0.1890998
 [7]  0.1775069  0.1176321 -0.1193875 -0.3366247

Largest  eigenvalues:
 [1] 98352225 96069038 90389142 85424350 84577911 83499850 82951243 80899027
 [9] 80133044 77925286

Smallest eigenvalues:
 [1]  0.36106262  0.35470095  0.30521951  0.28049301  0.09795188 -0.14067826
 [7] -0.21879958 -0.32645230 -0.50601919 -0.74705232

Largest  eigenvalues:
 [1] 101063573  95919795  89751196  86673460  85400345  83315771  83215808
 [8]  80776479  79901572  78102403

Smallest eigenvalues:
 [1]  0.39516504  0.38110504  0.37303341  0.35395212  0.30084641  0.20025858
 [7]  0.19057465  0.05271087 -0.23323571 -0.45740242

Largest  eigenvalues:
 [1] 99885413 96307683 89771770 86676171 85076885 83019073 82614375 80303697
 [9] 79603642 77103908

Smallest eigenvalues:
 [1]  0.39424520  0.37538102  0.33402201  0.30799472  0.12998411  0.06237170
 [7] -0.01022610 -0.02110173 -0.14673734 -0.98352635

Largest  eigenvalues:
 [1] 102415030  97022571  91070926  86939887  86838670  84548558  83326046
 [8]  82110262  80543798  78863805

Smallest eigenvalues:
 [1]  0.4361062  0.4008087  0.3928731  0.3721579  0.3497402  0.2675264
 [7]  0.2571315  0.2123516  0.0872545 -0.9087254

Largest  eigenvalues:
 [1] 100686623  96204911  90236622  86349195  85933155  84024063  82640005
 [8]  81536864  79876689  78492902

Smallest eigenvalues:
 [1]  0.25709191  0.20773856  0.18816360  0.13586418  0.10798095  0.03852193
 [7]  0.02163756 -0.10657031 -0.38902877 -0.39113221

Largest  eigenvalues:
 [1] 97962786 97177852 91204554 87453856 83910332 83684816 83071436 80588029
 [9] 79982093 77176841

Smallest eigenvalues:
 [1]  0.23437427  0.19959354  0.18937345  0.17051300  0.13882608 -0.01396215
 [7] -0.10656787 -0.23977589 -0.66053207 -0.74633591

Largest  eigenvalues:
 [1] 100688951  96970550  91036072  86620464  86402665  84094754  83237912
 [8]  81260138  80233082  77971581

Smallest eigenvalues:
 [1]  0.39539115  0.38491948  0.38317677  0.37115952  0.34755926  0.13455985
 [7]  0.11818590  0.02859528 -0.15486518 -0.16713950

Largest  eigenvalues:
 [1] 101464903  96415609  90436351  86115547  85857649  83436349  83034241
 [8]  81383073  79680016  78176041

Smallest eigenvalues:
 [1]  0.32181052  0.29800425  0.26860658  0.26126694  0.13959271  0.13234684
 [7]  0.11989553  0.09441495 -0.30411768 -0.37197913

Largest  eigenvalues:
 [1] 99272913 96154529 90791400 85592533 84541947 84031460 83034794 81909517
 [9] 80051732 78834820

Smallest eigenvalues:
 [1]  0.23763741  0.22498885  0.19990755  0.19477061  0.06445346 -0.01800488
 [7] -0.07818053 -0.17959615 -0.39533810 -0.51219625

Largest  eigenvalues:
 [1] 102580603  96734068  90517082  86660704  86622258  84227843  83180815
 [8]  81476213  80613448  78581549

Smallest eigenvalues:
 [1]  0.38655803  0.38053033  0.37836786  0.37447160  0.34251566  0.31336099
 [7]  0.20662509  0.20312479  0.02490699 -0.76132098

Largest  eigenvalues:
 [1] 100975974  96884353  90200365  87078794  85737971  83582689  83080706
 [8]  81070705  80166208  77944224

Smallest eigenvalues:
 [1]  0.30452042  0.26076954  0.24591417  0.20933430  0.20879046  0.12006577
 [7]  0.11093002  0.10421077 -0.05258623 -0.11677477

Largest  eigenvalues:
 [1] 98046924 97357580 90236940 86830032 85125294 84518639 82982591 81414080
 [9] 80253451 78326304

Smallest eigenvalues:
 [1]  0.35453342  0.34721438  0.31396398  0.25436984  0.21222583  0.18570879
 [7]  0.17974770  0.16935032 -0.06403733 -0.28670201

Largest  eigenvalues:
 [1] 100901761  98439209  92117787  87513390  86591803  85248430  84064220
 [8]  82635464  81333228  79881182

Smallest eigenvalues:
 [1]  0.30291194  0.29352072  0.27807454  0.24642630  0.16721350  0.13223166
 [7]  0.05848940  0.03110647 -0.17415915 -0.31237370

Largest  eigenvalues:
 [1] 99206653 96532968 90979201 86700362 83896114 83713637 83044172 81394988
 [9] 80109099 78018445

Smallest eigenvalues:
 [1]  0.30311467  0.28662159  0.20514807  0.20416644  0.17766178  0.14241885
 [7]  0.04313569 -0.04811775 -0.14723551 -0.43805896

Largest  eigenvalues:
 [1] 101484624  98259658  91842667  87784268  87095653  86361392  83678055
 [8]  82959433  81170121  80067975

Smallest eigenvalues:
 [1]  0.352469191  0.334595004  0.333016035  0.282206209  0.273129999
 [6]  0.249874447  0.242715658  0.178530461 -0.009845095 -0.035212668

Largest  eigenvalues:
 [1] 101179314  96377482  90500487  86121077  85594758  85129933  81983840
 [8]  81675278  79628776  78589350

Smallest eigenvalues:
 [1]  0.32187477  0.31711150  0.30079343  0.25019736  0.17840017  0.15371245
 [7]  0.15218466  0.04991640  0.04053776 -1.15377864

Largest  eigenvalues:
 [1] 98835537 96683404 90110651 86705912 84262716 83317116 82873178 80753057
 [9] 79684625 77432756

Smallest eigenvalues:
 [1]  0.46869881  0.41533301  0.30146510  0.29761191  0.25292186  0.24845649
 [7]  0.14603040  0.14203689  0.14073645 -0.06066743

Largest  eigenvalues:
 [1] 98312487 96530996 90043271 86662956 84414400 84151387 82658150 81286553
 [9] 79751922 78191785

Smallest eigenvalues:
 [1]  0.40722325  0.40587020  0.38908461  0.37695216  0.34354839  0.34192766
 [7]  0.28157473  0.12306142  0.05431251 -0.28492565

Largest  eigenvalues:
 [1] 99812417 97067209 90592236 86589785 85930944 84385994 83242951 81615158
 [9] 80037985 78537490

Smallest eigenvalues:
 [1]  0.3455527  0.3314203  0.3292558  0.3154814  0.2234377  0.2186212
 [7]  0.1724869  0.1548024 -0.1262626 -0.3177654

Largest  eigenvalues:
 [1] 98191025 97154803 90670897 86748933 84345006 83554780 82864815 80413533
 [9] 79946137 77448059

Smallest eigenvalues:
 [1]  0.332306158  0.327118441  0.257679499  0.214663146  0.205322934
 [6]  0.192454275  0.120975561 -0.002827462 -0.071015934 -0.225763956

Largest  eigenvalues:
 [1] 97852890 95569590 89472069 85485983 83942979 82683604 82166481 80129898
 [9] 79189124 77036463

Smallest eigenvalues:
 [1]  0.363993904  0.352198396  0.305208094  0.293656653  0.267788939
 [6]  0.092145809  0.072045715 -0.004516703 -0.200909374 -0.377911498

Largest  eigenvalues:
 [1] 102528153  96726632  90440910  86998267  86570636  84307025  82448692
 [8]  81482137  80157562  78901669

Smallest eigenvalues:
 [1]  0.28573037  0.25465013  0.24082600  0.20581372  0.13296159  0.11483030
 [7]  0.08728299  0.05801403 -0.27326674 -0.54683875

Largest  eigenvalues:
 [1] 100112079  95974471  90312484  85902115  84181482  83855105  82638373
 [8]  81437835  79843812  78124692

Smallest eigenvalues:
 [1]  0.41726805  0.37539765  0.34134341  0.33469012  0.27707074  0.24836518
 [7]  0.14073899 -0.03430227 -0.06985549 -0.09744168

Largest  eigenvalues:
 [1] 100125149  96940776  90427045  86810444  85601223  83919196  82892737
 [8]  80597307  80217406  77315787

Smallest eigenvalues:
 [1]  0.35943067  0.34771732  0.26697026  0.23575106  0.20975682  0.07241858
 [7]  0.07031827  0.03255753 -0.03004021 -0.63683594

Largest  eigenvalues:
 [1] 98176951 95855694 89868366 85716521 84250493 83576207 82547511 80650145
 [9] 79581857 77844258

Smallest eigenvalues:
 [1]  0.28557159  0.26551614  0.20700079  0.18209746  0.05065113  0.03942093
 [7] -0.12434641 -0.46087171 -0.46235863 -1.76492957

Largest  eigenvalues:
 [1] 100077096  96111195  90628436  85909160  85141567  83546863  82692603
 [8]  81186269  79790888  78086842

Smallest eigenvalues:
 [1]  0.4111483  0.3976203  0.3899111  0.3152590  0.2844035  0.2505617
 [7]  0.1305652  0.1212050  0.1033168 -0.1378011

Largest  eigenvalues:
 [1] 99797864 97089080 91148147 87114642 84556452 84300647 83274177 81589625
 [9] 80372537 78264324

Smallest eigenvalues:
 [1]  0.3981962  0.3915100  0.3087360  0.2800696  0.2657695  0.2197048
 [7]  0.1137246  0.0323599 -0.1035421 -0.3925046

Largest  eigenvalues:
 [1] 101217866  97054376  90976383  86474888  86319244  84343222  82996786
 [8]  81892272  79865724  78828586

Smallest eigenvalues:
 [1]  0.31907584  0.26461081  0.24424412  0.24124268  0.21878337  0.20317477
 [7]  0.05882125 -0.03371717 -0.16080534 -0.16909196

Largest  eigenvalues:
 [1] 100270889  96298468  90314915  86036619  85473291  83386635  82768166
 [8]  81110721  79674394  78109758

Smallest eigenvalues:
 [1]  0.322974616  0.289057372  0.256144347  0.221112409  0.201365784
 [6]  0.173328484  0.098822350 -0.001235241 -0.205880836 -0.348424094

Largest  eigenvalues:
 [1] 99247846 96545923 90800445 86694861 84103963 83458457 83221519 80904766
 [9] 80428559 77697529

Smallest eigenvalues:
 [1]  0.38964795  0.35431367  0.30614879  0.25479043  0.24739120  0.21091183
 [7]  0.03720553 -0.03017836 -0.23143603 -0.63521456

Largest  eigenvalues:
 [1] 99866998 95853008 89510093 86144748 85440584 83236861 82697758 80812974
 [9] 79563176 77652981

Smallest eigenvalues:
 [1]  0.4278225  0.3554092  0.2744333  0.2549966  0.2080785  0.1796390
 [7]  0.1720114  0.1236441 -0.3006015 -2.0346026

Largest  eigenvalues:
 [1] 100389684  97867325  91779092  87859077  85728815  84436443  84167199
 [8]  81944053  81203542  78948695

Smallest eigenvalues:
 [1]  0.27628790  0.24825376  0.22973939  0.19013909  0.14944336  0.11101696
 [7]  0.09605119  0.04553071 -0.02954497 -0.47174144

Largest  eigenvalues:
 [1] 99959915 97684741 91285233 86727062 85985063 84822032 83185092 82132222
 [9] 80007817 79048233

Smallest eigenvalues:
 [1]  0.4586213  0.4356107  0.4296516  0.3595828  0.3392151  0.2593681
 [7]  0.2081121  0.1499460  0.1321672 -0.3467527

Largest  eigenvalues:
 [1] 100032668  96454073  89929788  86566201  85320109  83907484  82520880
 [8]  81016567  80053027  78109317

Smallest eigenvalues:
 [1]  0.37401660  0.35299192  0.34660273  0.29139335  0.22928724  0.13283081
 [7] -0.03687561 -0.04373013 -0.10884025 -0.50693959

Largest  eigenvalues:
 [1] 101887158  96571551  90922154  87080143  86129900  84148089  82902701
 [8]  81719015  79920624  78478089

Smallest eigenvalues:
 [1]  0.25324256  0.24390059  0.24042318  0.21037344  0.10444766  0.09657504
 [7]  0.04774657  0.03866988 -0.02305990 -0.73335066

Largest  eigenvalues:
 [1] 99845827 96274593 89768098 86279661 86097051 84122010 82756492 81642906
 [9] 79551262 78363816

Smallest eigenvalues:
 [1]  0.25952697  0.25625951  0.24901677  0.22166837  0.14047541  0.09366133
 [7]  0.07579929  0.05913745  0.03263012 -0.03930151

Largest  eigenvalues:
 [1] 97230190 96859213 90344167 85788116 84310713 83410107 82365750 80199578
 [9] 79511159 76872913

Smallest eigenvalues:
 [1]  0.377682389  0.366795098  0.350204259  0.343668011  0.335416053
 [6]  0.140514283  0.104878472  0.046744973 -0.009289209 -0.183817665

Largest  eigenvalues:
 [1] 98036865 96519470 90046574 86770513 83818676 83678270 82880236 80883901
 [9] 80087804 77755691

Smallest eigenvalues:
 [1]  0.41340924  0.40592664  0.30104953  0.27654574  0.23550943  0.22383489
 [7]  0.21516928  0.05563605 -0.02222065 -0.02515350

Largest  eigenvalues:
 [1] 100624671  94961268  89339064  85383654  85150616  83403713  82044135
 [8]  81143069  79009458  77557667

Smallest eigenvalues:
 [1]  0.37696956  0.36206458  0.32771699  0.27784576  0.25140943  0.25009239
 [7]  0.24515108  0.10919220  0.06015397 -0.35363277

Largest  eigenvalues:
 [1] 99255327 96565905 89928233 86414858 84848455 83100742 82959381 80752947
 [9] 79571499 77578520

Smallest eigenvalues:
 [1]  0.453172460  0.434767575  0.423925150  0.406591966  0.355176310
 [6]  0.214539184  0.119763047  0.057494059  0.007929484 -0.687733849

Largest  eigenvalues:
 [1] 101723310  94876693  89674652  85797391  85251146  83131892  81970469
 [8]  80840817  79254368  77759348

Smallest eigenvalues:
 [1]  0.4507790  0.4130169  0.4026377  0.3753365  0.3571728  0.3431534
 [7]  0.3215998  0.2063801  0.2005658 -0.1656048

Largest  eigenvalues:
 [1] 99636062 96502443 90329448 86418834 84993051 84153691 82325849 81193672
 [9] 79786634 78187575

Smallest eigenvalues:
 [1]  4.080344e-01  3.899102e-01  3.327223e-01  3.099713e-01  2.427371e-01
 [6]  2.077694e-01  8.397607e-02 -4.113711e-05 -1.303795e-01 -2.282265e-01

Largest  eigenvalues:
 [1] 98693314 96591399 90050668 86410156 84300321 83036811 82594412 80252963
 [9] 79530475 77187704

Smallest eigenvalues:
 [1]  0.40816555  0.35098239  0.34943131  0.32001736  0.31357211  0.22871340
 [7]  0.16702336  0.09668769 -0.03566591 -0.15008584

Largest  eigenvalues:
 [1] 99746709 96096946 90357804 86594905 83839828 83503557 82914367 80875502
 [9] 79930388 77757554

Smallest eigenvalues:
 [1]  0.3067219  0.2878642  0.2868506  0.2729622  0.2635577  0.2501202
 [7]  0.1673381  0.1150373 -0.2070402 -0.2782853

Largest  eigenvalues:
 [1] 99896314 96541382 90053396 85970943 85826905 83394993 83119396 81285311
 [9] 79766616 78115813

Smallest eigenvalues:
 [1]  0.38952895  0.36599233  0.34030136  0.33864092  0.33726291  0.19689170
 [7]  0.16024410  0.09690631  0.09479776 -0.39220075

Largest  eigenvalues:
 [1] 100525698  96856986  90599566  86247700  85826123  84671025  83285939
 [8]  82110976  80398812  79134449

Smallest eigenvalues:
 [1]  0.449143928  0.409087978  0.408891749  0.361338504  0.313418767
 [6]  0.300932960  0.239251863  0.202284191 -0.008825494 -0.210481690

Largest  eigenvalues:
 [1] 100321684  96704281  90973381  86275423  85897483  83889489  83012778
 [8]  81378730  80093860  78347516

Smallest eigenvalues:
 [1]  0.2429087  0.2244373  0.2165091  0.1677806  0.1397006  0.1358201
 [7]  0.1124126 -0.0612381 -0.3202735 -0.3852067

Largest  eigenvalues:
 [1] 97274296 96796149 90165002 86842332 83744848 83545985 83391879 81355951
 [9] 80225509 77808512

Smallest eigenvalues:
 [1]  0.201515259  0.195937288  0.195769677  0.183496349  0.129163885
 [6]  0.093918476  0.068148830 -0.004682843 -0.260849965 -0.337359682

Largest  eigenvalues:
 [1] 99622690 96624333 90442226 86066789 85607733 83690048 83201759 80988805
 [9] 80056874 77868438

Smallest eigenvalues:
 [1]  0.24347053  0.19422175  0.18395027  0.16461483  0.15193739  0.13253342
 [7]  0.03672774 -0.09542403 -0.51484701 -2.88459197

Largest  eigenvalues:
 [1] 97671113 97282730 91210145 87175062 84602155 84460492 83336507 81263097
 [9] 80789266 78110652

Smallest eigenvalues:
 [1]  0.41563772  0.40135371  0.29373362  0.29113674  0.27563045  0.25013847
 [7]  0.13573349  0.13448045  0.06479809 -0.59213994

Largest  eigenvalues:
 [1] 100227496  96669698  90856256  86988401  85438243  84250775  82837042
 [8]  81462806  80185962  78639655

Smallest eigenvalues:
 [1]  0.37484661  0.37183664  0.32188823  0.24255355  0.21513574  0.16728868
 [7]  0.16181601  0.03835117 -0.04485363 -0.15669548

Largest  eigenvalues:
 [1] 100778812  96008010  89872430  86631543  85433844  84247367  82381155
 [8]  81540812  80020443  78538087

Smallest eigenvalues:
 [1]  0.38932276  0.34027222  0.30917936  0.26240392  0.23472337  0.20252948
 [7]  0.12977078  0.02302160 -0.08631194 -0.49892837

Largest  eigenvalues:
 [1] 99978302 96629214 89795661 86344218 86126199 83510648 82862504 80808469
 [9] 79902198 77928080

Smallest eigenvalues:
 [1]  0.38492639  0.32656522  0.30842612  0.30271984  0.23018713  0.09248447
 [7]  0.03068857 -0.16836597 -0.44606726 -0.81716592

Largest  eigenvalues:
 [1] 101692337  96174710  89914808  86371200  86053193  83331892  82964517
 [8]  80873759  80032349  77936425

Smallest eigenvalues:
 [1]  0.2302873  0.1470418  0.1312704  0.0271602 -0.0881455 -0.1027795
 [7] -0.1041649 -0.2075604 -0.3119751 -0.5068960

Largest  eigenvalues:
 [1] 99993529 96325023 90699705 85527482 85280096 83169131 82792332 81096518
 [9] 80078573 78226817

Smallest eigenvalues:
 [1]  0.18744523  0.13058936  0.10235315  0.06900952 -0.08161360 -0.20671691
 [7] -0.25101490 -0.53325805 -0.68114330 -0.86612294

Largest  eigenvalues:
 [1] 100653213  96148766  90531749  86402377  85492501  84226407  83277362
 [8]  81914492  80121459  78571749

Smallest eigenvalues:
 [1]  0.29407698  0.24180231  0.22236276  0.21254689  0.17567041  0.17284547
 [7]  0.08120150 -0.08693302 -0.18317307 -0.52064802

Largest  eigenvalues:
 [1] 100832092  96650495  90325466  86749979  85335025  84122265  82917483
 [8]  81421457  80345933  79003888

Smallest eigenvalues:
 [1]  0.264724915  0.258843811  0.195494610  0.184610529  0.088515470
 [6]  0.074309565  0.070999392  0.005328188 -0.124732863 -0.510606863

Largest  eigenvalues:
 [1] 99090567 98245541 91264745 87472478 85207490 83901145 83506328 80881842
 [9] 80319738 77599107

Smallest eigenvalues:
 [1]  0.277200359  0.268422037  0.265808825  0.250614237  0.222110378
 [6]  0.184631817  0.171212229  0.062031430 -0.006115577 -0.242918327

Largest  eigenvalues:
 [1] 98248985 95536017 90099901 85673315 84145439 83097797 82146941 80773034
 [9] 79004547 77325644

Smallest eigenvalues:
 [1]  0.27166956  0.26206803  0.26200433  0.22909717  0.22569074  0.21233238
 [7]  0.19328131  0.08194595  0.06850510 -0.44029953

Largest  eigenvalues:
 [1] 99545904 97664383 90991821 86921930 86116022 84113170 83468385 81701287
 [9] 80661948 78939909

Smallest eigenvalues:
 [1]  0.49263370  0.48892537  0.48226160  0.47728157  0.46201899  0.36719750
 [7]  0.18364653 -0.03835223 -0.06186405 -0.15636450

Largest  eigenvalues:
 [1] 100086755  97117772  90757907  86590835  85614187  83913922  83643923
 [8]  81366824  80476122  78320717

Smallest eigenvalues:
 [1]  0.39348412  0.36354909  0.33943151  0.31572349  0.28216984  0.12467170
 [7]  0.11318620  0.03912772 -0.12735329 -0.22818761

Largest  eigenvalues:
 [1] 101148275  96800842  90432169  86478185  86270065  83767656  83054250
 [8]  81361446  79924201  78332179

Smallest eigenvalues:
 [1]  0.40329922  0.36647583  0.35258265  0.29850903  0.27598431  0.23684841
 [7]  0.22174776  0.18389629 -0.04434122 -0.18925915

Largest  eigenvalues:
 [1] 99040882 97495889 90648621 86668296 85824282 84026148 83749449 81514765
 [9] 80313497 78251083

Smallest eigenvalues:
 [1]  0.3813611  0.3757567  0.3700627  0.2527970  0.2178727  0.1551922
 [7]  0.1539496  0.1356227 -0.1390212 -0.2505679

Largest  eigenvalues:
 [1] 101417838  97077264  90610871  87001198  86255021  84347372  82569053
 [8]  81315004  80022751  78541061

Smallest eigenvalues:
 [1]  0.3402880  0.3266425  0.3137778  0.3092483  0.2933842  0.1351560
 [7]  0.0852462 -0.1097143 -0.1452852 -0.3948485

Largest  eigenvalues:
 [1] 98994240 96068311 90021788 86216177 84135007 83495879 83398553 80988351
 [9] 80110106 77586769

Smallest eigenvalues:
 [1]  0.43791791  0.35005668  0.32257118  0.28767390  0.26560318  0.11048113
 [7]  0.10302134 -0.04881567 -0.16451591 -0.61562557

Largest  eigenvalues:
 [1] 100748707  97559421  90773956  86765083  86739104  84069552  83332761
 [8]  81216192  80480741  78135229

Smallest eigenvalues:
 [1]  0.4043422  0.3177594  0.2784231  0.2133265  0.1708052  0.1356024
 [7]  0.1063806 -0.1061425 -0.3245745 -0.4479671

Largest  eigenvalues:
 [1] 101088465  98012938  91491760  87103335  86974863  85056779  83794072
 [8]  82439630  80868958  79595643

Smallest eigenvalues:
 [1]  0.38536154  0.37811857  0.34988879  0.33522929  0.24079538  0.21059997
 [7]  0.16994271  0.15690070  0.09826273 -0.12992921

Largest  eigenvalues:
 [1] 99865629 96663461 89958666 86757419 85208582 84493959 82829475 81524590
 [9] 80246556 78532056

Smallest eigenvalues:
 [1]  0.49338410  0.46130421  0.29092271  0.28159190  0.26418500  0.16232420
 [7]  0.14546499  0.11954391  0.07641062 -0.08335265

Largest  eigenvalues:
 [1] 99095518 97559705 90856172 87389556 84912010 84475239 84178212 81920115
 [9] 80750953 78764136

Smallest eigenvalues:
 [1]  0.43359589  0.39525408  0.37295818  0.36851099  0.36717957  0.25495990
 [7]  0.23193364  0.04706044 -0.16496355 -0.23547278

Largest  eigenvalues:
 [1] 100979146  96760934  90216804  86955909  85901711  83736359  83567451
 [8]  81242317  80318405  78042261

Smallest eigenvalues:
 [1]  0.40018801  0.39909966  0.31738285  0.30590433  0.28671083  0.24230635
 [7]  0.11973661  0.10973128 -0.08889275 -0.18451396

Largest  eigenvalues:
 [1] 100293113  96752265  90346623  86358908  85730985  83223751  82740899
 [8]  80430259  79699411  77470363

Smallest eigenvalues:
 [1]  0.40202421  0.38881471  0.35932693  0.33676397  0.29138650  0.17240361
 [7]  0.14630249  0.06911886 -0.13262315 -0.50811128

Largest  eigenvalues:
 [1] 100832944  96431409  90353577  86205889  85747841  83495848  82696046
 [8]  80679546  79947946  77684708

Smallest eigenvalues:
 [1]  0.26356748  0.22451149  0.21447301  0.14232157  0.13137200 -0.07127335
 [7] -0.13443185 -0.33362772 -0.99837504 -1.18086786

Largest  eigenvalues:
 [1] 100390242  98173264  91893760  87500058  86828410  84880436  84328574
 [8]  82138988  81172268  78797919

Smallest eigenvalues:
 [1]  0.4800552  0.4462127  0.4354448  0.3948925  0.2379331  0.2322997
 [7]  0.2097992  0.1793300 -0.3530947 -0.5002601

Largest  eigenvalues:
 [1] 100981774  96558546  90758173  86707093  86050339  84256737  83570711
 [8]  81815479  80371989  78458984

Smallest eigenvalues:
 [1]  0.27571578  0.26065675  0.25578484  0.23576732  0.18466510  0.15187383
 [7] -0.02681751 -0.06218987 -0.08554207 -1.16660890

Largest  eigenvalues:
 [1] 101581680  97577060  90947364  87531363  86503107  83579168  83332011
 [8]  81221729  80484020  78278402

Smallest eigenvalues:
 [1]  0.3904782  0.3594291  0.3052958  0.2793544  0.2485757  0.2453688
 [7]  0.1745193  0.1448788 -0.1491973 -0.1536200

Largest  eigenvalues:
 [1] 99291814 96249964 90451849 86545287 83949247 83493776 82871926 80878488
 [9] 80000935 77843866

Smallest eigenvalues:
 [1]  0.3510358  0.3384971  0.2866311  0.2706063  0.2438889  0.2400042
 [7]  0.2266962  0.2144901 -0.2704189 -0.5343419

Largest  eigenvalues:
 [1] 99922899 96592092 90153468 85977694 85844645 84214918 82752700 81633795
 [9] 79530021 78308814

Smallest eigenvalues:
 [1]  0.4733122  0.4319661  0.3873925  0.3771174  0.3625619  0.3438730
 [7]  0.2243310  0.1794688  0.1773776 -0.1116724

Largest  eigenvalues:
 [1] 101970919  97791950  91585622  87189810  87172412  85360336  83643751
 [8]  82568142  80807703  79398275

Smallest eigenvalues:
 [1]  0.393039968  0.368643853  0.322298292  0.309749702  0.285880793
 [6]  0.282593643  0.268126063  0.194275494  0.164836530 -0.003649929

Largest  eigenvalues:
 [1] 98286634 97646409 90092264 87045466 84526804 83575419 83078846 80482249
 [9] 79939778 77654994

Smallest eigenvalues:
 [1]  0.38365932  0.37383337  0.34581177  0.28814205  0.28425873  0.22996887
 [7]  0.21079233  0.14885063  0.07927317 -0.05774738

Largest  eigenvalues:
 [1] 96888799 95893791 89510568 85933737 84050549 83440507 82893314 81102668
 [9] 79365895 77689381

Smallest eigenvalues:
 [1]  0.311420340  0.300188349  0.295505927  0.252008741  0.181267958
 [6]  0.108202712  0.029094620 -0.006237588 -0.038084783 -0.045977090

Largest  eigenvalues:
 [1] 98781381 96440684 90263526 86244606 84560070 83286834 82018701 80024254
 [9] 79678212 76733335

Smallest eigenvalues:
 [1]  0.39618532  0.37107574  0.35440561  0.34575269  0.23565279  0.20986112
 [7]  0.12936175  0.11495936  0.04073679 -0.42503105

Largest  eigenvalues:
 [1] 98620297 96919526 90063787 86732977 84629115 82889180 82558833 80006530
 [9] 79415205 77047451

Smallest eigenvalues:
 [1]  0.44735863  0.44641456  0.37255313  0.32364501  0.29331807  0.29022188
 [7]  0.23849349  0.02658452 -0.20918793 -0.59785198

Largest  eigenvalues:
 [1] 101056305  96996973  91054832  86710358  86100263  84533323  83184887
 [8]  82195266  80473665  79260218

Smallest eigenvalues:
 [1]  0.36241386  0.31138308  0.29292265  0.23617172  0.22013910  0.21675891
 [7]  0.15521651  0.10960781  0.03415315 -0.58779559

Largest  eigenvalues:
 [1] 101126333  96863151  90994802  86227800  86093682  84397758  82785691
 [8]  81685588  80365588  78695393

Smallest eigenvalues:
 [1]  0.506219235  0.417583088  0.346790814  0.332654503  0.317417865
 [6]  0.266494843  0.129736341  0.090086620  0.016767973 -0.008225712

Largest  eigenvalues:
 [1] 99381178 96437029 89975891 86274652 85570088 83339908 82528139 80251657
 [9] 79925509 77270287

Smallest eigenvalues:
 [1]  0.3439869  0.2665879  0.2534117  0.2417891  0.1754622  0.1615696
 [7]  0.1331950  0.0540091 -0.1143302 -0.6108836

Largest  eigenvalues:
 [1] 99073826 96700227 90978605 86337679 85072132 84380848 83281173 81916588
 [9] 80447986 78857262

Smallest eigenvalues:
 [1]  0.293402028  0.278644806  0.276265665  0.240825291  0.191697310
 [6]  0.128571887  0.102248489  0.004756226 -0.043267861 -0.527282814

Largest  eigenvalues:
 [1] 99882661 98129168 91292878 87586988 85730423 84926281 83523043 81873661
 [9] 80428391 78404257

Smallest eigenvalues:
 [1]  0.379407283  0.362086914  0.346272677  0.308077854  0.286368418
 [6]  0.283776227  0.202448530  0.129322070  0.009221141 -0.039161630

Largest  eigenvalues:
 [1] 98100239 95520350 89375854 85675253 84912679 83311565 82136337 80559403
 [9] 79253112 77508797

Smallest eigenvalues:
 [1]  0.4100102  0.3463401  0.3195339  0.3109376  0.2942632  0.2868886
 [7]  0.2791449  0.1249521 -0.0497405 -0.4112079

Largest  eigenvalues:
 [1] 99560966 95801734 90028359 85178451 84934083 83419193 82516631 80993146
 [9] 79630875 77892340

Smallest eigenvalues:
 [1]  0.2547524  0.2527505  0.2282470  0.2022748  0.1964301  0.1761039
 [7] -0.1720405 -0.3822107 -0.4299169 -0.6946195

Largest  eigenvalues:
 [1] 100708551  95602974  89658119  85451577  85323963  83347000  81973268
 [8]  80597570  79162671  77506090

Smallest eigenvalues:
 [1]  0.39484395  0.36896472  0.34554784  0.30024134  0.25104791  0.21104823
 [7]  0.18564306  0.12105521 -0.06337661 -0.11010582

Largest  eigenvalues:
 [1] 99723297 96361411 89807508 86075249 85378135 83795462 82235628 80751911
 [9] 79425592 77665325

Smallest eigenvalues:
 [1]  0.36284785  0.35740650  0.33983036  0.29340283  0.27773649  0.25658583
 [7]  0.22541331  0.14350461  0.01495241 -0.13980115

Largest  eigenvalues:
 [1] 101359059  97865910  91410205  86940631  86659298  84950120  83218493
 [8]  82184588  80381962  79064494

Smallest eigenvalues:
 [1]  0.43793085  0.39760352  0.39074365  0.34187650  0.34000102  0.33852246
 [7]  0.24277200  0.21697439  0.09572884 -0.34370367

Largest  eigenvalues:
 [1] 99219476 97108852 90424475 86727963 85708827 83794399 83475852 81306494
 [9] 80229615 77998140

Smallest eigenvalues:
 [1]  0.4972526  0.4639053  0.4385339  0.4284383  0.3638186  0.2602172
 [7]  0.2419404  0.1053181 -0.0941487 -0.3227498

Largest  eigenvalues:
 [1] 101822862  96408557  90340843  86922257  86340829  84112911  82873961
 [8]  81403520  80162161  78314967

Smallest eigenvalues:
 [1]  0.331858671  0.320957571  0.247665006  0.238869900  0.220157655
 [6]  0.211447520  0.208976691 -0.002574907 -0.166582416 -0.887740275

Largest  eigenvalues:
 [1] 99632081 97388221 91381184 87089156 85244696 84219380 83587030 81557863
 [9] 81006529 78211664

Smallest eigenvalues:
 [1]  0.36788190  0.32001120  0.31545956  0.31376330  0.24545454  0.19928379
 [7]  0.18519352  0.02475088 -0.01013018 -0.37512035

Largest  eigenvalues:
 [1] 102647292  96490275  90359486  87643116  86099837  84514729  82453163
 [8]  81840563  79922282  78958143

Smallest eigenvalues:
 [1]  0.3403537  0.3226680  0.2740128  0.2722914  0.2644779  0.2058532
 [7]  0.2050473  0.1799879 -0.1157739 -0.4702667

Largest  eigenvalues:
 [1] 99144565 96526106 90596256 86778793 84295126 84111618 83124020 81770148
 [9] 80025736 78757240

Smallest eigenvalues:
 [1]  0.37273813  0.31265552  0.30724930  0.29208617  0.12161757  0.11522665
 [7]  0.10921576  0.03942921 -0.11088957 -0.29827369

Largest  eigenvalues:
 [1] 99445561 96840434 90979856 85891147 85624261 83233686 82963795 80850504
 [9] 79762985 77757864

Smallest eigenvalues:
 [1]  0.21507247  0.21298813  0.19395247  0.12737758  0.09687688  0.07474328
 [7]  0.01717948  0.01104912 -0.08148290 -0.47219891

Largest  eigenvalues:
 [1] 97888482 97703120 91477933 87356903 84198046 84120936 83988286 81544958
 [9] 80593040 77878761

Smallest eigenvalues:
 [1]  0.37308596  0.35387240  0.29954254  0.27456920  0.23744850  0.20289497
 [7]  0.18591032  0.02410526 -0.09735906 -0.56366714

Largest  eigenvalues:
 [1] 99698470 96799376 90359588 86500388 85084278 83818599 83175088 81512281
 [9] 80280527 78611201

Smallest eigenvalues:
 [1]  0.34892941  0.30570820  0.27228825  0.20866940  0.18211246  0.18199969
 [7]  0.13957301  0.04012145 -0.16965244 -0.26689151

Largest  eigenvalues:
 [1] 97389063 96265473 89953125 86231064 83986486 83280922 82689191 80534935
 [9] 79766553 77147379

Smallest eigenvalues:
 [1]  0.37680995  0.34035917  0.31604257  0.27570143  0.20309732  0.18452736
 [7]  0.16348719  0.10820788  0.02574604 -0.50124354

Largest  eigenvalues:
 [1] 99646367 96788510 90390061 86588350 85510505 83555549 83176716 81156657
 [9] 80445605 78266078

Smallest eigenvalues:
 [1]  0.198487040  0.194549255  0.155245100  0.152756827  0.029231457
 [6] -0.006804909 -0.013351996 -0.121656373 -0.232257020 -0.500016815

Largest  eigenvalues:
 [1] 99240414 96292483 90691690 85967065 84001631 83101233 82837370 80658859
 [9] 79844506 77389724

Smallest eigenvalues:
 [1]  0.4267451893  0.4233246475  0.4021618790  0.3852301182  0.3708822417
 [6]  0.2731831692 -0.0007449758 -0.0074197543 -0.0529398758 -0.1992280678

Largest  eigenvalues:
 [1] 100570511  95148407  88976913  85919313  85527341  82772333  82523271
 [8]  80709668  79169621  77521104

Smallest eigenvalues:
 [1]  0.29090479  0.28820215  0.26432088  0.24056216  0.21820681  0.15305127
 [7]  0.13148121  0.02415131 -0.29209458 -0.39016864

Largest  eigenvalues:
 [1] 99001937 95491620 89269398 85456689 84621355 83065149 82521233 80438351
 [9] 79430348 77409064

Smallest eigenvalues:
 [1]  0.28404874  0.27036254  0.23151940  0.13913560  0.13131545  0.06670308
 [7] -0.04230993 -0.12395241 -0.14779080 -0.74805357

Largest  eigenvalues:
 [1] 100884631  97753043  91364766  86991891  86418275  84273222  83607786
 [8]  81827050  80474251  78734563

Smallest eigenvalues:
 [1]  0.4328600  0.4245368  0.4161147  0.4063520  0.3905964  0.3048738
 [7]  0.2307820  0.1584419  0.1256102 -0.1080835

Largest  eigenvalues:
 [1] 99831633 95908065 90059593 85734566 85230668 83701243 82267580 81102798
 [9] 79342012 78078385

Smallest eigenvalues:
 [1]  0.44679600  0.42377007  0.42075692  0.34206124  0.33230111  0.31449920
 [7]  0.22472654  0.20365782  0.08851559 -0.33627441

Largest  eigenvalues:
 [1] 100393817  97254427  90762479  86450057  86218972  84411331  83198256
 [8]  81836676  80040540  78737205

Smallest eigenvalues:
 [1]  0.190997265  0.186162773  0.182402608  0.160308937  0.083751504
 [6]  0.070974593  0.002285711 -0.011662083 -0.376131535 -0.948477094

Largest  eigenvalues:
 [1] 98524063 97254307 90755260 86866121 84913397 83980115 83596797 81657475
 [9] 80549619 78339363

Smallest eigenvalues:
 [1]  0.35947341  0.33645326  0.26217516  0.23367938  0.20683331  0.19621870
 [7]  0.16525453  0.11428263  0.05841062 -0.42754018

Largest  eigenvalues:
 [1] 99877032 97627347 90556755 87338228 84997829 84706766 83291459 81609259
 [9] 80698739 78454036

Smallest eigenvalues:
 [1]  0.247307854  0.243469569  0.237687753  0.216629177  0.202754675
 [6]  0.092330960  0.004475102 -0.054947023 -0.140016597 -0.232351759

Largest  eigenvalues:
 [1] 100186554  96168805  90329236  85635886  84647593  83768200  82599229
 [8]  81253919  79743218  77950176

Smallest eigenvalues:
 [1]  0.25972182  0.25059425  0.17261335  0.14187451  0.10833977  0.04218391
 [7] -0.03277217 -0.16094434 -0.42070023 -1.25671433

Largest  eigenvalues:
 [1] 100001529  97393912  91026739  86624232  86264630  83935050  82844603
 [8]  81412331  80074245  78462878

Smallest eigenvalues:
 [1]  0.35806642  0.35520400  0.23062769  0.22569461  0.20317648  0.15623837
 [7]  0.07324149  0.04390717 -0.11820527 -0.17180659

Largest  eigenvalues:
 [1] 99597645 97275510 90177420 86548833 85643354 83616296 83418027 80804323
 [9] 80181309 77766173

Smallest eigenvalues:
 [1]  0.28701483  0.23194268  0.22903914  0.21306152  0.19508947  0.16958079
 [7]  0.06159995 -0.32740951 -0.47267045 -0.61831650

Largest  eigenvalues:
 [1] 100976543  96134201  89826239  86429337  85741143  83532179  82981773
 [8]  80981013  79783573  77805706

Smallest eigenvalues:
 [1]  0.24279516  0.23622489  0.23012926  0.22570586  0.18211526  0.11449491
 [7]  0.09994666  0.06484078 -0.09762873 -0.43075741

Largest  eigenvalues:
 [1] 99279965 96751850 90718636 86323690 85319956 83611826 83276585 80961642
 [9] 80354313 77622645

Smallest eigenvalues:
 [1]  0.38794686  0.33809405  0.30313295  0.22434297  0.21235466  0.18180557
 [7]  0.10457038  0.06234384 -0.09688636 -0.39290492

Largest  eigenvalues:
 [1] 98984532 95681934 89048401 86023564 83950188 83116340 81927294 80310615
 [9] 79358089 76989419

Smallest eigenvalues:
 [1]  0.24836266  0.21266743  0.10305982  0.09731136  0.06365286  0.02732050
 [7]  0.02411234 -0.21930789 -0.25479932 -0.29050692

Largest  eigenvalues:
 [1] 99679786 96173093 90449520 85134128 84931584 83717569 82811696 81211423
 [9] 79909550 78290420

Smallest eigenvalues:
 [1]  0.45385413  0.39321620  0.34867710  0.33821243  0.33460574  0.26115108
 [7]  0.10940122  0.09625644 -0.01033738 -0.13699444

Largest  eigenvalues:
 [1] 99427503 97358968 90294885 86986612 85684684 83737764 83266973 80811354
 [9] 80074421 77467855

Smallest eigenvalues:
 [1]  0.42410989  0.38361422  0.34560381  0.33895464  0.32301962  0.30356709
 [7]  0.29681884  0.26066376  0.02122969 -0.18259312

Largest  eigenvalues:
 [1] 99955807 97428657 90937329 86637689 86248007 84847013 83170518 81997996
 [9] 80175256 78871810

Smallest eigenvalues:
 [1]  0.44245899  0.42751626  0.40490803  0.31406116  0.30340180  0.27662559
 [7]  0.24855024  0.19542661  0.11076843 -0.08850199

Largest  eigenvalues:
 [1] 101204554  96257271  90711391  86457056  85501447  84439312  82580171
 [8]  81819902  79778863  78464867

Smallest eigenvalues:
 [1]  0.31588335  0.29136636  0.28642596  0.27020694  0.26662616  0.16006694
 [7]  0.14925996  0.14711091  0.04028025 -0.23175618

Largest  eigenvalues:
 [1] 99460005 97456416 90900324 86572903 85421556 84162030 82976620 81375688
 [9] 79935294 78040747

Smallest eigenvalues:
 [1]  0.39565615  0.37680723  0.35811189  0.33834702  0.30986179  0.28168920
 [7]  0.23649542  0.11038323  0.07549815 -0.64563451

Largest  eigenvalues:
 [1] 100133693  97300735  90510679  86748829  86605075  85078644  83551626
 [8]  82277764  80423095  79057297

Smallest eigenvalues:
 [1]  0.25586073  0.24256663  0.20329761  0.16748236  0.10756114  0.08208523
 [7] -0.14255647 -0.17277764 -0.22898239 -0.38131806

Largest  eigenvalues:
 [1] 98877224 96823835 89754841 86319487 85298803 84210817 82955018 81264358
 [9] 80057130 78459494

Smallest eigenvalues:
 [1]  0.3230090  0.2943943  0.2928252  0.2698441  0.2555536  0.1605081
 [7]  0.1258876 -0.2555022 -0.2563254 -0.5642405

Largest  eigenvalues:
 [1] 100029797  96809429  90548057  86409947  85841085  83754786  83625660
 [8]  81369979  80406427  78344727

Smallest eigenvalues:
 [1]  0.46013335  0.45172698  0.37933118  0.35477214  0.33368496  0.33212310
 [7]  0.23573405  0.21858632  0.08841917 -0.01647791

Largest  eigenvalues:
 [1] 98741796 96664446 90100381 86584721 84688271 83574991 82908023 80627864
 [9] 79901763 77268093

Smallest eigenvalues:
 [1]  0.3779101  0.3721540  0.3415406  0.3081000  0.2855563  0.2656054
 [7]  0.2484234  0.1810401 -0.1259701 -0.5919691

Largest  eigenvalues:
 [1] 99105214 96123828 89948032 86626069 84050761 83186947 82847873 80233426
 [9] 79819175 77151568

Smallest eigenvalues:
 [1]  0.352348739  0.290859846  0.284488355  0.266559664  0.257935947
 [6]  0.193266438  0.009113708 -0.012312298 -0.019982819 -0.350382423

Largest  eigenvalues:
 [1] 99275851 98075499 91210454 87748557 85703596 84956508 83390584 81180174
 [9] 80873916 78117211

Smallest eigenvalues:
 [1]  0.40740684  0.34125705  0.28032934  0.27970711  0.26223554  0.17809201
 [7]  0.10190274  0.04231496  0.00806742 -0.80720759

Largest  eigenvalues:
 [1] 99715109 95379477 89691581 85853106 84475245 83260431 81933265 80609732
 [9] 79169886 77314398

Smallest eigenvalues:
 [1]  0.377260491  0.326692777  0.321614025  0.307795325  0.286824766
 [6]  0.078509067  0.048341098  0.009870761 -0.265951462 -0.543595123

Largest  eigenvalues:
 [1] 100861640  96260824  90046190  85922546  85834778  83940120  82146502
 [8]  81012453  79789192  77995383

Smallest eigenvalues:
 [1]  0.304449301  0.293732995  0.288601735  0.285795259  0.083624387
 [6]  0.082763101  0.073632232 -0.009529578 -0.132864793 -0.681461786

Largest  eigenvalues:
 [1] 99671057 95844936 90057854 85481707 84732712 82727493 82174569 80102899
 [9] 79318588 77107175

Smallest eigenvalues:
 [1]  0.46845287  0.43155178  0.42104952  0.39154198  0.38805607  0.32539189
 [7]  0.21714954  0.18806339  0.03685169 -0.12523500

Largest  eigenvalues:
 [1] 100123496  96151552  89660750  86352522  84853409  83151390  82439092
 [8]  80486149  79406546  77041972

Smallest eigenvalues:
 [1]  0.234963129  0.215578717  0.159159208  0.094570242  0.073241427
 [6]  0.057668746  0.001049839 -0.034124153 -0.046536557 -1.350489856

Largest  eigenvalues:
 [1] 102702822  97185491  91703988  87838422  86480263  85145899  83218522
 [8]  82454254  80443827  79106450

Smallest eigenvalues:
 [1]  0.36345346  0.30941397  0.25829211  0.24709930  0.24199553  0.18688051
 [7]  0.11249785  0.05197606 -0.14009560 -0.19988168

Largest  eigenvalues:
 [1] 99638794 96426152 89938378 85762403 85289697 83238317 82326783 80696879
 [9] 79436937 77713524

Smallest eigenvalues:
 [1]  0.2064835  0.2038126  0.1546624  0.1216712  0.0451268  0.0181933
 [7] -0.1072878 -0.3903535 -0.4671638 -1.0560489

Largest  eigenvalues:
 [1] 98184452 97553685 91070823 86898805 85213966 84681657 82980625 81204877
 [9] 80512739 77854518

Smallest eigenvalues:
 [1]  0.43006129  0.41948602  0.39302868  0.36717094  0.31140421  0.29346683
 [7]  0.25834340  0.17057346 -0.09687251 -0.14070740

Largest  eigenvalues:
 [1] 98950552 96608828 89558237 86644176 84919745 83108440 83022169 80581548
 [9] 79640043 77388041

Smallest eigenvalues:
 [1]  0.44421067  0.41728523  0.40631615  0.38573123  0.31705101  0.27197940
 [7]  0.24308161  0.14681293  0.06298365 -0.65569114

Largest  eigenvalues:
 [1] 99088612 96500805 90202450 86408842 84757276 83060922 82809392 80622844
 [9] 79834002 77555554

Smallest eigenvalues:
 [1]  0.3260899  0.2938251  0.2754448  0.2607610  0.2417266  0.2351440
 [7]  0.1956722  0.1130951 -0.2668751 -0.4026913

Largest  eigenvalues:
 [1] 101520109  97164022  90960803  86258191  86215708  83986764  82858126
 [8]  81446908  80072676  78283860

Smallest eigenvalues:
 [1]  0.471729760  0.445851319  0.380950250  0.375796247  0.275314041
 [6]  0.235208604  0.168679532  0.088743823 -0.006149734 -0.402542540

Largest  eigenvalues:
 [1] 100595255  96332790  90081730  86584230  86063565  84805234  82578697
 [8]  81869669  79873112  78807383

Smallest eigenvalues:
 [1]  0.392574909  0.323227841  0.264275981  0.252799316  0.238876125
 [6]  0.227615335  0.200830252  0.041784983 -0.006614034 -0.108080453

Largest  eigenvalues:
 [1] 100762607  96707435  90541590  86584934  85628613  85229283  83068335
 [8]  82270394  80231814  78984955

Smallest eigenvalues:
 [1]  0.40519056  0.37007143  0.32743284  0.31850236  0.31575536  0.28210140
 [7]  0.24574488  0.22704934  0.07715977 -0.03278965

Largest  eigenvalues:
 [1] 100240231  96424402  90179426  86214014  85569065  83626347  82334800
 [8]  80834413  79544488  77902464

Smallest eigenvalues:
 [1]  0.41225718  0.38215567  0.36886156  0.26053381  0.22753264  0.16553038
 [7]  0.10917071  0.06955956 -0.56813493 -0.59725692

Largest  eigenvalues:
 [1] 99824524 97281407 90775003 86522876 86363463 83719662 83471638 80944465
 [9] 80264267 77761691

Smallest eigenvalues:
 [1]  0.21474917  0.21037460  0.20895953  0.18273155  0.17798000  0.11727051
 [7]  0.02795542  0.01352027 -0.30015233 -0.53471066

Largest  eigenvalues:
 [1] 98833116 96859634 90718039 86612346 84966168 83705134 83534268 81244852
 [9] 80202804 77814034

Smallest eigenvalues:
 [1]  0.33054363  0.31714123  0.31127685  0.30968255  0.18828159  0.18696858
 [7]  0.07079336 -0.05126187 -0.21514980 -0.69903244

Largest  eigenvalues:
 [1] 100895559  95495595  89628997  85972704  85723392  83801830  81931669
 [8]  81130744  79290178  77871736

Smallest eigenvalues:
 [1]  0.30787214  0.27796940  0.25956291  0.25672811  0.20404935  0.11322161
 [7]  0.09856056 -0.11611236 -0.14190489 -0.23225321

Largest  eigenvalues:
 [1] 100951158  96861480  91035093  86119147  85608333  84141413  82542283
 [8]  81393987  80074680  78226729

Smallest eigenvalues:
 [1]  0.44443009  0.43524738  0.36923795  0.31517234  0.29267114  0.24828446
 [7]  0.22830373  0.06689916 -0.02593872 -0.24431659

Largest  eigenvalues:
 [1] 101042233  97670728  91169261  87110163  86472134  85295635  83329473
 [8]  82462170  80260519  79203703

Smallest eigenvalues:
 [1]  2.179788e-01  2.100277e-01  2.076166e-01  1.994445e-01  1.231648e-01
 [6]  3.651859e-02  4.330197e-05 -3.749344e-01 -4.338104e-01 -8.534398e-01

Largest  eigenvalues:
 [1] 99260075 96329449 90225616 85939512 85284896 84589449 83119924 81703875
 [9] 79953740 78409856

Smallest eigenvalues:
 [1]  0.28824889  0.28033143  0.22677680  0.21238950  0.18512684  0.09991076
 [7]  0.09185984  0.07305105 -0.02590437 -0.22247670

Largest  eigenvalues:
 [1] 97111755 97004984 89964628 86612650 83491548 83097118 82525378 80003343
 [9] 79570390 76870339

Smallest eigenvalues:
 [1]  0.418407311  0.415534907  0.386480525  0.379556646  0.280339956
 [6]  0.181208609  0.108048974 -0.001095688 -0.153554310 -0.214763853

Largest  eigenvalues:
 [1] 100567332  95263971  89702030  85304646  84703051  83147391  82604433
 [8]  80814607  79694823  77716387

Smallest eigenvalues:
 [1]  0.4956499  0.4760013  0.4670619  0.3805585  0.3481619  0.3148870
 [7]  0.2722805  0.2324156  0.2058396 -0.1207783

Largest  eigenvalues:
 [1] 100310975  96384137  90198434  86346192  86112040  83594443  83040168
 [8]  81126391  79824167  77749250

Smallest eigenvalues:
 [1]  0.20448030  0.18144414  0.17740617  0.16937166  0.15550766  0.11872069
 [7]  0.09445057 -0.07012099 -0.10272554 -0.13203024

Largest  eigenvalues:
 [1] 99405212 95748036 89940197 85699934 84857378 83998991 82631351 81390858
 [9] 79466973 78315757

Smallest eigenvalues:
 [1]  0.4451035  0.4266185  0.3914764  0.3860346  0.3414694  0.2951384
 [7]  0.1540427  0.1252575  0.1008103 -0.5550346

Largest  eigenvalues:
 [1] 99765650 95582564 89332909 85774827 85055904 83098730 82561010 80719186
 [9] 79497425 77683525

Smallest eigenvalues:
 [1]  0.3160270  0.2892428  0.2747357  0.2288929  0.2265579  0.2079793
 [7]  0.1217725  0.0316530 -0.1088142 -0.3470824

Largest  eigenvalues:
 [1] 99040206 96422647 90697487 85858616 85469413 84761903 82982737 81800592
 [9] 80064562 78784216

Smallest eigenvalues:
 [1]  0.4651646  0.3107724  0.3101555  0.2824105  0.2178087  0.2160932
 [7]  0.1095507  0.0721208 -0.3617690 -0.5908036

Largest  eigenvalues:
 [1] 100362525  96904267  91268895  86132560  86006762  83557376  83390343
 [8]  81288675  80243744  78378847

Smallest eigenvalues:
 [1]  0.38868526  0.34683812  0.32353636  0.32238483  0.24837171  0.18955717
 [7]  0.13432165  0.04198960 -0.06460492 -0.23390628

Largest  eigenvalues:
 [1] 99919675 96820131 90125085 86445168 85794325 84237649 82937776 81578278
 [9] 79835306 78269959

Smallest eigenvalues:
 [1]  0.37311825  0.36972448  0.34270298  0.34008906  0.33211904  0.17576808
 [7]  0.16723274  0.12966235  0.08624482 -0.02075481

Largest  eigenvalues:
 [1] 100086518  95902673  90119445  85842675  84581413  84272580  82596578
 [8]  81703288  80025570  78681901

Smallest eigenvalues:
 [1]  0.30881388  0.27243168  0.25884345  0.23250052  0.19309561  0.16723259
 [7]  0.10246137  0.04040194 -0.14089564 -0.25350740

Largest  eigenvalues:
 [1] 99657533 97532976 90747322 86626788 85641425 84391298 83386709 81503493
 [9] 80568493 78390741

Smallest eigenvalues:
 [1]  0.24463514  0.21844144  0.18165696  0.17303054  0.13643230  0.05197567
 [7] -0.04922595 -0.06065563 -0.08286892 -0.63467387

Largest  eigenvalues:
 [1] 98060817 96703834 90558880 86282344 83616317 83094716 82880062 80589608
 [9] 79737879 77146465

Smallest eigenvalues:
 [1]  0.21663736  0.19417719  0.17739353  0.13572463  0.13132323  0.10317923
 [7]  0.08028882 -0.07406903 -0.30661969 -0.33970460

Largest  eigenvalues:
 [1] 99896726 96453623 89998986 85923121 85418809 85305090 82235699 82048315
 [9] 79589906 78819091

Smallest eigenvalues:
 [1]  0.51327769  0.47274899  0.36001167  0.33464594  0.30419647  0.27134758
 [7]  0.21620494  0.19975064 -0.05327562 -0.21927458

Largest  eigenvalues:
 [1] 99554077 96970869 90513599 86752614 85478780 84137016 83109249 81307119
 [9] 80312570 78523084

Smallest eigenvalues:
 [1]  0.34245120  0.33703236  0.31645378  0.30957622  0.29882817  0.18180118
 [7]  0.15382880  0.01757532 -0.20525686 -0.26333565

Largest  eigenvalues:
 [1] 98819968 96536508 90173802 86464275 84920258 84158385 83064242 81550721
 [9] 80258485 78500536

Smallest eigenvalues:
 [1]  0.47149807  0.46933557  0.43265550  0.40862105  0.28662916  0.19070740
 [7]  0.18953012  0.15282231  0.03081602 -0.06932745

Largest  eigenvalues:
 [1] 98447453 97895091 91194764 87384178 84858116 84623625 83034910 80906728
 [9] 80576462 77632363

Smallest eigenvalues:
 [1]  0.31309406  0.22926712  0.22379404  0.20734590  0.13822084  0.11147504
 [7]  0.01610159 -0.07663903 -0.30658487 -1.14533747

Largest  eigenvalues:
 [1] 100063896  98569363  91840572  87619550  86992570  84620386  84132713
 [8]  81683606  80841963  78161452

Smallest eigenvalues:
 [1]  0.23699729  0.23574788  0.22415042  0.18785558  0.16502717  0.11216462
 [7]  0.01113985 -0.07831166 -0.35582282 -0.66083180

Largest  eigenvalues:
 [1] 99855928 97291562 91134981 87408119 85178122 84097459 83378486 81219289
 [9] 80756285 77792490

Smallest eigenvalues:
 [1]  0.40938699  0.40497708  0.38389218  0.32635873  0.28461028  0.19933101
 [7]  0.15149618  0.14903744 -0.01757108 -0.22750128

Largest  eigenvalues:
 [1] 98972156 96687780 90331592 85947453 85845368 83787374 82951271 81289427
 [9] 79566265 77802825

Smallest eigenvalues:
 [1]  0.35800394  0.31259346  0.31075941  0.26987087  0.19032206  0.09711144
 [7]  0.07420255 -0.00278496 -0.02229466 -0.05083056

Largest  eigenvalues:
 [1] 97654481 96591357 90118915 86282097 84164496 84013902 82634424 81237556
 [9] 79460941 77876820

Smallest eigenvalues:
 [1]  0.09394667  0.03464270  0.01420493  0.01394758 -0.05270145 -0.12205341
 [7] -0.15597161 -0.19860629 -0.46390066 -0.73604692

Largest  eigenvalues:
 [1] 98836111 96454337 89991742 85568270 85528688 84383824 82863591 81950467
 [9] 79424769 78517130

Smallest eigenvalues:
 [1]  0.32853099  0.32488451  0.30678680  0.28087943  0.24718031  0.14338928
 [7] -0.02343517 -0.03214751 -0.08411257 -0.60704692

Largest  eigenvalues:
 [1] 100384077  96641395  89685871  85842347  85380365  83393178  81681901
 [8]  80187571  78934890  76935248

Smallest eigenvalues:
 [1]  0.4313435  0.4150248  0.4097807  0.2934095  0.2311940  0.2203699
 [7]  0.1825480  0.1282958  0.1277575 -0.4107511

Largest  eigenvalues:
 [1] 99352215 96010157 89697132 85921731 84983810 83528410 82300190 80913603
 [9] 79534610 77749033

Smallest eigenvalues:
 [1]  0.4314470  0.4008653  0.3801594  0.3162361  0.2700170  0.2661314
 [7]  0.2191119  0.1767977 -0.1669867 -0.3904630

Largest  eigenvalues:
 [1] 101471359  95120397  89769489  85400105  84629324  82888008  81613822
 [8]  80521157  79326385  77820404

Smallest eigenvalues:
 [1]  0.39233761  0.35841107  0.34893938  0.27862364  0.19057811  0.05633138
 [7] -0.13416829 -0.17038230 -0.68389569 -1.49265958

Largest  eigenvalues:
 [1] 99861595 97551231 91390210 86941398 86360513 84490578 83845045 81693101
 [9] 80854582 78545998

Smallest eigenvalues:
 [1]  0.27228578  0.26075399  0.23250886  0.22587276  0.22433658  0.21678978
 [7]  0.21343736  0.14712862  0.01910522 -0.55556833

Largest  eigenvalues:
 [1] 99863374 96633282 90690760 85670239 85446954 83674163 82627108 81332909
 [9] 79701708 78136863

Smallest eigenvalues:
 [1]  0.41902382  0.31229784  0.29942695  0.28044150  0.27321020  0.23520273
 [7]  0.02549636 -0.09897169 -0.14524003 -0.23738846

Largest  eigenvalues:
 [1] 100117057  96078151  89647092  86359739  85386295  82425277  82137457
 [8]  79673602  79277254  76578930

Smallest eigenvalues:
 [1]  0.313430049  0.250841235  0.222226866  0.111620935  0.097479814
 [6]  0.062645253  0.062467936  0.007186818 -0.097425043 -0.189550821

Largest  eigenvalues:
 [1] 96454977 96264513 89950923 85510968 84103076 82875140 82773899 80106079
 [9] 79241447 77097145

Smallest eigenvalues:
 [1]  0.43801219  0.43195103  0.33991264  0.32067627  0.24395068  0.23884219
 [7]  0.23509164  0.23079284  0.01354983 -0.06906893

Largest  eigenvalues:
 [1] 100268014  95437137  89218950  85432872  84557123  82924115  81825278
 [8]  80289200  79118828  77169264

Smallest eigenvalues:
 [1]  0.35727265  0.34357011  0.33833948  0.33599097  0.21770200  0.20204036
 [7]  0.11892617  0.09337013  0.02774419 -0.38989145

Largest  eigenvalues:
 [1] 98678682 96582434 90875657 86157545 84469035 83570950 83294510 81169433
 [9] 80248695 77876590

Smallest eigenvalues:
 [1]  0.34504011  0.33240924  0.29920790  0.25345707  0.11818112  0.08088973
 [7]  0.00466336 -0.12445963 -0.39288758 -1.11295579

Largest  eigenvalues:
 [1] 99487526 97497026 91416960 87228282 85494876 83994299 83674735 81552643
 [9] 80850089 78674596

Smallest eigenvalues:
 [1]  0.22451401  0.20716344  0.18076921  0.15532263  0.13958293  0.10940484
 [7] -0.03693148 -0.20207682 -0.31562009 -0.71839444

Largest  eigenvalues:
 [1] 99131684 96613556 90677841 86771170 84403972 83827670 83274666 81091855
 [9] 80355039 77447836

Smallest eigenvalues:
 [1]  0.4411756  0.4348785  0.4176587  0.3883593  0.3433553  0.2834340
 [7]  0.2757746  0.2216968  0.1718022 -0.2249895

Largest  eigenvalues:
 [1] 100530481  98120690  91249223  87475784  86820402  85058625  83767097
 [8]  82076360  80932534  79291314

Smallest eigenvalues:
 [1]  0.40701262  0.36444763  0.31798034  0.25170800  0.24253319  0.23246722
 [7]  0.19037237  0.02353331 -0.01980566 -0.22281943

Largest  eigenvalues:
 [1] 99845822 95658921 89016624 86086192 85597304 83460777 81663203 80292147
 [9] 79241119 77504940

Smallest eigenvalues:
 [1]  0.42938860  0.42232802  0.38569818  0.35964695  0.33818541  0.20711774
 [7]  0.19604398 -0.01116782 -0.04836319 -0.53445122

Largest  eigenvalues:
 [1] 101518396  94843250  89187008  85484258  84811305  82791289  81557457
 [8]  80374253  79213162  77397827

Smallest eigenvalues:
 [1]  0.36791286  0.34202708  0.32387201  0.31664417  0.28536432  0.17959381
 [7]  0.16217525  0.02244408 -0.22787515 -0.43247088

Largest  eigenvalues:
 [1] 100703462  97275422  91144866  87125103  85610313  83823161  83707504
 [8]  81483061  80394763  78061853

Smallest eigenvalues:
 [1]  0.5107679  0.4504307  0.3862566  0.3419404  0.3312794  0.2159643
 [7]  0.1122371  0.1102816 -0.2765152 -0.3566640

Largest  eigenvalues:
 [1] 99078199 96680604 90302250 86910674 84734243 83850855 82994355 80314676
 [9] 80063684 76824722

Smallest eigenvalues:
 [1]  0.33584651  0.33415630  0.32597759  0.30133554  0.22612872  0.22086517
 [7]  0.20920614  0.03269466 -0.15333993 -0.38172266

Largest  eigenvalues:
 [1] 99820028 97404656 90906689 87495730 85379794 83847134 83510644 81360701
 [9] 80530741 78630872

Smallest eigenvalues:
 [1]  0.301103904  0.294335396  0.259228732  0.192033088  0.181042400
 [6]  0.143889505  0.079508826  0.003081642 -0.144245990 -0.199709327

Largest  eigenvalues:
 [1] 100435240  96489309  90450238  86025577  85977384  83498022  82882485
 [8]  81189264  79561519  77670875

Smallest eigenvalues:
 [1]  0.42058418  0.38554597  0.34851068  0.34202552  0.26997938  0.26894196
 [7]  0.25655286  0.19736059  0.17361859 -0.04413678

Largest  eigenvalues:
 [1] 99023161 96328445 89498440 85939871 85019576 83613597 82511049 80909543
 [9] 79519530 77831932

Smallest eigenvalues:
 [1]  0.303192171  0.284061189  0.276148216  0.222682643  0.138140092
 [6]  0.075580999  0.030817723  0.002024801 -0.177952722 -0.521314087

Largest  eigenvalues:
 [1] 98725310 97580545 90253903 87267628 84928209 84775015 83481571 81797897
 [9] 80483111 78610177

Smallest eigenvalues:
 [1]  0.428196559  0.415758367  0.365618094  0.295780025  0.123686959
 [6]  0.085966011 -0.002675043 -0.005514798 -0.041399761 -0.607787564

Largest  eigenvalues:
 [1] 102246914  97222191  91532156  87259224  86631117  85115018  83364369
 [8]  82330333  80937789  79645197

Smallest eigenvalues:
 [1]  0.36001287  0.34460250  0.33253890  0.31142534  0.27089841  0.14060762
 [7]  0.13114054  0.07209750 -0.08634331 -0.10732603

Largest  eigenvalues:
 [1] 98960149 96631249 90166884 86295350 85633049 84523381 83360410 81636240
 [9] 80434764 78751342

Smallest eigenvalues:
 [1]  0.40110068  0.40027748  0.36613797  0.30691530  0.29299316  0.24761910
 [7]  0.19348533  0.18056832 -0.06352012 -0.39490320

Largest  eigenvalues:
 [1] 99190839 97048944 90358567 86920677 85502055 84489028 83120603 81592879
 [9] 80147074 78063945

Smallest eigenvalues:
 [1]  0.23402296  0.20905008  0.15574005  0.14781863  0.12052754  0.03904151
 [7] -0.10691209 -0.23401472 -0.28549672 -0.99044935

Largest  eigenvalues:
 [1] 99852865 96104803 89936406 85870498 85648658 83073587 82628393 80266874
 [9] 79838077 77168405

Smallest eigenvalues:
 [1]  0.39287275  0.35641504  0.31726594  0.29033461  0.24813164  0.23218553
 [7]  0.20493214  0.11985202 -0.09807594 -0.32267281

Largest  eigenvalues:
 [1] 100785766  97954033  91459099  87305294  85739899  84749753  83584723
 [8]  82068323  80623709  78907177

Smallest eigenvalues:
 [1]  0.44039214  0.38914058  0.33762984  0.27897675  0.25412127  0.22211749
 [7]  0.17817647  0.15202289  0.01488218 -0.38695905

Largest  eigenvalues:
 [1] 99035829 95416130 89679895 85535195 84195744 83664067 82045703 81058725
 [9] 79311509 77559423

Smallest eigenvalues:
 [1]  0.40858082  0.40521180  0.30371451  0.29712132  0.27515423  0.25037619
 [7]  0.24976230 -0.07136325 -0.11142482 -0.29703450

Largest  eigenvalues:
 [1] 98290876 96847976 89861045 86704813 84829844 83418411 83184992 80727021
 [9] 79849618 77473252

Smallest eigenvalues:
 [1]  0.50001869  0.48056690  0.45702531  0.42109877  0.35495694  0.33042460
 [7]  0.26665534  0.20704247  0.04311262 -0.21360849

Largest  eigenvalues:
 [1] 98458955 95819253 89130851 86173134 84160807 82613242 82450887 79972690
 [9] 79304380 76704803

Smallest eigenvalues:
 [1]  0.41008871  0.36344470  0.34268481  0.29853210  0.25101946  0.24574792
 [7]  0.22968143  0.04133598 -0.30323964 -0.44287712

Largest  eigenvalues:
 [1] 98132036 96491732 90177666 87031928 84109503 83890086 82120280 80236934
 [9] 79500776 76348342

Smallest eigenvalues:
 [1]  0.41635527  0.39643040  0.34462347  0.29699288  0.27856264  0.27633244
 [7]  0.21301526 -0.03490948 -0.07132088 -0.14723872

Largest  eigenvalues:
 [1] 100182234  97458515  90841058  87326625  85193836  83740341  83566000
 [8]  81157167  80434009  78044381

Smallest eigenvalues:
 [1]  0.5011361  0.4473885  0.4085632  0.3734306  0.3569594  0.3425141
 [7]  0.3147804  0.1579448 -0.1015685 -0.1517036

Largest  eigenvalues:
 [1] 99997485 97337152 90526962 87366636 85435426 83885100 83615386 81339841
 [9] 80533277 78148861

Smallest eigenvalues:
 [1]  0.26944587  0.26677659  0.25188427  0.19706187  0.19094033  0.16749463
 [7]  0.04769111 -0.04008435 -0.10509525 -0.28368797

Largest  eigenvalues:
 [1] 98566473 95915344 89453277 85926248 83534674 83381619 82784036 80750362
 [9] 79692712 77439922

Smallest eigenvalues:
 [1]  0.2153345142  0.1939085964  0.1783041464  0.1749744866  0.1323146071
 [6]  0.0185963799  0.0179228280  0.0001136309 -0.1547130021 -0.6087427639

Largest  eigenvalues:
 [1] 99681387 97848433 91536831 87002576 86205368 84552707 83970519 81543450
 [9] 80739268 78766264

Smallest eigenvalues:
 [1]  0.3573017  0.2914597  0.2488881  0.2255140  0.2112320  0.2087011
 [7]  0.1851237  0.1510627 -0.1110930 -0.1696028

Largest  eigenvalues:
 [1] 98206731 97225029 90111972 87011527 84788976 84212436 83524015 81557421
 [9] 80208759 78308652

Smallest eigenvalues:
 [1]  0.39170285  0.38582195  0.36164078  0.34324168  0.24266822  0.18796943
 [7]  0.16663398  0.12344121 -0.06960817 -0.24356689

Largest  eigenvalues:
 [1] 99602379 95738048 90139200 85051029 85005273 83970663 82203712 81271847
 [9] 79593405 78369460

Smallest eigenvalues:
 [1]  0.241406146  0.205457182  0.175996030  0.114242355  0.028364592
 [6] -0.001623815 -0.040325178 -0.050156833 -0.105969594 -1.096258568

Largest  eigenvalues:
 [1] 96473892 96445053 90300185 86560825 84074536 83788270 82943163 80813232
 [9] 79930273 77412527

Smallest eigenvalues:
 [1]  0.3460029  0.3436308  0.2975445  0.2004709  0.1655647  0.1128766
 [7]  0.1059864  0.0746796 -0.3253435 -0.3711266

Largest  eigenvalues:
 [1] 99960749 95942548 89512582 85939005 85633281 83355638 82201548 80867582
 [9] 79145410 77698468

Smallest eigenvalues:
 [1]  0.48700056  0.45409093  0.30948753  0.27380197  0.25708323  0.23950863
 [7]  0.19118523  0.01871397 -0.03601040 -0.15158764

Largest  eigenvalues:
 [1] 101933391  95814947  89992127  86156429  86049128  84311823  82828632
 [8]  81791293  79972087  78492243

Smallest eigenvalues:
 [1]  0.37699948  0.37519356  0.35384173  0.27425011  0.17658792  0.13112822
 [7]  0.10639095  0.06759279 -0.30924561 -0.31977748

Largest  eigenvalues:
 [1] 99748655 96621129 90583358 86275206 85704672 83824880 83241075 81054063
 [9] 80102118 78052289

Smallest eigenvalues:
 [1]  0.3486065  0.3483375  0.2722571  0.2378871  0.2126639  0.1877540
 [7]  0.1561237  0.1462085  0.1169284 -0.7154846

Largest  eigenvalues:
 [1] 100714671  96207745  90393997  85878802  85157288  84832759  82251210
 [8]  81741992  80053172  78765077

Smallest eigenvalues:
 [1]  0.40945523  0.36068517  0.33821367  0.31492065  0.30492223  0.24771585
 [7]  0.21971653  0.10456932  0.08611411 -0.53191484

Largest  eigenvalues:
 [1] 100627244  97149857  90818865  86216991  86078127  83387766  82763225
 [8]  80912453  79698911  77996692

Smallest eigenvalues:
 [1]  0.37616993  0.30844994  0.29948855  0.29302885  0.28062970  0.25498822
 [7]  0.09802171 -0.17180103 -0.17929620 -0.26260563

Largest  eigenvalues:
 [1] 100292963  94851270  88654424  85248640  85180907  82420885  81408968
 [8]  79632993  78669713  76620845

Smallest eigenvalues:
 [1]  0.31929532  0.30962218  0.29295754  0.24546210  0.21094489  0.19175648
 [7]  0.17828202  0.17541633  0.03272447 -0.22744769

Largest  eigenvalues:
 [1] 100381947  99194313  92415504  88099414  86235582  85547398  84166551
 [8]  82457502  80744271  79147537

Smallest eigenvalues:
 [1]  0.27281924  0.26796610  0.18828748  0.10242334  0.06776861  0.02514408
 [7] -0.00851845 -0.05583437 -0.13812955 -0.69661165

Largest  eigenvalues:
 [1] 99081514 96558866 90062751 87117164 85339180 84460402 83340506 81671399
 [9] 80628647 78539530

Smallest eigenvalues:
 [1]  0.30717755  0.29788919  0.26579308  0.23907166  0.15675273  0.12863165
 [7]  0.03914482  0.02203505 -0.12625111 -0.15345823

Largest  eigenvalues:
 [1] 97482224 96098462 89463039 85843192 84518083 83108755 82502543 80586704
 [9] 79379983 77319352

Smallest eigenvalues:
 [1]  0.4606964  0.4498573  0.4341361  0.4044638  0.3919605  0.3316422
 [7]  0.2380871  0.1760859  0.1019369 -0.4003220

Largest  eigenvalues:
 [1] 100604794  96812981  90701168  86606166  86605272  84628723  83045897
 [8]  81737390  80209181  78645595

Smallest eigenvalues:
 [1]  0.30228558  0.25753183  0.22673132  0.21083375  0.20051458  0.18972953
 [7]  0.05001417  0.02248299  0.01528388 -0.15330618

Largest  eigenvalues:
 [1] 99188761 96610294 90349265 85927443 85134621 83987185 83304831 81333384
 [9] 80259932 78479361

Smallest eigenvalues:
 [1]  0.42042496  0.38610917  0.38150603  0.33045975  0.25849543  0.24859809
 [7]  0.23124638  0.14220413  0.02119718 -0.22765793

Largest  eigenvalues:
 [1] 99944934 98200225 91945060 87390475 85814126 84375425 84051618 81818587
 [9] 80967894 78799771

Smallest eigenvalues:
 [1]  0.38343928  0.33848989  0.30908607  0.30526491  0.20031416  0.11286690
 [7]  0.08906204  0.03632128 -0.04255738 -0.45585753

Largest  eigenvalues:
 [1] 102182210  96686791  90995083  87280922  85906787  83754025  83025937
 [8]  81323481  80255935  78467902

Smallest eigenvalues:
 [1]  0.4750651  0.4068162  0.3756430  0.3544322  0.3413545  0.2973791
 [7]  0.2837976  0.2378219 -0.2185010 -0.2210471

Largest  eigenvalues:
 [1] 101140201  97438254  91063380  87163038  85714724  84884044  83065281
 [8]  82030700  80455347  79198026

Smallest eigenvalues:
 [1]  0.32136750  0.21399019  0.18043269  0.15871306  0.14574535  0.14278759
 [7] -0.07996082 -0.22705698 -0.94096321 -1.10915730

Largest  eigenvalues:
 [1] 103055853  97258656  91779731  87641210  86572058  84846449  83524813
 [8]  82503978  81026538  79412852

Smallest eigenvalues:
 [1]  0.23222786  0.22005381  0.18717196  0.17872592  0.16086927  0.09212912
 [7]  0.08113099  0.04326307 -0.02664769 -0.86511128

Largest  eigenvalues:
 [1] 99072419 95656343 89881616 85711273 84921930 83176239 82371409 80627638
 [9] 79437988 77473306

Smallest eigenvalues:
 [1]  0.3327723  0.2615081  0.2528973  0.1895453  0.1799604  0.1628178
 [7]  0.1122068  0.1076461 -0.5657305 -0.8363164

Largest  eigenvalues:
 [1] 97856589 97555784 90034761 86781599 84638618 83504340 82633273 80300762
 [9] 79648626 77383186

Smallest eigenvalues:
 [1]  0.22536684  0.22404784  0.20396321  0.18298110  0.15406155  0.15017093
 [7]  0.07459641 -0.12694544 -0.16485056 -0.30890061

Largest  eigenvalues:
 [1] 98642539 96418073 90315739 85953238 84734391 83532528 83346682 81336835
 [9] 79894132 78001855

Smallest eigenvalues:
 [1]  0.318252765  0.292149770  0.281236994  0.280918317  0.221670301
 [6]  0.187539017  0.019108335 -0.002302866 -0.033659372 -0.266602106

Largest  eigenvalues:
 [1] 99154911 95670807 89216985 85470097 85323502 82882334 82723448 80424940
 [9] 79083555 77042314

Smallest eigenvalues:
 [1]  0.48120013  0.43843719  0.38673201  0.37938179  0.34662840  0.32160201
 [7]  0.26332508  0.12799789  0.02297657 -0.19224168

Largest  eigenvalues:
 [1] 99818555 96095514 90240701 86108313 85073632 83941909 82376942 80907664
 [9] 79513458 77962168

Smallest eigenvalues:
 [1]  0.19925156  0.19048414  0.17757749  0.16026219  0.08552460  0.04335418
 [7] -0.12007095 -0.17869306 -0.18050936 -0.32592975

Largest  eigenvalues:
 [1] 98135464 95340878 89123007 85453541 83474616 82613520 82222039 80257643
 [9] 79035371 76923155

Smallest eigenvalues:
 [1]  0.28870140  0.27843684  0.26552235  0.25904209  0.25445189  0.14223807
 [7]  0.13281769  0.11806811 -0.01231800 -0.05015492

Largest  eigenvalues:
 [1] 99491554 97576782 91146108 86545697 84906426 84079424 83366713 81287722
 [9] 80529554 78191431

Smallest eigenvalues:
 [1]  0.42556016  0.39155007  0.35295703  0.33511458  0.29968992  0.23966884
 [7]  0.21359940  0.14313916  0.08460275 -0.02408846

Largest  eigenvalues:
 [1] 100931028  98003410  91352237  87354120  85384000  84630653  83416583
 [8]  81805581  80510207  78914111

Smallest eigenvalues:
 [1]  0.160722979  0.144748428  0.136866407  0.014927617 -0.001412761
 [6] -0.056523043 -0.061078867 -0.239256716 -0.454745064 -0.581751132

Largest  eigenvalues:
 [1] 99807441 96608260 90865118 85686586 85561036 83710720 82584821 80718669
 [9] 80300226 77814264

Smallest eigenvalues:
 [1]  0.36234276  0.34660526  0.23632228  0.20939052  0.18651477  0.13723656
 [7]  0.11044171  0.01413601 -0.11785535 -0.26152863

Largest  eigenvalues:
 [1] 99389840 97641834 90995572 87360147 85782404 84407542 84065748 81640133
 [9] 80720287 78736745

Smallest eigenvalues:
 [1]  0.35629740  0.32473997  0.31765388  0.28564839  0.27751105  0.24946310
 [7]  0.16394921  0.09332484  0.05364107 -0.03790259

Largest  eigenvalues:
 [1] 99571820 96472763 90178981 86741060 84820233 84156958 83077389 81496666
 [9] 80520244 78698790

Smallest eigenvalues:
 [1]  0.39064716  0.37546323  0.35244183  0.28480280  0.28476617  0.22359175
 [7]  0.17017990  0.10015471 -0.03243227 -0.12594887

Largest  eigenvalues:
 [1] 100732499  97298912  90996749  86840039  85574160  84983889  83243074
 [8]  81859287  80523171  78790227

Smallest eigenvalues:
 [1]  0.41563345  0.38329100  0.37926199  0.33635050  0.27179922  0.26776038
 [7]  0.19182910 -0.05103619 -0.39895147 -0.56471587

Largest  eigenvalues:
 [1] 100812333  96917794  90842963  87093805  86373138  84611564  83466561
 [8]  81758990  80578012  78522752

Smallest eigenvalues:
 [1]  0.34737729  0.29420362  0.28489043  0.26263417  0.20039635  0.08699910
 [7]  0.02964714 -0.02127512 -0.05699699 -0.35888419

Largest  eigenvalues:
 [1] 100147469  95762190  89850309  85711668  84648001  83232160  82791093
 [8]  80846581  79755876  77551271

Smallest eigenvalues:
 [1]  0.32936896  0.30372161  0.28639874  0.22515018  0.20464420  0.17621093
 [7]  0.11744887  0.05547025 -0.24301547 -0.46635999

Largest  eigenvalues:
 [1] 99324445 97247730 90687592 86969984 84428925 83492839 83329475 80942189
 [9] 80147785 77811074

Smallest eigenvalues:
 [1]  0.32438539  0.29941732  0.24235070  0.22480898  0.17024942  0.15118652
 [7]  0.10088109  0.05756656  0.01024561 -0.15598137

Largest  eigenvalues:
 [1] 98549610 97600248 90612052 87268322 84593843 84212596 83829975 81374844
 [9] 80445977 78036966

Smallest eigenvalues:
 [1]  0.22368749  0.20008031  0.19020969  0.17622172  0.15936609  0.03497386
 [7] -0.17139976 -0.21479082 -0.48165974 -0.97830895

Largest  eigenvalues:
 [1] 103768561  98002752  92704337  87863250  86891909  85394090  83834648
 [8]  83092695  81282032  80324444

Smallest eigenvalues:
 [1]  0.29846452  0.29798040  0.29494894  0.28715100  0.22423160  0.22199886
 [7]  0.13102250  0.08985633  0.06845518 -0.07427156

Largest  eigenvalues:
 [1] 98620540 96003762 90086528 86596876 84103513 83348577 82386692 80904266
 [9] 79690206 78029737

Smallest eigenvalues:
 [1]  0.32011884  0.30053309  0.26848868  0.24542315  0.19039616  0.18839554
 [7] -0.02646633 -0.13935248 -0.20101674 -0.34284844

Largest  eigenvalues:
 [1] 100293075  95324435  89988464  85411789  84424643  83556057  82320486
 [8]  81294669  79347289  77999922

Smallest eigenvalues:
 [1]  0.30105920  0.28140832  0.27238707  0.25628928  0.23476222  0.17424607
 [7]  0.15644698  0.05970213 -0.05346660 -0.41323885

Largest  eigenvalues:
 [1] 100404962  97110757  90786915  86405772  86047936  84316539  82929739
 [8]  81503491  80221304  78315313

Smallest eigenvalues:
 [1]  0.22598577  0.21445521  0.21257769  0.13307714  0.13199657  0.01155900
 [7] -0.03719501 -0.14590301 -0.26088304 -0.33472360

Largest  eigenvalues:
 [1] 100286439  97781764  91453710  87098836  85553875  83872049  83665515
 [8]  81467068  80631218  78286592

Smallest eigenvalues:
 [1]  0.29032224  0.28855289  0.26282363  0.17125115  0.14116691  0.11350614
 [7]  0.09050936  0.02684284 -0.22362210 -0.27603654

Largest  eigenvalues:
 [1] 99484417 98162240 91258435 87795351 84801165 83976330 83734703 81265105
 [9] 80664108 77824817

Smallest eigenvalues:
 [1]  0.35995603  0.33047329  0.32894565  0.26805780  0.22057293  0.15076656
 [7] -0.01595369 -0.13517904 -0.41781460 -0.49061356

Largest  eigenvalues:
 [1] 99834399 96394873 89549916 86725008 85396958 83054161 82409560 80277030
 [9] 79629651 77646566

Smallest eigenvalues:
 [1]  0.440572888  0.392050526  0.380539404  0.323483267  0.274082681
 [6]  0.219388090  0.085302929  0.074388317  0.006626811 -0.082493569

Largest  eigenvalues:
 [1] 98558017 96682197 89926321 86566586 85325007 83088849 82938912 80542993
 [9] 79608660 77204900

Smallest eigenvalues:
 [1]  0.38294816  0.38066726  0.32429630  0.32004647  0.25961218  0.25541012
 [7]  0.18078584  0.11359822  0.05837036 -0.37177632

Largest  eigenvalues:
 [1] 100212858  97158386  90520190  86597469  86037378  84892867  83135682
 [8]  82143749  80126730  78843396

Smallest eigenvalues:
 [1]  0.482332156  0.464447794  0.456611013  0.388993918  0.378561311
 [6]  0.347969702  0.285027003  0.123552149  0.004680041 -0.327349814

Largest  eigenvalues:
 [1] 100740726  96812003  90522470  86970578  84931058  83449081  83278956
 [8]  80887030  80341046  77767742

Smallest eigenvalues:
 [1]  0.34192816  0.33848486  0.31597353  0.30732485  0.25858441  0.25780066
 [7]  0.19814994  0.15678728 -0.09072235 -0.36683178

Largest  eigenvalues:
 [1] 100925719  97471814  91265856  87217066  87050841  85274634  83843689
 [8]  82437694  80604936  78952684

Smallest eigenvalues:
 [1]  0.285809143  0.272496852  0.264854738  0.236057127  0.222256767
 [6]  0.218822214 -0.007260748 -0.051954505 -0.128675267 -0.508773575

Largest  eigenvalues:
 [1] 100188323  96523389  90521516  86467991  85542453  84125414  83139716
 [8]  81733571  80268596  78302731

Smallest eigenvalues:
 [1]  0.31070614  0.30120851  0.22254950  0.14685084  0.12964470  0.11789596
 [7]  0.10502754  0.05188713 -0.14477462 -0.16640862

Largest  eigenvalues:
 [1] 99952725 96569244 89739423 85824251 85818433 83791477 82295301 80731608
 [9] 79503524 77630535

Smallest eigenvalues:
 [1]  0.48705859  0.47855575  0.42951581  0.40513507  0.28474430  0.25147949
 [7]  0.21732966  0.13657549  0.07933952 -0.41109732

Largest  eigenvalues:
 [1] 100439337  96698042  90395635  86592191  86031332  83147978  82949924
 [8]  80658073  79794977  77477865

Smallest eigenvalues:
 [1]  0.3934724  0.3689057  0.3640745  0.3520970  0.3458520  0.3453258
 [7]  0.3137613  0.2217387  0.1270074 -0.1457992

Largest  eigenvalues:
 [1] 98530727 96894582 90314404 86204884 84660381 83550466 82799419 80692281
 [9] 79951152 77735957

Smallest eigenvalues:
 [1]  0.3758499  0.3308763  0.2931784  0.2589691  0.2572563  0.2486185
 [7]  0.1277425  0.1015791 -0.2067078 -0.2563001

Largest  eigenvalues:
 [1] 99792372 97095764 90472616 86272618 86196097 83759904 83120628 81132627
 [9] 79939673 77789683

Smallest eigenvalues:
 [1]  0.29312602  0.25532621  0.25071290  0.16029843  0.12300439  0.11595944
 [7] -0.08749474 -0.15135258 -0.22943554 -0.26699709

Largest  eigenvalues:
 [1] 98755460 97097379 90267272 86943944 85573683 83711578 83131635 81101623
 [9] 80541261 77703704

Smallest eigenvalues:
 [1]  0.37300520  0.34729712  0.33309853  0.25952996  0.24023835  0.20535809
 [7]  0.19495173  0.08991581 -0.06080220 -0.21516376

Largest  eigenvalues:
 [1] 100244353  96718973  90839770  86114660  84882537  84294235  82933442
 [8]  81720044  80253604  78565605

Smallest eigenvalues:
 [1]  0.408900329  0.359104791  0.306862713  0.284010465  0.251176487
 [6]  0.248207346  0.182228310  0.165924948 -0.007629804 -0.419598726

Largest  eigenvalues:
 [1] 99782063 96229346 89711878 85878833 85285953 83999558 82541030 81351799
 [9] 79723553 78201600

Smallest eigenvalues:
 [1]  0.37455898  0.36979165  0.36369826  0.34393633  0.30188863  0.18009467
 [7]  0.17721636  0.09165441 -0.10767542 -0.24823568

Largest  eigenvalues:
 [1] 99695079 96444418 90525937 86263861 85382900 83713314 82843075 80916788
 [9] 80042707 78096870

Smallest eigenvalues:
 [1]  0.3404867  0.3269050  0.3183764  0.2898138  0.2886690  0.2229904
 [7]  0.2086984  0.1589362 -0.2174432 -0.3429633

Largest  eigenvalues:
 [1] 99766079 96514548 90663288 85437252 85168320 83102100 82424714 80546603
 [9] 79596699 77688030

Smallest eigenvalues:
 [1]  0.1704127405  0.1479135358  0.1329266855  0.0539817197  0.0004596179
 [6] -0.0302180883 -0.2925952864 -0.2990572104 -0.4613620406 -0.7795846016

Largest  eigenvalues:
 [1] 99838491 94986761 88703523 85582885 85054651 83105792 81538577 80407305
 [9] 78481908 77112431

Smallest eigenvalues:
 [1]  0.39341720  0.39137842  0.36600789  0.34876083  0.34712210  0.31338305
 [7]  0.22653195  0.13162288  0.08894038 -0.18268360

Largest  eigenvalues:
 [1] 99653649 97337399 90715213 86785401 85905448 85116427 83059783 82026067
 [9] 80193403 78742340

Smallest eigenvalues:
 [1]  0.40544191  0.39270392  0.34488020  0.29564885  0.29119464  0.17988292
 [7]  0.16777600 -0.02571681 -0.06720081 -0.20956030

Largest  eigenvalues:
 [1] 101420733  96591345  90333904  86610655  85165072  83219828  82741592
 [8]  80643886  80070446  77578321

Smallest eigenvalues:
 [1]  0.365549372  0.336342457  0.327276931  0.325600667  0.245103707
 [6]  0.146167930  0.078552521 -0.003528213 -0.032648796 -0.248893136

Largest  eigenvalues:
 [1] 99974780 96706051 90257919 86666479 85505143 83858032 83252173 81135345
 [9] 79992340 77671213

Smallest eigenvalues:
 [1]  0.4087225  0.3553458  0.3122703  0.3079115  0.2989448  0.2790082
 [7]  0.2089619 -0.2225661 -0.3132425 -0.4818820

Largest  eigenvalues:
 [1] 101745770  97358429  91165051  86938146  86896739  85354391  83502420
 [8]  82247328  80833195  79212337

Smallest eigenvalues:
 [1]  0.250289284  0.224418451  0.197426478  0.167028608  0.154578957
 [6]  0.061015199  0.058019220  0.005735497 -0.056804080 -0.445752694

Largest  eigenvalues:
 [1] 99032926 95655786 89953932 85471640 83743846 83085670 82503909 80754398
 [9] 79683087 77522270

Smallest eigenvalues:
 [1]  0.398523547  0.326966080  0.304939195  0.266477505  0.253632628
 [6]  0.219817412  0.208272397  0.193460432  0.004620064 -0.217424971

Largest  eigenvalues:
 [1] 102134025  97561114  91144046  87042263  86828886  85464790  82888537
 [8]  82364217  80430794  79524399

Smallest eigenvalues:
 [1]  0.4728044  0.4656492  0.4561668  0.3977354  0.3709171  0.3232007
 [7]  0.1727159  0.1707283  0.1255730 -0.1470081

Largest  eigenvalues:
 [1] 99137403 97361514 91155358 86865276 85350337 84065232 83681962 81421617
 [9] 80454230 78353481

Smallest eigenvalues:
 [1]  0.510679527  0.503585171  0.489978859  0.468186197  0.388010467
 [6]  0.204411722  0.176497312  0.077626287 -0.004377843 -0.109294510

Largest  eigenvalues:
 [1] 101119507  96262378  90683449  86254096  85453929  84263209  82599357
 [8]  81696451  80262742  78742735

Smallest eigenvalues:
 [1]  0.41712961  0.37808716  0.33390456  0.27718078  0.25251986  0.24656301
 [7]  0.21192470  0.08193734 -0.08327945 -0.56399842

Largest  eigenvalues:
 [1] 100232827  95666089  89985269  85387341  84828673  83624169  82221193
 [8]  81208440  79380560  77889899

Smallest eigenvalues:
 [1]  0.31865111  0.27956852  0.27401201  0.18406549  0.12795188  0.10204782
 [7] -0.04608224 -0.17698766 -0.71114611 -0.71669829

Largest  eigenvalues:
 [1] 100722853  95629722  90117024  86209676  85260980  83086579  82739223
 [8]  80661998  79516961  77511018

Smallest eigenvalues:
 [1]  0.35796167  0.34670746  0.32727107  0.31442367  0.28488570  0.20606400
 [7]  0.14691519  0.08122901 -0.06728842 -0.07993234

Largest  eigenvalues:
 [1] 97715761 97472371 90580325 87198539 84809247 84345815 83854582 81443009
 [9] 80549672 78360682

Smallest eigenvalues:
 [1]  0.39807409  0.34964297  0.34798642  0.34723362  0.25903954  0.23996865
 [7]  0.22856945 -0.03202365 -0.03421357 -0.09779054

Largest  eigenvalues:
 [1] 101990746  96091454  90661284  85869882  85432075  83573266  82648774
 [8]  81450918  80050383  78452292

Smallest eigenvalues:
 [1]  0.2873604  0.2406175  0.2061073  0.2011479  0.1902358  0.1536395
 [7]  0.1124333 -0.2234221 -0.4596491 -0.6485345

Largest  eigenvalues:
 [1] 99564501 96852184 90329734 86185316 86149131 84745531 83093047 82055684
 [9] 80419288 79138111

Smallest eigenvalues:
 [1]  0.47004829  0.44956302  0.44267843  0.41641997  0.29400124  0.27615740
 [7]  0.23620663  0.19153958  0.05505231 -0.28395448

Largest  eigenvalues:
 [1] 101822799  95588151  89962860  85771998  85528959  84461459  82526882
 [8]  81932156  79729073  78585406

Smallest eigenvalues:
 [1]  0.39988943  0.39573224  0.34824211  0.34144804  0.24589599  0.21536802
 [7]  0.15810475 -0.04470396 -0.44130334 -0.48927460

Largest  eigenvalues:
 [1] 100696277  97073120  91024100  86484220  86063969  83793930  83541767
 [8]  81210780  80556301  78115354

Smallest eigenvalues:
 [1]  0.20243819  0.18510106  0.17889320  0.13828097  0.10988136  0.02487937
 [7] -0.12089513 -0.16308249 -0.46969175 -0.59273974

Largest  eigenvalues:
 [1] 96975298 96851230 90696985 85979179 84635902 83683700 82880403 80906835
 [9] 79486018 77656533

Smallest eigenvalues:
 [1]  0.44000187  0.43291636  0.40586284  0.27166974  0.23015984  0.23014177
 [7]  0.19486857  0.10130970  0.02942627 -0.14694322

Largest  eigenvalues:
 [1] 101005444  96606843  90825138  86454296  85864228  85126736  82552402
 [8]  82087973  80075289  79113881

Smallest eigenvalues:
 [1]  0.38337602  0.31651394  0.25776147  0.19781490  0.19752167  0.17745764
 [7]  0.16425644 -0.01201535 -0.06950816 -0.18728402

Largest  eigenvalues:
 [1] 100680856  96622146  89827767  86436023  85994600  83697388  82870635
 [8]  81406986  79571289  78119638

Smallest eigenvalues:
 [1]  0.35876576  0.33979949  0.33836701  0.28337005  0.24039554  0.21917536
 [7]  0.20099556  0.16876098  0.03103076 -0.22149992

Largest  eigenvalues:
 [1] 99113266 97382714 90484455 86363318 85808817 83374894 83246100 80982902
 [9] 79790139 77842249

Smallest eigenvalues:
 [1]  0.30704835  0.30059959  0.25458824  0.25182827  0.24333213  0.17932177
 [7]  0.12094803  0.08543251 -0.21105746 -0.25820691

Largest  eigenvalues:
 [1] 102719903  95426719  89809700  86750476  84965634  82797623  81655048
 [8]  80375620  79100341  77381358

Smallest eigenvalues:
 [1]  0.42679419  0.32386659  0.29310488  0.29146631  0.27622499  0.25293305
 [7]  0.21391153  0.18370350  0.02282517 -0.05050702

Largest  eigenvalues:
 [1] 98550730 97114267 90287374 86880211 84634536 84423393 83019364 81748979
 [9] 80006841 78405093

Smallest eigenvalues:
 [1]  0.3945600  0.3717346  0.3651580  0.3503336  0.3344669  0.2426653
 [7]  0.2390838  0.2340258  0.2213380 -0.2072164

Largest  eigenvalues:
 [1] 100292519  95593452  89802370  85482948  85023997  83494446  82969683
 [8]  81247408  79493536  78058754

Smallest eigenvalues:
 [1]  0.41175699  0.38950545  0.37019013  0.27659328  0.22818304  0.22329321
 [7]  0.17571895  0.16590123 -0.06489391 -0.13017483

Largest  eigenvalues:
 [1] 100714880  96331880  90563322  85895636  85737579  83855689  83128647
 [8]  81672731  80057270  78298742

Smallest eigenvalues:
 [1]  0.33259183  0.26277909  0.25582576  0.15664283  0.11910796  0.08702104
 [7]  0.08638394  0.04786710 -0.02142092 -0.54841125

Largest  eigenvalues:
 [1] 101079005  96226361  90560154  86781477  85781753  83419942  82610130
 [8]  81135152  79510985  77827368

Smallest eigenvalues:
 [1]  0.29145410  0.28940441  0.28539643  0.27684333  0.24991573  0.17277188
 [7]  0.14198307  0.13868467 -0.06712417 -0.34832525

Largest  eigenvalues:
 [1] 99839585 97558645 91041026 86668962 85634480 83919678 83657479 81456298
 [9] 80769672 78405713

Smallest eigenvalues:
 [1]  0.3659842  0.3102182  0.2757366  0.1942331  0.1621468  0.1327081
 [7]  0.1161523 -0.1193468 -0.4714288 -1.1234355

Largest  eigenvalues:
 [1] 100120411  95067585  89655472  85290975  84566217  82979898  82263876
 [8]  80749480  79420574  77756921

Smallest eigenvalues:
 [1]  0.41803534  0.41721241  0.38583510  0.36892736  0.27840538  0.20295123
 [7]  0.14769918 -0.08107825 -0.37907701 -0.56662463

Largest  eigenvalues:
 [1] 101190582  97473309  91087423  87103766  86753855  84669109  83374669
 [8]  81743584  80644548  78819328

Smallest eigenvalues:
 [1]  0.264440038  0.261302296  0.250507518  0.219007688  0.111351566
 [6] -0.009447189 -0.060410237 -0.155182861 -0.214761296 -0.275850826

Largest  eigenvalues:
 [1] 97300180 96496643 89569576 86302990 84445005 83679459 83399361 81090628
 [9] 79716052 77759145

Smallest eigenvalues:
 [1]  0.351377848  0.322099500  0.258535921  0.227862233  0.192618418
 [6]  0.077790198  0.002088115 -0.062672817 -0.072426539 -0.457051687

Largest  eigenvalues:
 [1] 99161783 97043638 90640092 86870746 84568056 83674564 83509187 81141610
 [9] 80561007 77723502

Smallest eigenvalues:
 [1]  0.26510224  0.24366621  0.23567284  0.20010371  0.19667448  0.09535692
 [7]  0.05411813  0.05142078 -0.01293108 -1.32696707

Largest  eigenvalues:
 [1] 98877560 96346937 90337112 86955955 84188119 83359184 83158510 80410901
 [9] 79865629 77303655

Smallest eigenvalues:
 [1]  0.36294479  0.32656185  0.30063109  0.23799529  0.23594865  0.16724540
 [7]  0.09899271  0.07269330 -0.10635215 -0.25563710

Largest  eigenvalues:
 [1] 97943590 97658277 91337719 87510018 84578346 84350388 83904824 81545545
 [9] 80892202 78356047

Smallest eigenvalues:
 [1]  0.36448038  0.36092519  0.30790760  0.19249257  0.16092006  0.13192366
 [7]  0.12767409 -0.08773287 -0.19788144 -0.31153076

Largest  eigenvalues:
 [1] 99118012 95927907 89643185 85769287 83928818 83213203 82669605 80719785
 [9] 79747531 77614972

Smallest eigenvalues:
 [1]  0.37299605  0.37080168  0.34490453  0.23245295  0.16211870  0.11187644
 [7]  0.09310969  0.05888227  0.02774412 -0.47810554

Largest  eigenvalues:
 [1] 98847872 95704298 89929228 85668684 84324652 83150749 82135949 80373656
 [9] 79393614 77241742

Smallest eigenvalues:
 [1]  0.3654140  0.3639396  0.2700087  0.2425750  0.2097143  0.1994774
 [7]  0.1685570  0.1422004 -0.2465139 -0.8535758

Largest  eigenvalues:
 [1] 101031270  97607230  91216830  87437073  87208573  85000879  83779530
 [8]  82517317  81319962  79485477

Smallest eigenvalues:
 [1]  0.37756211  0.35707023  0.31013111  0.25855774  0.24972376  0.21986272
 [7]  0.19937933  0.17107446  0.01772496 -0.38013997

Largest  eigenvalues:
 [1] 100625497  96742162  90228993  86167595  86151306  84978859  82573800
 [8]  82156086  79655341  78872017

Smallest eigenvalues:
 [1]  0.29637362  0.26541427  0.21256339  0.13147735  0.11995527  0.08847063
 [7]  0.07888055  0.07576163 -0.15932322 -0.16633398

Largest  eigenvalues:
 [1] 99629171 97178791 90142819 86637236 85506526 84884121 82594718 81708845
 [9] 79900855 78551549

Smallest eigenvalues:
 [1]  0.36918140  0.33746030  0.30363949  0.25635045  0.22278268  0.15809756
 [7]  0.11328799  0.10264674  0.09228072 -0.31414494

Largest  eigenvalues:
 [1] 100237773  97468072  90975938  86529424  86491726  84490034  83128205
 [8]  81620157  80264674  78614998

Smallest eigenvalues:
 [1]  0.48746975  0.42804782  0.38237090  0.35137848  0.23523077  0.19529961
 [7]  0.18590550  0.11081368 -0.01036798 -0.05483418

Largest  eigenvalues:
 [1] 101559603  96283142  90106012  86430813  85733876  84300694  82860232
 [8]  81854428  80322220  79160084

Smallest eigenvalues:
 [1]  0.23069636  0.19847419  0.18645255  0.18342945  0.17660938  0.16117962
 [7]  0.05844873  0.05785838 -0.14585089 -0.17686044

Largest  eigenvalues:
 [1] 98797306 97225687 91113411 86562186 84381667 84118531 83850382 81578674
 [9] 80791603 78784199

Smallest eigenvalues:
 [1]  0.31301908  0.28865658  0.23418857  0.21748037  0.20898878  0.19808066
 [7]  0.08039183 -0.02541776 -0.31413862 -0.53179421

Largest  eigenvalues:
 [1] 99016543 96395819 90037457 85934655 85717561 84060569 82631090 81492826
 [9] 79555577 78113633

Smallest eigenvalues:
 [1]  0.29495076  0.26979096  0.16716006  0.15481753  0.14343851  0.09630921
 [7]  0.08757449  0.03861197 -0.33909293 -0.70389865

Largest  eigenvalues:
 [1] 100364994  99298096  91969083  88500661  85814875  84577894  84267616
 [8]  81450962  81017860  78380314

Smallest eigenvalues:
 [1]  0.504165080  0.481779180  0.480484346  0.429342979  0.351170782
 [6]  0.181205306  0.179632311  0.169740833  0.003942749 -0.415198764

Largest  eigenvalues:
 [1] 100267166  96260307  90445915  86136702  85746688  83153787  82901198
 [8]  80849151  79840261  77759292

Smallest eigenvalues:
 [1]  0.459367692  0.445354706  0.442430569  0.360310259  0.360070971
 [6]  0.208156373  0.117585269  0.062752206  0.005082227 -0.055283008

Largest  eigenvalues:
 [1] 100734725  96919100  90533411  86503961  86419019  83443070  82993396
 [8]  80859570  79928987  77646468

Smallest eigenvalues:
 [1]  0.41883301  0.40392273  0.40272711  0.36922306  0.31088072  0.30017431
 [7]  0.23915287  0.19467860 -0.00484238 -0.11970782

Largest  eigenvalues:
 [1] 99048805 96857803 90395370 86433890 85509437 84099527 82986809 81235491
 [9] 79853614 78054478

Smallest eigenvalues:
 [1]  0.37305885  0.34292566  0.31243975  0.29748108  0.28279151  0.28245676
 [7]  0.20158352  0.10425514  0.09690102 -0.32276797

Largest  eigenvalues:
 [1] 99266230 96646604 90314080 86210092 85521793 83125494 82459614 80408551
 [9] 79981197 77427535

Smallest eigenvalues:
 [1]  0.25257677  0.24833787  0.24525369  0.22113854  0.17727591  0.14420024
 [7]  0.02056847 -0.09038714 -0.22483375 -0.30338038

Largest  eigenvalues:
 [1] 99784920 97063648 90513858 86349233 85343418 83373627 83271900 80836752
 [9] 80070929 77852464

Smallest eigenvalues:
 [1]  0.29107821  0.26983041  0.24440567  0.24162767  0.15029000  0.13614359
 [7] -0.01840315 -0.21758626 -0.22537564 -0.53432662

Largest  eigenvalues:
 [1] 99338404 97091234 90730625 86977483 84429142 83533028 82913978 80358747
 [9] 80157220 76910699

Smallest eigenvalues:
 [1]  0.24130045  0.20314681  0.19653209  0.16530125  0.05373587 -0.07767991
 [7] -0.43888231 -0.46250494 -0.57706930 -0.59423605

Largest  eigenvalues:
 [1] 100679651  96125329  90279822  86086794  85627394  82962730  82660767
 [8]  80590934  79714757  77621774

Smallest eigenvalues:
 [1]  0.4513555  0.4395810  0.3989247  0.3163798  0.3141766  0.2624468
 [7]  0.2529045  0.2158083  0.2142145 -0.2581155

Largest  eigenvalues:
 [1] 99280284 96072349 89845912 85680086 84651303 83648126 82634971 81188130
 [9] 79696445 78214870

Smallest eigenvalues:
 [1]  0.26327661  0.25086315  0.15826147  0.11698081  0.11205674  0.07093853
 [7]  0.04307898 -0.04792343 -0.21239492 -0.27197809

Largest  eigenvalues:
 [1] 98391139 98339029 91494569 87681283 84693217 84515827 83062952 81004947
 [9] 80465181 77551276

Smallest eigenvalues:
 [1]  0.31059584  0.28013624  0.25760606  0.25069301  0.23275873  0.19809033
 [7]  0.15495099 -0.09969918 -0.27102077 -0.86708071

Largest  eigenvalues:
 [1] 99935203 95408417 89639282 85448136 84210873 82568516 82387424 80446297
 [9] 79554764 77509883

Smallest eigenvalues:
 [1]  0.429791082  0.399800940  0.367065060  0.296889719  0.266736304
 [6]  0.187573407  0.184407380  0.005299774 -0.371528840 -0.393313658

Largest  eigenvalues:
 [1] 101397321  96915509  90898814  86580357  86520920  84233308  83077648
 [8]  81728488  80163450  78542180

Smallest eigenvalues:
 [1]  0.178607060  0.168467081  0.152444934  0.132923045  0.094316349
 [6]  0.045755101  0.008685834 -0.214910880 -0.309180505 -0.492545401

Largest  eigenvalues:
 [1] 97000752 96469525 90796317 86195042 83851956 83583798 83512469 81443948
 [9] 80187644 78178850

Smallest eigenvalues:
 [1]  0.39470246  0.35168882  0.34099159  0.31248679  0.27238824  0.24946498
 [7]  0.24126221  0.08727550  0.04523319 -0.33821218

Largest  eigenvalues:
 [1] 99834711 95388530 89635008 85725581 84232498 82903260 82040029 80462840
 [9] 79198427 77383331

Smallest eigenvalues:
 [1]  0.390595698  0.353993018  0.352561443  0.301648010  0.241667049
 [6]  0.230481264  0.112275392  0.040195216  0.007146699 -0.863131735

Largest  eigenvalues:
 [1] 99860242 98444524 91387579 87946868 86565474 84792777 84324043 82014287
 [9] 81247293 78580211

Smallest eigenvalues:
 [1]  0.39742498  0.37957379  0.37753286  0.34683340  0.31766746  0.25507606
 [7]  0.10755867  0.01612215 -0.03687619 -0.52369557

Largest  eigenvalues:
 [1] 99078373 97222478 90397259 86772349 85841832 83589852 83423184 80988049
 [9] 80396912 77763608

Smallest eigenvalues:
 [1]  0.34055685  0.28053254  0.25944124  0.20635931  0.18468359  0.15524465
 [7]  0.14931058  0.05787631  0.04978985 -0.23463472

Largest  eigenvalues:
 [1] 101450361  95965016  89961918  85962548  85385783  83715332  83121423
 [8]  81409335  80121723  78276711

Smallest eigenvalues:
 [1]  0.26751673  0.21974072  0.21838493  0.17946892  0.14986593  0.12942314
 [7]  0.09194865  0.03147040  0.01433878 -0.91998753

Largest  eigenvalues:
 [1] 100349084  97559250  91524516  86706315  86114605  83851137  83275845
 [8]  81395244  80256047  78362904

Smallest eigenvalues:
 [1]  0.32559656  0.31924570  0.30633525  0.24005081  0.21683844  0.19756116
 [7]  0.07209748  0.06429756 -0.24223085 -0.55130555

Largest  eigenvalues:
 [1] 98141386 97694379 90660327 87431772 84997964 83863562 83662669 81007988
 [9] 80368226 77761801

Smallest eigenvalues:
 [1]  0.31348287  0.29623303  0.25752401  0.25312998  0.20229314  0.19716505
 [7]  0.12282798  0.01839462 -0.05453195 -0.07950966

Largest  eigenvalues:
 [1] 99406667 96954899 90786031 86367413 85403798 85063129 83148989 81724834
 [9] 80648340 79166536

Smallest eigenvalues:
 [1]  0.39560641  0.31463287  0.30129619  0.25235800  0.20560578  0.17392572
 [7]  0.16633730  0.04815968 -0.08761367 -0.11713124

Largest  eigenvalues:
 [1] 101888325  96645704  90571942  86675599  86629661  84612929  82992575
 [8]  81703451  80438407  78645504

Smallest eigenvalues:
 [1]  0.43443319  0.38983099  0.38828640  0.38511926  0.28281465  0.26809482
 [7]  0.13368367  0.08780331 -0.03263017 -0.36072287

Largest  eigenvalues:
 [1] 102174629  96149205  90764896  86340185  86022945  84054468  82554362
 [8]  81363195  79919745  78301673

Smallest eigenvalues:
 [1]  0.19988466  0.17372512  0.16045127  0.14436531  0.06499410  0.02886763
 [7]  0.02220141 -0.01502777 -0.08168773 -1.04228761

Largest  eigenvalues:
 [1] 98730711 98398034 91581949 87032003 85699460 84416650 84152274 81985147
 [9] 80759685 78950237

Smallest eigenvalues:
 [1]  0.20339890  0.18280366  0.16854999  0.14735899  0.10550489  0.09107712
 [7]  0.04560014 -0.02731637 -0.12814439 -1.11334461

Largest  eigenvalues:
 [1] 99513541 98116917 90779729 87434985 86470169 84791865 83879004 82085772
 [9] 80702896 78865795

Smallest eigenvalues:
 [1]  0.46227307  0.41995442  0.40845207  0.35688425  0.26812686  0.18647004
 [7]  0.15733774 -0.01411357 -0.02026205 -0.12638831

Largest  eigenvalues:
 [1] 101943157  96815399  91274154  86310206  86193948  84627394  83176234
 [8]  82168123  80349328  79075514

Smallest eigenvalues:
 [1]  0.331410719  0.324665613  0.240219821  0.213022834  0.191196033
 [6]  0.151736223  0.108498625  0.092559887 -0.009961564 -0.112796507

Largest  eigenvalues:
 [1] 98137369 97715986 90708042 87843639 84871108 84681346 83764714 81807036
 [9] 80748654 78978313

Smallest eigenvalues:
 [1]  0.38143199  0.31140571  0.29760754  0.27347634  0.23957733  0.16701707
 [7]  0.12689540  0.03313372 -0.59249306 -0.67746960

Largest  eigenvalues:
 [1] 101256029  96816315  90201478  87268076  85813543  84414550  83014006
 [8]  81679726  80025982  78788737

Smallest eigenvalues:
 [1]  0.34067687  0.28775980  0.26414525  0.21414570  0.20163309  0.18085737
 [7]  0.07917522 -0.12137968 -0.38725617 -0.68208733

Largest  eigenvalues:
 [1] 101861278  96809971  91133423  86587790  85959178  84541025  82840449
 [8]  82006674  80179007  79064039

Smallest eigenvalues:
 [1]  0.43372245  0.31659040  0.28499450  0.24518496  0.21852120  0.20446099
 [7]  0.16948993  0.10645704 -0.06172721 -0.31112806

Largest  eigenvalues:
 [1] 100764275  97248407  90530598  86547799  86418994  83747570  82661302
 [8]  81147751  79958926  78334743

Smallest eigenvalues:
 [1]  0.39012743  0.38696761  0.34404646  0.31316234  0.25527803  0.23683761
 [7]  0.11423121  0.09969124 -0.39028251 -0.78020804

Largest  eigenvalues:
 [1] 100091193  97389485  90497342  87488863  86409875  84086532  83896798
 [8]  81473909  80573273  78432231

Smallest eigenvalues:
 [1]  0.35585856  0.32410142  0.27363188  0.27126139  0.26717090  0.24941770
 [7]  0.15436801  0.12444986  0.04458591 -0.21875618

Largest  eigenvalues:
 [1] 98274014 96569642 90124448 85864282 84454531 83539953 83000264 80950603
 [9] 79694661 77654519

Smallest eigenvalues:
 [1]  0.28133152  0.27686925  0.19555317  0.17725589  0.15588834  0.07969386
 [7] -0.13463858 -0.13474443 -0.29868215 -0.34122695

Largest  eigenvalues:
 [1] 100423814  97712812  91160801  86590597  86440211  84875792  83438980
 [8]  81579099  80726140  78867894

Smallest eigenvalues:
 [1]  0.44267403  0.39947466  0.39250608  0.38838185  0.33379538  0.22413418
 [7]  0.11791490  0.10812335 -0.03633909 -0.18620301

Largest  eigenvalues:
 [1] 101254538  95959749  90592960  86338954  85366262  84241660  82868886
 [8]  81737692  80385589  78512917

Smallest eigenvalues:
 [1]  0.058185343  0.045899067 -0.009036044 -0.095725922 -0.102067948
 [6] -0.419780578 -0.490942268 -0.577191487 -0.619417892 -0.629020273

Largest  eigenvalues:
 [1] 98745231 95751881 89881040 85754808 85326027 83279781 82531111 80654227
 [9] 79443775 77523193

Smallest eigenvalues:
 [1]  0.3815785  0.3771295  0.3669656  0.2891872  0.2705186  0.2034987
 [7]  0.1451879 -0.2175073 -0.4532708 -0.6015415

Largest  eigenvalues:
 [1] 102334527  97444676  91470668  87787297  86232091  85113045  83968880
 [8]  82644459  81392255  79485012

Smallest eigenvalues:
 [1]  0.33497666  0.33352712  0.28057664  0.25698945  0.24507983  0.20697409
 [7]  0.08222553  0.02525762 -0.10619800 -0.25851396

Largest  eigenvalues:
 [1] 100611638  96785725  90474451  86772944  85929264  84553506  82495070
 [8]  81432507  80003968  78826244

Smallest eigenvalues:
 [1]  0.34431829  0.33498789  0.31293014  0.27834956  0.25846283  0.14380849
 [7]  0.11407259  0.10549554  0.09734466 -0.58854530

Largest  eigenvalues:
 [1] 98530229 95456355 89491894 85752857 83242262 82637660 82416853 79977600
 [9] 79501800 77001605

Smallest eigenvalues:
 [1]  0.26914031  0.26043122  0.21459412  0.18736925  0.14845907  0.07874544
 [7]  0.07784031 -0.07986671 -0.11959565 -0.56059877

Largest  eigenvalues:
 [1] 100168323  96413539  90601393  86137388  85399523  83666577  82988120
 [8]  81320765  79949432  77905892

Smallest eigenvalues:
 [1]  0.324614884  0.300514232  0.241329757  0.210709473  0.181934668
 [6]  0.074295440 -0.003249435 -0.261985101 -0.745352569 -0.787918799

Largest  eigenvalues:
 [1] 100872449  96125695  90148649  86504400  85893125  83542410  83344412
 [8]  81473869  79951673  78172869

Smallest eigenvalues:
 [1]  0.4126539  0.3869167  0.3744963  0.3601519  0.2221537  0.2091842
 [7]  0.1893213  0.1313180  0.0200826 -0.3045735

Largest  eigenvalues:
 [1] 97502569 95960855 89958405 86134029 83986446 83671794 82740539 81221121
 [9] 79782728 78024310

Smallest eigenvalues:
 [1]  0.43017845  0.37502626  0.33592130  0.32069081  0.26739616  0.15049299
 [7]  0.13443244  0.11395836  0.09017143 -1.49593903

Largest  eigenvalues:
 [1] 99560769 97625660 90787546 87559973 85534275 84317603 83400278 81148311
 [9] 80563357 77676716

Smallest eigenvalues:
 [1]  0.29604206  0.28609854  0.27902571  0.18123724  0.15591815  0.15373248
 [7]  0.14184828  0.08133732 -0.13209641 -0.14122370

Largest  eigenvalues:
 [1] 99442783 98054270 90843246 87375130 85136854 84555745 83834471 81961115
 [9] 80863790 79211299

Smallest eigenvalues:
 [1]  0.30215302  0.29498304  0.27217667  0.18138157  0.15288255  0.09410219
 [7]  0.07540122 -0.01853222 -0.17238622 -0.65238838

Largest  eigenvalues:
 [1] 98617735 97640564 90659621 87431634 84573203 84363064 83562997 81014055
 [9] 80559671 77778796

Smallest eigenvalues:
 [1]  0.4719555  0.4191241  0.4017873  0.3946956  0.3100844  0.2386480
 [7]  0.2080490  0.1821500  0.1732654 -0.1435028

Largest  eigenvalues:
 [1] 100018414  96118663  90179985  85989212  85349571  83936897  83065475
 [8]  81361935  80194895  78343777

Smallest eigenvalues:
 [1]  0.38092432  0.37331536  0.36546693  0.33524821  0.31116440  0.29576574
 [7]  0.27999347  0.14919343 -0.04972975 -0.10721190

Largest  eigenvalues:
 [1] 99341004 96720040 90125667 86525729 84743930 83263974 83109008 80556628
 [9] 79890796 77481245

Smallest eigenvalues:
 [1]  0.3149938  0.2929249  0.2919076  0.2691387  0.2530930  0.2189553
 [7]  0.1633777 -0.1250496 -0.1351757 -0.2087045

Largest  eigenvalues:
 [1] 99214869 95374009 89099764 85327212 83988379 83052767 81965904 80396034
 [9] 79026188 77137711

Smallest eigenvalues:
 [1]  0.38470707  0.36276823  0.32190500  0.31549949  0.24761274  0.19812443
 [7]  0.18693791  0.17074537  0.06933354 -0.06727256

Largest  eigenvalues:
 [1] 99385392 97297662 91560212 86507002 85558391 84630434 83751830 81861043
 [9] 80840652 79188213

Smallest eigenvalues:
 [1]  0.4767251  0.4685349  0.4592432  0.4261618  0.3912516  0.1817691
 [7]  0.1446941  0.1424519  0.1089849 -0.1850407

Largest  eigenvalues:
 [1] 99707867 96429166 90404432 86623224 84995145 83766173 83280705 81274566
 [9] 80399680 78260579

Smallest eigenvalues:
 [1]  0.2335448  0.2188832  0.1917935  0.1887423  0.1814929  0.1771487
 [7]  0.1374852  0.1250975  0.0291889 -0.4680119

Largest  eigenvalues:
 [1] 98273574 95556179 89645458 85187870 84717587 83354037 82165557 81011708
 [9] 79350423 77963325

Smallest eigenvalues:
 [1]  0.24620507  0.21858558  0.16894975  0.16317197  0.11723825  0.11471277
 [7]  0.07251718  0.03986858 -0.22640104 -0.67176309

Largest  eigenvalues:
 [1] 100307190  99384901  91745488  88751023  86341941  84866710  84488179
 [8]  82059309  81219494  78597738

Smallest eigenvalues:
 [1]  0.40935323  0.36159548  0.35488266  0.27146720  0.26311898  0.20870304
 [7]  0.20025516  0.14263318  0.04805744 -0.37529690

Largest  eigenvalues:
 [1] 98369697 97128000 90598943 86561343 84596563 83697747 82945593 80843120
 [9] 79734379 77661114

Smallest eigenvalues:
 [1]  0.41175047  0.40325180  0.38193799  0.32003994  0.31042846  0.15598854
 [7]  0.01868788 -0.16359973 -0.16971565 -0.42800350

Largest  eigenvalues:
 [1] 100046220  96074520  90304809  86282093  85217762  83876506  82653421
 [8]  81248500  79979128  77990133

Smallest eigenvalues:
 [1]  0.31383343  0.31346078  0.30712925  0.22542448  0.13625960  0.09530084
 [7]  0.07769367  0.02423000 -0.05204557 -0.47005584

Largest  eigenvalues:
 [1] 97444898 95450355 89190082 85364723 83621098 82385667 82116662 79651376
 [9] 79031394 76281828

Smallest eigenvalues:
 [1]  0.3649556  0.3617310  0.3465880  0.3138276  0.2880125  0.2199215
 [7]  0.1851893  0.1616141  0.1586361 -0.3439481

Largest  eigenvalues:
 [1] 99209694 97291195 90361566 87057798 85288629 83809225 83634870 81373930
 [9] 80299198 78520711

Smallest eigenvalues:
 [1]  0.3348225  0.2801413  0.2484938  0.2172986  0.1930259  0.1568888
 [7]  0.1414990  0.1396131 -0.1103372 -0.2650043

Largest  eigenvalues:
 [1] 100621004  98328826  91112993  87377093  86293644  84418602  83566065
 [8]  81626027  80593884  78446852

Smallest eigenvalues:
 [1]  0.42444327  0.40028739  0.38148784  0.35453648  0.33268600  0.13847818
 [7]  0.07952187 -0.11291591 -0.32223058 -0.38480346

Largest  eigenvalues:
 [1] 100681739  96322714  89959821  86517018  85930799  83737572  83347117
 [8]  81367308  79856829  78171240

Smallest eigenvalues:
 [1]  0.252656626  0.205776058  0.190594967  0.176824356  0.045604410
 [6]  0.019306513  0.008340649 -0.361401912 -0.570848304 -0.730683188

Largest  eigenvalues:
 [1] 99868714 96852705 90632588 86656771 85648597 83796916 83331936 81629172
 [9] 80039851 78519484

Smallest eigenvalues:
 [1]  0.4593528  0.3893255  0.3766599  0.2768965  0.2762782  0.2307830
 [7]  0.2254736  0.1759479  0.1135783 -0.4528005

Largest  eigenvalues:
 [1] 100667360  97969492  91271475  87586299  86067439  84314707  84071188
 [8]  81646420  80853880  78544220

Smallest eigenvalues:
 [1]  0.3510299  0.3385034  0.3071948  0.2622282  0.2389058  0.2286450
 [7]  0.2059410  0.1711556 -0.1566071 -0.2463768

Largest  eigenvalues:
 [1] 101135713  97331335  91088702  86463126  86217393  85231831  83052736
 [8]  82441990  80273258  79246940

Smallest eigenvalues:
 [1]  0.38199830  0.36769959  0.34301811  0.27746184  0.24689443  0.20405738
 [7]  0.13544772  0.09483139  0.02030478 -0.29501974

Largest  eigenvalues:
 [1] 100070271  97831866  90674020  87372477  86161733  83547958  83443165
 [8]  80634948  80082929  77361695

Smallest eigenvalues:
 [1]  0.37438582  0.36976021  0.36179464  0.29333067  0.26613039  0.17165153
 [7]  0.10566550 -0.05698757 -0.35655390 -0.53352759

Largest  eigenvalues:
 [1] 99754859 97038948 90564293 86860615 85797785 83472579 83331213 80749316
 [9] 80108506 77673032

Smallest eigenvalues:
 [1]  0.25802055  0.23450663  0.19880209  0.12702044  0.04113767 -0.04967580
 [7] -0.19115228 -0.47149969 -0.65365914 -0.93581442

Largest  eigenvalues:
 [1] 101019653  95378962  89771927  86277076  85231362  83096589  82535764
 [8]  81129720  79165978  77504679

Smallest eigenvalues:
 [1]  0.21278067  0.18949278  0.17242776  0.17118907  0.14233052  0.05991912
 [7] -0.01893210 -0.09684069 -0.48836254 -0.50731041

Largest  eigenvalues:
 [1] 101324263  97593997  91172686  86937931  86348242  84510021  83278593
 [8]  81952751  80202144  78877555

Smallest eigenvalues:
 [1]  0.4208265  0.3639878  0.3512899  0.3200594  0.3047338  0.3015686
 [7]  0.1895072  0.1145783 -0.1150118 -0.2139220

Largest  eigenvalues:
 [1] 98304620 96803604 90375890 86727246 84451429 83412327 83214771 80882046
 [9] 80019738 77655596

Smallest eigenvalues:
 [1]  0.281698680  0.281533700  0.256546252  0.226088006  0.223708356
 [6]  0.114270740  0.042818163 -0.008678622 -0.110736070 -0.670415958

Largest  eigenvalues:
 [1] 101185348  95931724  90257581  85508157  85226809  83616697  82490658
 [8]  81426756  79604431  78339732

Smallest eigenvalues:
 [1]  0.41761241  0.41240658  0.40091710  0.38198660  0.32071976  0.20906311
 [7]  0.20716043  0.06956320 -0.03745066 -0.28607350

Largest  eigenvalues:
 [1] 100107626  95440889  89734629  85230717  85144758  83736904  81605045
 [8]  81087241  79128540  77867393

Smallest eigenvalues:
 [1]  0.27061737  0.24703151  0.21959191  0.21580823  0.20473005  0.09554137
 [7]  0.09530508  0.03834050 -0.00343953 -0.65423020

Largest  eigenvalues:
 [1] 97373393 96531587 89583693 86630878 84122586 83154770 82961964 80584070
 [9] 79549766 77363139

Smallest eigenvalues:
 [1]  0.45769452  0.45009303  0.38659504  0.37669354  0.31433898  0.30734342
 [7]  0.20366714 -0.04075146 -0.05591965 -0.14335648

Largest  eigenvalues:
 [1] 99188706 96982154 90366313 87330640 84912837 84207054 83155853 80761380
 [9] 80219596 77161211

Smallest eigenvalues:
 [1]  0.22911217  0.21858659  0.20267879  0.19897631  0.16634976  0.16516647
 [7]  0.08447713 -0.10646781 -0.29848244 -0.75932235

Largest  eigenvalues:
 [1] 100997519  95839491  90022919  85331119  85081897  83519569  82181898
 [8]  81148935  79458950  78014497

Smallest eigenvalues:
 [1]  0.26766870  0.19766377  0.17798173  0.13205080  0.08800957  0.06668416
 [7]  0.02950838 -0.30796337 -0.39058239 -0.63176470

Largest  eigenvalues:
 [1] 98400709 96399953 90571587 85834627 83960791 83487740 82802189 80871257
 [9] 79688763 77709510

Smallest eigenvalues:
 [1]  0.21429646  0.17650710  0.09560023  0.08547053  0.04900958 -0.02548114
 [7] -0.04340883 -0.09511792 -0.32107678 -0.52381986

Largest  eigenvalues:
 [1] 98373351 97829063 91124969 87540051 84895878 84133526 83649371 81194542
 [9] 80430064 77705409

Smallest eigenvalues:
 [1]  0.28248161  0.27376209  0.23778535  0.22887318  0.19865703  0.08801103
 [7]  0.06218977 -0.02285149 -0.03258565 -0.21379139

Largest  eigenvalues:
 [1] 99775512 95900627 89777322 85890169 84313045 83424790 82164998 80652110
 [9] 79573174 77165731

Smallest eigenvalues:
 [1]  0.36781521  0.35982334  0.34962791  0.19485981  0.17790083  0.14009971
 [7]  0.10921436  0.07310026  0.01995280 -0.26795094

Largest  eigenvalues:
 [1] 99350483 96550470 90255423 86075781 85722055 84140992 82926836 81623876
 [9] 79775301 78340079

Smallest eigenvalues:
 [1]  0.45371415  0.39124476  0.37421891  0.33444789  0.33157732  0.27601170
 [7]  0.24610685  0.08682787 -0.23062857 -0.35493993

Largest  eigenvalues:
 [1] 100327411  96759475  90697455  86292802  86045450  83552283  83337019
 [8]  81348333  79960664  78119926

Smallest eigenvalues:
 [1]  0.046636993  0.035359558  0.017449824  0.015862257  0.003537427
 [6] -0.032252855 -0.057342307 -0.230057749 -0.771263406 -1.590312342

Largest  eigenvalues:
 [1] 98867425 97698841 90795929 86793252 86540610 84406671 83874382 81610980
 [9] 80659906 78197657

Smallest eigenvalues:
 [1]  0.25804756  0.20071648  0.18647683  0.12117166  0.10024445  0.07416415
 [7] -0.26325448 -0.28874537 -0.54908138 -0.56308618

Largest  eigenvalues:
 [1] 102526834  97000175  91134028  87858330  85963653  84814061  83161686
 [8]  82594866  80275596  79336479

Smallest eigenvalues:
 [1]  0.33775875  0.28745714  0.27183690  0.24930744  0.17070333  0.16259579
 [7]  0.09871793 -0.07408996 -0.11719351 -0.38557054

Largest  eigenvalues:
 [1] 101683941  96630367  91170559  87129730  85827565  84988288  83111650
 [8]  82408866  80399078  79339477

Smallest eigenvalues:
 [1]  0.42968072  0.42110958  0.27611702  0.19894934  0.19619133  0.18425263
 [7]  0.09758404  0.02732125 -0.03617361 -0.33772064

Largest  eigenvalues:
 [1] 102347794  97012443  91408971  87163646  86707997  85616970  83160776
 [8]  82520728  80953667  79679345

Smallest eigenvalues:
 [1]  0.28548938  0.25116030  0.24486995  0.16885419  0.16038230  0.05720970
 [7]  0.04422642 -0.13743450 -0.17777822 -0.63440488

Largest  eigenvalues:
 [1] 97395646 97316126 91209863 86695776 84558729 83838743 83675876 81342631
 [9] 80230173 78057431

Smallest eigenvalues:
 [1]  0.442776082  0.391623751  0.382725334  0.381279589  0.363850334
 [6]  0.345549336  0.009804477 -0.026025911 -0.105962376 -0.498362344

Largest  eigenvalues:
 [1] 100614042  96615725  90226930  87168205  85422308  84184218  83317242
 [8]  81496710  80456269  78427014

Smallest eigenvalues:
 [1]  0.42694793  0.35639499  0.35108276  0.29871305  0.28908353  0.22087682
 [7]  0.15976578 -0.09342316 -0.30558180 -0.68065358

Largest  eigenvalues:
 [1] 99334108 96674672 89862788 86993738 85068975 83904600 82886322 80664032
 [9] 80266133 77517598

Smallest eigenvalues:
 [1]  0.4308011  0.4142717  0.3650295  0.2857384  0.2464918  0.2453967
 [7]  0.1959111  0.0494940 -0.1635359 -0.2395798

Largest  eigenvalues:
 [1] 101114828  95268029  89294177  85195923  84768918  83245343  81631967
 [8]  80659045  78996872  77528946

Smallest eigenvalues:
 [1]  0.31449603  0.28985626  0.27663390  0.26592695  0.25166567  0.23601603
 [7]  0.18660474  0.09371916 -0.03140952 -0.24225762

Largest  eigenvalues:
 [1] 100782930  96312558  90388534  86503552  84976835  82939980  82667309
 [8]  80232093  79705663  77225659

Smallest eigenvalues:
 [1]  0.31111033  0.29720889  0.23327700  0.20128001  0.16892894  0.16055564
 [7]  0.15787289  0.13501886  0.04273853 -0.12985173

Largest  eigenvalues:
 [1] 100255203  98760425  91698089  87815922  85382115  84930929  83717184
 [8]  82113265  80877654  78963829

Smallest eigenvalues:
 [1]  0.3480369  0.2696630  0.2564487  0.2496769  0.1517936  0.1402594
 [7]  0.1061727  0.1011491 -0.1454205 -0.1460305

Largest  eigenvalues:
 [1] 100222935  97756015  90993038  87357335  86067421  83820499  83637554
 [8]  80867492  80424331  77863631

Smallest eigenvalues:
 [1]  0.48081342  0.42919507  0.41925864  0.38888139  0.37344706  0.34659120
 [7]  0.31291955  0.25326989  0.10653370 -0.04490726

Largest  eigenvalues:
 [1] 100458943  96766794  90109848  86481009  85526355  83631147  82577029
 [8]  80983043  79670597  77857202

Smallest eigenvalues:
 [1]  0.36236035  0.31721020  0.31392624  0.27677729  0.20533656  0.16221101
 [7]  0.12907441  0.06818734 -0.40674266 -0.63878229

Largest  eigenvalues:
 [1] 101319137  97773478  91592450  87673146  86144334  84143571  83948516
 [8]  81581962  80763609  78613598

Smallest eigenvalues:
 [1]  0.4045498  0.3879079  0.3610878  0.3578397  0.2485032  0.1659034
 [7]  0.1249912  0.1003893 -0.1786400 -0.4457197

Largest  eigenvalues:
 [1] 99521787 96679611 90377359 86724952 85679579 84283571 83030569 81399752
 [9] 80313216 78438244

Smallest eigenvalues:
 [1]  0.41404505  0.39003060  0.35982916  0.30239082  0.27486520  0.24478899
 [7]  0.12962633  0.07244005 -0.02504669 -0.40874128

Largest  eigenvalues:
 [1] 100712253  96385478  90780036  85742161  85702015  83942962  82912727
 [8]  81655551  80211888  78999273

Smallest eigenvalues:
 [1]  0.3485337  0.3354698  0.3048705  0.3021327  0.2908771  0.2593732
 [7]  0.2220939  0.1163274 -0.2397182 -0.6077688

Largest  eigenvalues:
 [1] 99154721 97038249 90799939 86935918 85068815 83761234 83203080 81082837
 [9] 80412269 77848777

Smallest eigenvalues:
 [1]  0.4233766  0.4147364  0.3510396  0.3332425  0.2905806  0.2784367
 [7]  0.1803975 -0.3335088 -0.3669966 -0.5229525

Largest  eigenvalues:
 [1] 100372986  96036649  89563607  86116582  85666577  83186631  83057644
 [8]  80827217  79748104  77722181

Smallest eigenvalues:
 [1]  0.38983166  0.38487340  0.37208787  0.29054224  0.23320137  0.20777219
 [7]  0.12504140  0.09933004 -0.19143744 -0.31194636

Largest  eigenvalues:
 [1] 101281899  96173435  90944062  85988172  85939280  83550130  83153112
 [8]  81393977  80269444  78406345

Smallest eigenvalues:
 [1]  0.347569103  0.327372172  0.321848328  0.307483784  0.156288232
 [6]  0.154681260  0.058509231  0.017588019 -0.001766918 -0.033815865

Largest  eigenvalues:
 [1] 100144452  96846882  90758827  86306564  84719137  83682019  83028101
 [8]  81175517  80204826  78000990

Smallest eigenvalues:
 [1]  0.4090389  0.3627915  0.3476506  0.2782087  0.2762533  0.2727793
 [7]  0.2249399  0.1626167  0.1073839 -0.1032556

Largest  eigenvalues:
 [1] 99077168 96435042 90374970 85718440 84933027 84228130 82886459 81868980
 [9] 80053463 78669893

Smallest eigenvalues:
 [1]  0.45102002  0.42739909  0.41265141  0.38966948  0.38052585  0.33418660
 [7]  0.23188719  0.17593409  0.06790079 -0.10139031

Largest  eigenvalues:
 [1] 99702125 95783662 89036761 86248118 85341539 82890255 82297361 80565432
 [9] 79180315 77493682

Smallest eigenvalues:
 [1]  0.3942416  0.3892888  0.3819386  0.3360190  0.3339390  0.2560155
 [7]  0.2171359  0.1761208  0.1394933 -0.1150816

Largest  eigenvalues:
 [1] 98087575 97105412 90307908 86497525 85434288 83918838 83789166 81430940
 [9] 80320173 78199214

Smallest eigenvalues:
 [1]  0.29877799  0.28556724  0.25028831  0.19129003  0.13790622  0.07852385
 [7] -0.05774839 -0.14290567 -0.33090174 -0.60924416

Largest  eigenvalues:
 [1] 101291665  97586212  91113511  86552832  86371197  83884344  82870623
 [8]  81098482  79868608  78015487

Smallest eigenvalues:
 [1]  0.3266034  0.2723108  0.2449150  0.2311140  0.1198034  0.1179327
 [7]  0.1075270 -0.1579041 -0.1602187 -0.7164355

Largest  eigenvalues:
 [1] 99383581 98286507 91591050 87427128 86095739 84900683 83745485 81538270
 [9] 80781832 78196081

Smallest eigenvalues:
 [1]  0.34855606  0.34089552  0.32322032  0.29137096  0.27673292  0.25805268
 [7]  0.21791098  0.07110441 -0.14859563 -0.20484002

Largest  eigenvalues:
 [1] 101274472  97595123  91036971  86858103  86441183  84799633  83100157
 [8]  82292071  79960284  79035603

Smallest eigenvalues:
 [1]  0.27889303  0.27844637  0.25990528  0.13658687  0.01831973 -0.02484048
 [7] -0.03088235 -0.06261795 -0.13665732 -0.34273962

Largest  eigenvalues:
 [1] 100074790  95776483  90026420  85701913  85645614  84236822  83057760
 [8]  81940416  79774724  78626849

Smallest eigenvalues:
 [1]  0.34981741  0.29878845  0.27855108  0.17326761  0.16220631  0.04052916
 [7] -0.02611012 -0.15787457 -0.46048301 -0.89547548

Largest  eigenvalues:
 [1] 101282510  96123958  90086878  86211614  86175111  84701277  83370964
 [8]  81868580  80364939  79008676

Smallest eigenvalues:
 [1]  0.25906603  0.24811292  0.21993695  0.17488631  0.16174391  0.13402113
 [7]  0.07151616 -0.12408328 -0.23128794 -0.31582863

Largest  eigenvalues:
 [1] 98357885 97898636 91055033 87630008 84249133 84212096 83200764 80525443
 [9] 80271323 77117444

Smallest eigenvalues:
 [1]  0.23641698  0.20624225  0.18525294  0.17828785  0.11896606  0.10187315
 [7]  0.09210105  0.07195074 -0.34791008 -0.39390754

Largest  eigenvalues:
 [1] 99279474 96983457 90290189 85953735 85443268 83968328 82975647 81413902
 [9] 79719412 78205437

Smallest eigenvalues:
 [1]  0.4176070  0.3575368  0.3371788  0.3099605  0.2687841  0.2678587
 [7]  0.2664475  0.2237560  0.1549113 -0.2692582

Largest  eigenvalues:
 [1] 97899285 97087837 90624117 87204323 84559126 84362741 83237295 81828180
 [9] 79855049 78508596

Smallest eigenvalues:
 [1]  0.4343852  0.3819684  0.3702191  0.3689260  0.3273773  0.2060304
 [7]  0.1560160  0.1375543  0.1360155 -0.0694369

Largest  eigenvalues:
 [1] 100596365  96241883  90286789  86486005  85636894  84608034  82696311
 [8]  81814079  80096788  78693955

Smallest eigenvalues:
 [1]  0.37689905  0.34435708  0.32177875  0.31315594  0.29307640  0.17395796
 [7] -0.05786294 -0.13821481 -0.47884541 -0.60791327

Largest  eigenvalues:
 [1] 101828461  95977289  90461838  86693038  85907921  83882449  82858439
 [8]  81562928  79926236  78434530

Smallest eigenvalues:
 [1]  0.410316943  0.381908199  0.345209941  0.305669916  0.280893197
 [6]  0.250456104  0.244696198  0.002926307 -0.107938224 -0.138693776

Largest  eigenvalues:
 [1] 101117928  96405711  90885059  86158471  86119029  84222275  82927994
 [8]  81732255  80105695  78583906

Smallest eigenvalues:
 [1]  0.234059808  0.180942142  0.137386047  0.126149825  0.096684587
 [6]  0.007760464 -0.100625359 -0.289805122 -0.609480439 -0.669918702

Largest  eigenvalues:
 [1] 101062858  96805132  90903998  86473085  86108250  83979731  82866543
 [8]  81496307  79945722  78378804

Smallest eigenvalues:
 [1]  0.3912443  0.3851973  0.3690836  0.3456639  0.3437930  0.3189483
 [7]  0.2900501  0.1871427  0.1122719 -0.5214423

Largest  eigenvalues:
 [1] 99491156 95950766 89387673 85990538 84566929 83501811 82155362 80685271
 [9] 79356582 77568494

Smallest eigenvalues:
 [1]  0.3677983  0.3479690  0.3411484  0.2568955  0.2333802  0.2273164
 [7]  0.1390135  0.1368217 -0.1093204 -0.1799333

Largest  eigenvalues:
 [1] 100204052  97147167  90234945  87077710  85176039  84392041  83608051
 [8]  81724587  80291790  78362499

Smallest eigenvalues:
 [1]  0.366966922  0.362717654  0.360335019  0.319582916  0.200745930
 [6]  0.152922374  0.003352582 -0.266448190 -0.352148435 -0.417930394

Largest  eigenvalues:
 [1] 98862982 97074532 90402106 86536506 85739899 84152294 83675610 81267876
 [9] 80425882 78232969

Smallest eigenvalues:
 [1]  0.45191717  0.43950038  0.40385806  0.31130142  0.30891949  0.24313667
 [7]  0.20693017  0.19572590  0.05756002 -0.26955153

Largest  eigenvalues:
 [1] 100191604  97316183  90636333  86957543  85624644  83963100  83498253
 [8]  81238812  80220408  77968545

Smallest eigenvalues:
 [1]  0.23397825  0.23241502  0.21649592  0.14441482  0.13952662 -0.05654203
 [7] -0.05932610 -0.18019992 -0.26937088 -0.55667726

Largest  eigenvalues:
 [1] 98077439 96837182 89745826 86305853 85808576 84771427 82953900 82168849
 [9] 79855603 78859366

Smallest eigenvalues:
 [1]  0.27269166  0.22345738  0.21728267  0.19267097  0.14376271  0.13499501
 [7]  0.12867720  0.06938402 -0.06350760 -0.67379346

Largest  eigenvalues:
 [1] 98964379 98300823 91549033 87909320 85856434 84752260 84327194 81612079
 [9] 81088527 78579785

Smallest eigenvalues:
 [1]  0.09957522  0.01537536 -0.03509050 -0.09849262 -0.19101268 -0.23046605
 [7] -0.30163899 -0.35958915 -0.45000353 -0.88915703

Largest  eigenvalues:
 [1] 100914053  97237217  91082370  87023629  85721450  84231415  83590468
 [8]  81749584  80299963  78846282

Smallest eigenvalues:
 [1]  0.292016404  0.271769531  0.257989998  0.243381681  0.176269431
 [6]  0.175803107  0.153864046  0.143341840  0.002725585 -0.602384881

Largest  eigenvalues:
 [1] 99269626 96884936 90201947 86848869 84824305 83790576 83315979 81216337
 [9] 80153990 77782459

Smallest eigenvalues:
 [1]  0.43850415  0.41442870  0.39690383  0.31029263  0.29555572  0.26145934
 [7]  0.20976765 -0.02291559 -0.04284741 -0.13635327

Largest  eigenvalues:
 [1] 100488694  97264099  90541710  86668662  85887328  84417592  83592227
 [8]  81848523  80511793  78859929

Smallest eigenvalues:
 [1]  0.39471192  0.35063669  0.33547207  0.31752616  0.25248833  0.21683236
 [7]  0.14449475  0.10680065 -0.01933623 -0.46130736

Largest  eigenvalues:
 [1] 100714282  97595167  90849772  87053747  86745183  85106698  83634857
 [8]  82408726  80519700  79249400

Smallest eigenvalues:
 [1]  0.31469041  0.28954432  0.28607079  0.23634182  0.21461819  0.17977594
 [7]  0.04595727 -0.01096688 -0.06073514 -0.31440006

Largest  eigenvalues:
 [1] 101740353  96052238  89905945  85822559  85731355  83648055  82538546
 [8]  81118497  79552874  77860594

Smallest eigenvalues:
 [1]  0.4266116  0.4232172  0.3428957  0.2922577  0.2827195  0.2725651
 [7]  0.2696178  0.1932111 -0.1911917 -0.7601754

Largest  eigenvalues:
 [1] 101173753  97329449  91054267  87101393  86942104  85009815  83247482
 [8]  81759686  80539331  78747386

Smallest eigenvalues:
 [1]  0.25483398  0.25440119  0.23748573  0.22084413  0.17672952  0.16243410
 [7]  0.02964144 -0.04834645 -0.05541758 -0.24170052

Largest  eigenvalues:
 [1] 99360354 96528295 90375623 85879135 85443810 83638858 83388456 81259125
 [9] 80032915 77992215

Smallest eigenvalues:
 [1]  0.16150796  0.14893433  0.12487696  0.11568954  0.09019838  0.04326606
 [7] -0.17314327 -0.32297092 -0.37563042 -0.91476655

Largest  eigenvalues:
 [1] 101571118  96558076  91032209  86394127  85889716  84227305  83198967
 [8]  82085763  80231043  78902193

Smallest eigenvalues:
 [1]  0.38059240  0.37732561  0.30066847  0.27935410  0.20453661  0.18769102
 [7]  0.16705004 -0.02377098 -0.06607792 -0.15777434

Largest  eigenvalues:
 [1] 97769102 96040358 89655288 85462809 84788605 82716880 82389853 80290862
 [9] 79236402 77259572

Smallest eigenvalues:
 [1]  0.34634746  0.34456714  0.31802433  0.30331161  0.25942431  0.20890988
 [7]  0.11439959  0.06513766 -0.05693716 -0.11050370

Largest  eigenvalues:
 [1] 97163083 96693999 89776939 86245439 83854771 83526176 83134265 80874637
 [9] 79826742 77696086

Smallest eigenvalues:
 [1]  0.3327129  0.2659533  0.2532687  0.2311225  0.1893002  0.1541538
 [7]  0.1534513 -0.2784342 -0.3589102 -0.5319046

Largest  eigenvalues:
 [1] 98857234 95325149 89070634 85749929 84193565 82773254 82649383 80221392
 [9] 79692741 77003069

Smallest eigenvalues:
 [1]  0.34699249  0.32355695  0.26134788  0.26043983  0.24538748  0.11462200
 [7] -0.01941008 -0.14688981 -0.38380129 -0.42099434

Largest  eigenvalues:
 [1] 100877535  96950164  91136541  86613296  85924105  83512648  83299860
 [8]  81277984  80381521  78392708

Smallest eigenvalues:
 [1]  0.35352883  0.34702510  0.28566263  0.26065976  0.25682427  0.21360104
 [7]  0.19858020  0.13274861  0.04398071 -0.74566347

Largest  eigenvalues:
 [1] 101152950  98571292  92099932  87450988  86815567  85309913  83897342
 [8]  82538033  81000907  79556619

Smallest eigenvalues:
 [1]  0.23099717  0.19234303  0.19049139  0.17347833  0.14079204  0.10579074
 [7] -0.04458064 -0.11949034 -0.18821758 -0.71881989

Largest  eigenvalues:
 [1] 99149007 96423716 90537904 85998970 84346569 83400727 82734627 81071001
 [9] 79948076 77831385

Smallest eigenvalues:
 [1]  0.40578246  0.40120171  0.36721794  0.29197626  0.26971145  0.24563370
 [7]  0.19323597  0.16704558  0.02607803 -0.14519548

Largest  eigenvalues:
 [1] 101094098  97456695  90817216  86939295  86357833  84231530  83308246
 [8]  81530512  80419921  78530715

Smallest eigenvalues:
 [1]  0.43480910  0.43024832  0.34838111  0.34697034  0.31205261  0.27063612
 [7]  0.24961073  0.09841438  0.03930832 -0.10974630

Largest  eigenvalues:
 [1] 100410007  95976350  89771216  86088452  85320377  83678883  81978746
 [8]  80686078  79253905  77664165

Smallest eigenvalues:
 [1]  0.12694587  0.11058854  0.09271166  0.04838720 -0.12021239 -0.34345029
 [7] -0.36671085 -0.37713947 -0.57213810 -1.32014857

Largest  eigenvalues:
 [1] 101692263  96698341  91559543  86348629  85602278  84743556  83027174
 [8]  81845159  80408631  78734620

Smallest eigenvalues:
 [1]  0.30295159  0.24034660  0.18536516  0.14431746  0.07786097  0.05587312
 [7]  0.01111916 -0.03639185 -0.53998312 -0.80037665

Largest  eigenvalues:
 [1] 100508711  97044238  91670005  86100600  85731527  83901156  83543296
 [8]  81738543  80527078  78656792

Smallest eigenvalues:
 [1]  0.52021728  0.42617878  0.38904175  0.38063202  0.37129728  0.36387846
 [7]  0.26677558  0.20513106 -0.05435247 -0.06675711

Largest  eigenvalues:
 [1] 98965763 96971076 90741985 87212870 84881984 83888714 83681774 81383664
 [9] 80243575 78080073

Smallest eigenvalues:
 [1]  0.43839355  0.41715438  0.41245214  0.39575751  0.34503093  0.30450687
 [7]  0.19916598  0.03750747 -0.13176149 -0.38965613

Largest  eigenvalues:
 [1] 99573308 96204127 89716219 86118311 85478658 83099156 82622446 80610382
 [9] 79593611 77458026

Smallest eigenvalues:
 [1]  0.44322180  0.42419448  0.38989221  0.38334586  0.28226819  0.26188999
 [7]  0.19171159  0.05948086  0.03502478 -0.12676357

Largest  eigenvalues:
 [1] 99096988 96959306 90650842 86678173 84879439 84109293 83414527 81296531
 [9] 80353293 78258981

Smallest eigenvalues:
 [1]  0.5031935  0.3989250  0.3523077  0.2419549  0.1935245  0.1816304
 [7]  0.1386767 -0.2046599 -0.2665340 -0.9005747

Largest  eigenvalues:
 [1] 101811653  96421445  90087933  86874496  86140971  84036068  82219944
 [8]  81227335  79629624  78153957

Smallest eigenvalues:
 [1]  0.49387907  0.48732465  0.41093407  0.34014672  0.30539747  0.30035957
 [7]  0.22659959  0.20825811  0.17899060 -0.02690145

Largest  eigenvalues:
 [1] 100462069  96442940  90685831  85980553  85882056  83677279  82570602
 [8]  81045179  79710196  77872311

Smallest eigenvalues:
 [1]  0.372865009  0.350135488  0.326463316  0.286492580  0.275191241
 [6]  0.205101118  0.163899184  0.026730037 -0.006885879 -0.047835749

Largest  eigenvalues:
 [1] 99305474 96532758 90429288 85980661 85635220 83519321 82964695 81092529
 [9] 79936555 77943309

Smallest eigenvalues:
 [1]  0.183239535  0.176508156  0.130695142  0.113508046  0.009426349
 [6] -0.032568176 -0.105138535 -0.208262216 -0.404034721 -0.740318726

Largest  eigenvalues:
 [1] 99122978 96826230 91160166 86329732 84955365 84484244 83330964 82133618
 [9] 80283935 78694275

Smallest eigenvalues:
 [1]  0.38560188  0.38326858  0.30925081  0.30901290  0.28005665  0.27002888
 [7]  0.21241842  0.12391159 -0.05900234 -0.06148758

Largest  eigenvalues:
 [1] 100333631  96955965  90285904  86472662  85505195  84268466  82433271
 [8]  81050267  79880259  78150643

Smallest eigenvalues:
 [1]  0.4919522  0.4479297  0.4265404  0.3869061  0.3124770  0.2323936
 [7]  0.2064273  0.1780105 -0.1603598 -0.2175354

Largest  eigenvalues:
 [1] 99772885 95187705 89557611 85534514 84364679 83027378 82448144 80532996
 [9] 79621432 77417830

Smallest eigenvalues:
 [1]  0.37648509  0.35191103  0.30851276  0.24298059  0.19149177  0.04675491
 [7] -0.04104796 -0.11084363 -0.15927765 -0.62363850

Largest  eigenvalues:
 [1] 103600093  95505630  90364267  86619516  85529716  83770080  82524436
 [8]  81749559  79696699  78564238

Smallest eigenvalues:
 [1]  0.24465153  0.21438791  0.16754235  0.15725125  0.15548894  0.09914795
 [7]  0.06914302 -0.02671311 -0.59366857 -0.67332483

Largest  eigenvalues:
 [1] 97593231 97100954 91290536 86250441 84521084 83732977 83569607 81068775
 [9] 80385668 78071593

Smallest eigenvalues:
 [1]  0.31603021  0.25718825  0.24489518  0.21849013  0.11428810  0.09603519
 [7] -0.11128751 -0.20718250 -0.29433289 -0.31132038

Largest  eigenvalues:
 [1] 98202102 96764274 90308841 86543478 85294905 84179369 83892647 81906522
 [9] 80044359 78418258

Smallest eigenvalues:
 [1]  0.43904139  0.43133331  0.40709788  0.37590294  0.33397495  0.32255071
 [7]  0.29591741  0.27096567  0.04106674 -0.05712327

Largest  eigenvalues:
 [1] 99274917 95867007 89981923 85547503 85104921 82963617 82438046 80870998
 [9] 79513364 77919176

Smallest eigenvalues:
 [1]  0.46325498  0.46166157  0.41252004  0.37321712  0.28191879  0.24531393
 [7]  0.12045733  0.11024800 -0.06605865 -0.24644531

Largest  eigenvalues:
 [1] 99991117 96735833 89926256 87346369 85117088 84076131 83279852 81550169
 [9] 80395504 78260830

Smallest eigenvalues:
 [1]  0.4330849  0.4020024  0.3748423  0.3565680  0.3196545  0.2676867
 [7]  0.2016224 -0.1449578 -0.1619819 -0.1895933

Largest  eigenvalues:
 [1] 100826966  96334744  90113451  86719380  85305835  84022201  82716086
 [8]  81373764  80094463  78277733

Smallest eigenvalues:
 [1]  0.37326317  0.35846725  0.33249559  0.29447213  0.26408315  0.24215250
 [7]  0.17350547  0.13258136 -0.03018616 -0.22135213

Largest  eigenvalues:
 [1] 98672876 95550127 89031868 85314589 84821619 82649630 82264051 80302608
 [9] 78897366 77093016

Smallest eigenvalues:
 [1]  0.30931218  0.22960786  0.20197239  0.17829339  0.16589960  0.15570694
 [7]  0.14120589  0.08351061  0.08255726 -0.23851626

Largest  eigenvalues:
 [1] 97380230 96461449 89803184 86526466 83796984 82897063 82702519 80203091
 [9] 79389668 76746654

Smallest eigenvalues:
 [1]  0.3685795526  0.3436715158  0.3386713514  0.3251806977  0.3068118526
 [6]  0.1570954217  0.1191157870  0.0959234791 -0.0001471406 -0.2346708568

Largest  eigenvalues:
 [1] 98584082 97074468 90272150 87104656 84946612 83837832 83212349 80895421
 [9] 80482347 77588447

Smallest eigenvalues:
 [1]  2.699266e-01  2.144292e-01  1.541071e-01  1.337610e-01  1.026406e-01
 [6]  1.160841e-02 -5.443407e-05 -2.568958e-01 -2.684043e-01 -3.527842e-01

Largest  eigenvalues:
 [1] 100053133  96130595  89871001  86291939  83713037  83591538  82574397
 [8]  80998614  80034563  77576627

Smallest eigenvalues:
 [1]  0.4142776  0.3941530  0.3503994  0.3407098  0.3139414  0.2799652
 [7]  0.1966966  0.1318278 -0.4223764 -0.8069486

Largest  eigenvalues:
 [1] 101187856  97086018  91198856  86706254  86510063  83761188  83425056
 [8]  81393989  80443295  78397806

Smallest eigenvalues:
 [1]  0.30941771  0.30524832  0.24366669  0.23749408  0.20493327  0.13285847
 [7]  0.05133460 -0.03890257 -0.06084318 -0.71883526

Largest  eigenvalues:
 [1] 100828793  97602180  90835926  87287453  87012492  85930345  83414172
 [8]  82723922  80838955  79531443

Smallest eigenvalues:
 [1]  0.369029169  0.362691359  0.353588306  0.351764783  0.281286091
 [6]  0.241423926  0.211884033  0.003464372 -0.158582853 -0.326647637

Largest  eigenvalues:
 [1] 99680297 96454207 90543015 86500074 84885370 83790105 83199382 81344508
 [9] 80110954 77972854

Smallest eigenvalues:
 [1]  0.3065613  0.2431831  0.2391782  0.2155183  0.2091817  0.1693003
 [7]  0.1271607 -0.1995080 -0.4066203 -0.6307664

Largest  eigenvalues:
 [1] 100736918  97179415  90516850  87000776  86405839  85212160  83163229
 [8]  82302833  80445913  78931862

Smallest eigenvalues:
 [1]  0.29851823  0.28557206  0.27017650  0.26763524  0.24716206  0.13499916
 [7]  0.05028756 -0.04307928 -0.09889282 -0.86216406

Largest  eigenvalues:
 [1] 100182985  96941737  90878840  86562059  86087658  84230416  83401960
 [8]  82014258  79990195  78720963

Smallest eigenvalues:
 [1]  0.3991817  0.3872397  0.3676609  0.3582896  0.2542244  0.2037604
 [7]  0.1913263 -0.0472565 -0.0839502 -0.1719341

Largest  eigenvalues:
 [1] 100383297  96503062  90378690  86093233  85765825  83773704  82515951
 [8]  80920970  79955056  78090956

Smallest eigenvalues:
 [1]  0.30670780  0.20326089  0.19665993  0.08159352  0.01349483 -0.07291564
 [7] -0.07379954 -0.15452279 -0.43753416 -0.79354714

Largest  eigenvalues:
 [1] 100999884  97758210  90739158  87082463  86505883  83925578  83557227
 [8]  81219474  80524907  78460703

Smallest eigenvalues:
 [1]  0.34253604  0.32545313  0.21630120  0.18977162  0.18198331  0.15796592
 [7]  0.04390050  0.03035574 -0.19699336 -0.69375317

Largest  eigenvalues:
 [1] 100340136  95827951  89074954  86099129  85926024  83820325  82560747
 [8]  81277341  79579839  77787326

Smallest eigenvalues:
 [1]  0.39181683  0.36493295  0.32830043  0.29035042  0.27416137  0.14307365
 [7]  0.05806362  0.03507854 -0.01639568 -0.35564321

Largest  eigenvalues:
 [1] 100219678  96000098  90427975  85680377  85486644  83267441  82873168
 [8]  81001057  79617517  77669430

Smallest eigenvalues:
 [1]  0.28810119  0.26425975  0.22160193  0.18028787  0.13756265  0.09173279
 [7]  0.08807529 -0.02224719 -0.21659059 -0.57088636

Largest  eigenvalues:
 [1] 98290070 97297714 90550965 86609295 84377950 83578526 83227989 80728442
 [9] 80157389 77845012

Smallest eigenvalues:
 [1]  0.26401529  0.25813804  0.21829104  0.18125884  0.14915006  0.11737341
 [7]  0.05911547 -0.03183136 -0.39064279 -0.74577689

Largest  eigenvalues:
 [1] 99400100 96245545 90205652 86111153 84716775 83718335 83257677 81417377
 [9] 79878080 78055283

Smallest eigenvalues:
 [1]  0.314146831  0.311850730  0.282658927  0.270622221  0.251437362
 [6]  0.245090507  0.193428267  0.004988796 -0.084706632 -0.481487450

Largest  eigenvalues:
 [1] 98820704 95808176 90287906 85149618 84254193 83955721 82333538 80875807
 [9] 79932485 78220179

Smallest eigenvalues:
 [1]  0.32886736  0.29330735  0.25424508  0.24053868  0.13802277  0.10934938
 [7]  0.10691209 -0.01604612 -0.25335859 -0.66526531

Largest  eigenvalues:
 [1] 98344307 94573027 88820751 84807629 83326604 82914148 81831053 80239657
 [9] 79073759 77121216

Smallest eigenvalues:
 [1]  0.326326924  0.317189115  0.199457293  0.174002643  0.152673245
 [6]  0.122916336  0.094855930  0.088665521 -0.001178807 -0.070555217

Largest  eigenvalues:
 [1] 99187907 97492326 91580242 86535210 84754837 83813793 83574985 81216735
 [9] 80419874 78327326

Smallest eigenvalues:
 [1]  0.36695691  0.30716757  0.30560135  0.27392456  0.23536602  0.23473709
 [7]  0.18030186  0.09647028 -0.02844927 -0.04304868

Largest  eigenvalues:
 [1] 100996121  95881516  89901016  85548608  85544263  82925269  82075044
 [8]  80319229  79352083  77309452

Smallest eigenvalues:
 [1]  0.4316303  0.4208347  0.4133128  0.3999564  0.3875765  0.3682845
 [7]  0.2417644  0.1244756 -0.1259745 -0.2933479

Largest  eigenvalues:
 [1] 100243806  96963715  90417763  87469165  84641066  83935936  83425260
 [8]  80999256  80653669  77612974

Smallest eigenvalues:
 [1]  0.364297489  0.349647931  0.345258262  0.282858177  0.274275485
 [6]  0.170002337  0.130009132 -0.009954598 -0.252593864 -0.333487135

Largest  eigenvalues:
 [1] 101075882  97118586  91436235  86907756  85475047  85010052  83357766
 [8]  82274281  80581721  78937387

Smallest eigenvalues:
 [1]  0.33993250  0.30180280  0.28043381  0.26909891  0.15660651  0.02907121
 [7]  0.02043404 -0.11279720 -0.32588131 -0.35657728

Largest  eigenvalues:
 [1] 102546257  95989900  90513981  87235312  85327544  83693600  82108944
 [8]  81402140  79434442  78185465

Smallest eigenvalues:
 [1]  0.13374824  0.12737801  0.07047947  0.04598225  0.02741508 -0.07748124
 [7] -0.18293921 -0.39316521 -0.75688512 -0.94082273

Largest  eigenvalues:
 [1] 100435793  95682934  89327609  85997398  85536713  83341614  82840831
 [8]  81174876  79395631  78082072

Smallest eigenvalues:
 [1]  0.30400737  0.27763694  0.27182902  0.21953290  0.13900133  0.06927903
 [7]  0.02531365 -0.02921070 -0.07107304 -0.29811185

Largest  eigenvalues:
 [1] 100803965  97284221  91030870  86848065  85460286  84452314  82993850
 [8]  81851253  79995740  78540146

Smallest eigenvalues:
 [1]  0.36284994  0.35930795  0.29081657  0.28677139  0.27247123  0.23139737
 [7]  0.00371644 -0.03468379 -0.04270706 -0.25026637

Largest  eigenvalues:
 [1] 98644947 96013791 89642430 86044874 85497503 83341279 83253306 81119507
 [9] 79537651 77764447

Smallest eigenvalues:
 [1]  0.41542279  0.40919142  0.32106334  0.29829831  0.25126733  0.20882237
 [7]  0.16565436  0.15521824  0.04021373 -0.06157143

Largest  eigenvalues:
 [1] 98434634 98312635 90868593 87791355 85197744 84544722 84065491 81618217
 [9] 80794946 78728256

Smallest eigenvalues:
 [1]  0.32733372  0.30418752  0.29672656  0.25926005  0.24656299  0.18691614
 [7]  0.08692670  0.02636084 -0.03448850 -0.65844271

Largest  eigenvalues:
 [1] 98981019 95675266 89068969 86184630 84603629 83052050 82908943 80381501
 [9] 79346067 77114293

Smallest eigenvalues:
 [1]  0.32821947  0.32414124  0.30149772  0.25790374  0.24369459  0.16258789
 [7]  0.15852172 -0.01110554 -0.11072379 -0.33605135

Largest  eigenvalues:
 [1] 99765026 97884729 91514202 87019737 85693192 84455431 83787676 81665821
 [9] 80592654 78865850

Smallest eigenvalues:
 [1]  0.477988568  0.439918247  0.420547977  0.416711566  0.388852499
 [6]  0.369853239  0.359176576  0.093815923  0.009193506 -0.187239575

Largest  eigenvalues:
 [1] 102321485  96058157  90121770  86665887  85952561  83385499  82313344
 [8]  81017521  79693527  77974300

Smallest eigenvalues:
 [1]  0.28042652  0.27298275  0.26165338  0.17415352  0.16970502  0.11993403
 [7]  0.08453356 -0.06023711 -0.16631739 -0.64947397

Largest  eigenvalues:
 [1] 98831808 97073287 90303978 87019229 85522093 84281777 83999382 81883623
 [9] 80757423 78722295

Smallest eigenvalues:
 [1]  0.32248869  0.31578689  0.29279027  0.24579734  0.19024994  0.14878104
 [7]  0.08520810  0.01025207 -0.09484912 -0.11261377

Largest  eigenvalues:
 [1] 99867887 96849253 90443120 86820842 84560983 84159666 82857191 81326005
 [9] 80112184 78032646

Smallest eigenvalues:
 [1]  0.35910779  0.29510038  0.23580913  0.19271113  0.18948207  0.17597670
 [7]  0.12359647  0.08433964 -0.37427932 -1.22831509

Largest  eigenvalues:
 [1] 102045698  96946137  91274498  86788916  86701640  84415063  83315986
 [8]  81846463  80661233  79132255

Smallest eigenvalues:
 [1]  0.363616209  0.333862215  0.299872341  0.287371719  0.280834803
 [6]  0.163472046  0.088348115  0.053377984 -0.001669046 -0.198216750

Largest  eigenvalues:
 [1] 97952091 97308012 90802000 86852861 85124266 83682051 83488447 81009563
 [9] 80472052 78041363

Smallest eigenvalues:
 [1]  0.270115388  0.262921215  0.244589065  0.233387432  0.194780113
 [6]  0.043349180 -0.003913576 -0.022667061 -0.384858870 -1.387337587

Largest  eigenvalues:
 [1] 102304323  96186394  90478927  86172171  85277837  84946744  82929901
 [8]  82333781  80745454  79384467

Smallest eigenvalues:
 [1]  0.34068413  0.32926307  0.30087145  0.26145782  0.23951875  0.20125075
 [7]  0.15595911 -0.07579312 -0.13727473 -0.40966281

Largest  eigenvalues:
 [1] 100114791  96292819  90500274  86344339  85142094  84134377  83052809
 [8]  81744618  80280563  78825498

Smallest eigenvalues:
 [1]  0.42491928  0.37954428  0.37297111  0.29147008  0.27333599  0.24918844
 [7]  0.23339043  0.17011509  0.06384430 -0.09017256

Largest  eigenvalues:
 [1] 99575642 96864583 90142779 85659676 85658192 83644555 82619231 81087148
 [9] 79559156 77931575

Smallest eigenvalues:
 [1]  0.3939280  0.3377544  0.3215833  0.2963347  0.2746435  0.2677547
 [7]  0.2015931 -0.2629492 -0.5839031 -3.8464995

Largest  eigenvalues:
 [1] 100922082  97671625  91264838  87954535  86314430  84359730  84139855
 [8]  81760624  81299610  78557200

Smallest eigenvalues:
 [1]  0.32088035  0.31744686  0.30103063  0.29481377  0.27594865  0.26108038
 [7]  0.16518321  0.12722545 -0.08706957 -0.27501656

Largest  eigenvalues:
 [1] 100273562  97121781  90838631  87419830  84787780  84043070  82983785
 [8]  81227731  79960444  77983994

Smallest eigenvalues:
 [1]  0.24572507  0.23614287  0.21264002  0.19828196  0.16916035  0.13890045
 [7]  0.09421075 -0.06775645 -0.31290185 -0.32677093

Largest  eigenvalues:
 [1] 99405571 96076769 89929090 85829093 84054022 83149491 82967646 80633162
 [9] 79905228 77307982

Smallest eigenvalues:
 [1]  0.37238334  0.35661176  0.33587332  0.29549755  0.26025956  0.22205667
 [7]  0.20527115  0.09473500 -0.08733787 -0.13594070

Largest  eigenvalues:
 [1] 101085009  95991368  89933883  85984642  85371243  83283580  82534865
 [8]  80688811  79889005  77669161

Smallest eigenvalues:
 [1]  0.38325622  0.37433127  0.35638512  0.34526758  0.29069659  0.21939822
 [7]  0.14711047  0.06178511 -0.16737429 -0.27145050

Largest  eigenvalues:
 [1] 102456189  96914885  91040338  86575318  86246201  84851069  82918014
 [8]  82082334  80506878  79062735

Smallest eigenvalues:
 [1]  0.38830062  0.36589516  0.30289503  0.28406847  0.25031188  0.22519916
 [7]  0.17228382  0.09458279 -0.06773608 -0.54111833

Largest  eigenvalues:
 [1] 101005871  97144376  91149610  87036393  85894894  85214494  83509107
 [8]  82582804  80762431  79512342

Smallest eigenvalues:
 [1]  0.30592772  0.28896238  0.27320002  0.24951541  0.21908713  0.16324041
 [7]  0.12205861  0.10553916 -0.08769211 -0.19439733

Largest  eigenvalues:
 [1] 99800001 95795117 89620278 85284659 84669473 83213809 81827975 80585188
 [9] 79196320 77552068

Smallest eigenvalues:
 [1]  0.25353134  0.24053701  0.23073527  0.20957257  0.06601571  0.04604083
 [7] -0.02223759 -0.09850560 -0.16573659 -0.51260834

Largest  eigenvalues:
 [1] 100776786  95631711  90409479  85456160  85336095  84229884  81973502
 [8]  81224267  79504897  78599382

Smallest eigenvalues:
 [1]  0.4614451  0.4348184  0.3962426  0.3887389  0.3603514  0.3155989
 [7]  0.2520493  0.2461396  0.2287887 -0.2481496

Largest  eigenvalues:
 [1] 99701718 97512481 91147917 87292494 85569796 84748410 83365225 81979962
 [9] 80290429 78835435

Smallest eigenvalues:
 [1]  0.3090049  0.3005691  0.2968760  0.2870542  0.2592391  0.1824990
 [7]  0.1736249  0.1336746  0.1108898 -0.2203779

Largest  eigenvalues:
 [1] 99368167 97309959 90002579 86841031 85346731 84870510 82260459 81221258
 [9] 79615811 78285058

Smallest eigenvalues:
 [1]  0.36065884  0.33551938  0.33280822  0.32370304  0.24106259  0.21798514
 [7]  0.16689562  0.03816438 -0.10593044 -0.50646967

Largest  eigenvalues:
 [1] 101133501  96907438  90479610  87419778  86163932  84278151  83095809
 [8]  81766994  80164837  78594944

Smallest eigenvalues:
 [1]  0.43527786  0.41320526  0.33337971  0.30641895  0.28805246  0.23480365
 [7]  0.17088297  0.05456974 -0.22101630 -0.24807195

Largest  eigenvalues:
 [1] 100620921  96347390  90487914  86304336  84519158  83933288  82844205
 [8]  81496051  79854748  78143750

Smallest eigenvalues:
 [1]  0.37862062  0.37376140  0.37064563  0.33097662  0.31758120  0.21952049
 [7]  0.13968060  0.11130327 -0.00912987 -0.08427104

Largest  eigenvalues:
 [1] 100069182  96385364  90256717  86081809  85736345  84005751  83026416
 [8]  81335926  80089040  78345930

Smallest eigenvalues:
 [1]  0.28301277  0.25694003  0.25320549  0.24988598  0.21796066  0.17372590
 [7]  0.06343940 -0.02439735 -0.08598000 -0.16698327

Largest  eigenvalues:
 [1] 99883796 95993256 90381932 85345268 84627389 83282699 82672981 80894983
 [9] 79982998 77743056

Smallest eigenvalues:
 [1]  0.394588379  0.390381477  0.336382184  0.296214815  0.220447110
 [6]  0.220320340  0.199348915  0.164899920  0.046990396 -0.001264787

Largest  eigenvalues:
 [1] 100308045  95554374  89008297  85940560  85276677  82772401  81793295
 [8]  80312709  78695704  76927181

Smallest eigenvalues:
 [1]  0.44616818  0.43960791  0.41195382  0.28453839  0.27981420  0.20707246
 [7]  0.08480005 -0.02752333 -0.12172163 -0.50072316

Largest  eigenvalues:
 [1] 100471635  95447019  89100818  86100794  85797561  82976443  81959392
 [8]  80117094  79014002  76957356

Smallest eigenvalues:
 [1]  0.42099546  0.39497382  0.37298879  0.27331070  0.20722276  0.17317986
 [7]  0.11844832  0.10351708  0.09758702 -0.14186559

Largest  eigenvalues:
 [1] 98795512 95993503 90048666 85865312 84832881 83287406 82399807 80710592
 [9] 79187092 77531886

Smallest eigenvalues:
 [1]  0.48712872  0.46427235  0.41083878  0.31821220  0.28871053  0.21946862
 [7]  0.18450459  0.16148368  0.10439500 -0.03160107

Largest  eigenvalues:
 [1] 99358770 96101435 89994107 86253701 84757307 83300231 82955629 80848946
 [9] 79864016 77401440

Smallest eigenvalues:
 [1]  0.38754752  0.36931491  0.36142321  0.34325075  0.27382299  0.25633746
 [7]  0.18681497  0.08162637 -0.03105068 -0.33989398

Largest  eigenvalues:
 [1] 100864829  96430389  90953801  85840555  85293455  84349415  82871402
 [8]  81962387  80243396  78823094

Smallest eigenvalues:
 [1]  0.24067772  0.23601800  0.23389428  0.22292071  0.19497830  0.17731891
 [7]  0.05400771  0.03995535  0.03620340 -0.40447297

Largest  eigenvalues:
 [1] 98788145 97536594 90660213 87389991 84648845 83752437 83207883 81067480
 [9] 80226184 77605041

Smallest eigenvalues:
 [1]  0.33820942  0.27030640  0.25417173  0.24169389  0.23283821  0.21590241
 [7]  0.11376314 -0.02883595 -0.36754236 -0.52181972

Largest  eigenvalues:
 [1] 98714581 96619065 90177018 86330976 85087416 83535697 83397654 81047739
 [9] 80317048 77769693

Smallest eigenvalues:
 [1]  0.39174009  0.32524347  0.28985309  0.20054168  0.19237940  0.19101722
 [7]  0.08940818 -0.16670370 -0.36047134 -0.69079710

Largest  eigenvalues:
 [1] 99933812 96941147 90721368 86553256 86308703 84021580 83779304 81701466
 [9] 80165372 78247997

Smallest eigenvalues:
 [1]  0.18655005  0.16577837  0.16232250  0.14449290  0.13726420  0.13112099
 [7]  0.04560549 -0.08578619 -0.26467629 -0.49880046

Largest  eigenvalues:
 [1] 99435510 96448369 90309291 86130237 85275077 83390968 82995682 80821385
 [9] 79946695 77931005

Smallest eigenvalues:
 [1]  0.43185323  0.42270272  0.35919220  0.35080242  0.25128398  0.22136257
 [7]  0.20891948  0.18867283  0.03289081 -0.07837342

Largest  eigenvalues:
 [1] 98227670 97430090 90584809 87115553 84484684 84093028 83699023 81379141
 [9] 80377975 78157463

Smallest eigenvalues:
 [1]  0.21032160  0.20371226  0.19698221  0.17061765  0.16168591  0.11740691
 [7]  0.08660657  0.07002979 -0.10805552 -0.34508916

Largest  eigenvalues:
 [1] 97897138 97844230 90883487 87200596 84399309 83941594 83668966 81248549
 [9] 80312936 77879668

Smallest eigenvalues:
 [1]  0.4118170  0.4008201  0.3674775  0.2898745  0.2822209  0.2502554
 [7]  0.1976928  0.1682335  0.1251252 -0.1704450

Largest  eigenvalues:
 [1] 97546410 96201668 89523473 85630605 84643386 83212585 83049254 80791726
 [9] 79651894 77824843

Smallest eigenvalues:
 [1]  0.44186199  0.42570971  0.39274271  0.37123195  0.34994851  0.28412068
 [7]  0.27076251  0.19424168  0.01129769 -0.01776899

Largest  eigenvalues:
 [1] 100065712  95659183  89647526  86140537  84547486  83502801  82186782
 [8]  80715714  79542008  77738227

Smallest eigenvalues:
 [1]  0.32713925  0.30784757  0.29809931  0.25883863  0.21649066  0.18439788
 [7]  0.16696320  0.13225522  0.08932447 -0.51157525

Largest  eigenvalues:
 [1] 99056474 97901050 90941608 86907480 85943776 84056548 83838397 81504439
 [9] 80534993 78485352

Smallest eigenvalues:
 [1]  0.4576806  0.4543102  0.3405121  0.3332690  0.3051610  0.2015817
 [7]  0.1932974  0.1443592 -0.2023058 -0.5885060

Largest  eigenvalues:
 [1] 99461250 96593725 90747950 86917715 84744431 84146285 83510223 81733760
 [9] 80488536 78311084

Smallest eigenvalues:
 [1]  0.32506477  0.31850666  0.29879996  0.27480250  0.23378666  0.21813274
 [7]  0.10411059  0.05257262 -0.16681207 -0.54536420

Largest  eigenvalues:
 [1] 101515212  97973693  91925690  87233013  86740063  84159941  83903875
 [8]  81658078  80668435  78680359

Smallest eigenvalues:
 [1]  0.276156753  0.262510726  0.243310284  0.174719473  0.090094527
 [6]  0.080125926  0.009127941 -0.023264543 -0.049654436 -0.250950890

Largest  eigenvalues:
 [1] 97035674 94675517 88018423 85020305 84023748 82244669 81925478 79716882
 [9] 78317532 76419387

Smallest eigenvalues:
 [1]  0.375420251  0.331734607  0.292932432  0.255818150  0.182293959
 [6]  0.143995165  0.081662550 -0.004589589 -0.315916134 -0.369067254

Largest  eigenvalues:
 [1] 99956406 96929096 89844489 86778996 85067232 83608526 82739479 80589682
 [9] 79990646 77277768

Smallest eigenvalues:
 [1]  0.45135554  0.45099710  0.44210050  0.41641268  0.29732456  0.25091161
 [7]  0.23932332  0.23155627 -0.05122225 -0.27781981

Largest  eigenvalues:
 [1] 99443371 96233487 89679343 86206202 85366398 83828236 82464618 80993610
 [9] 79639737 77883084

Smallest eigenvalues:
 [1]  0.322345994  0.311841269  0.306704379  0.227729906  0.181674396
 [6]  0.142532968  0.036632283  0.018214785  0.001388422 -0.135509565

Largest  eigenvalues:
 [1] 97642845 96213358 89542657 85702869 84271301 82836222 82292405 79811486
 [9] 79482891 76532962

Smallest eigenvalues:
 [1]  0.28481610  0.28279875  0.25455030  0.21957068  0.21225153  0.10422880
 [7] -0.01635793 -0.05413075 -0.13564742 -0.37879992

Largest  eigenvalues:
 [1] 98729612 96217519 89388901 86163221 84532864 83021909 82487956 80266098
 [9] 79640379 77147473

Smallest eigenvalues:
 [1]  0.37861828  0.36425935  0.33924189  0.33146964  0.32595628  0.28190339
 [7]  0.12957517  0.07153319 -0.09206744 -0.10984948

Largest  eigenvalues:
 [1] 98290129 97119354 90094559 86151959 85602654 83825482 82819916 80355804
 [9] 80040197 77390833

Smallest eigenvalues:
 [1]  0.4690518  0.3944267  0.3436349  0.3237457  0.2576546  0.2271785
 [7]  0.2166449  0.1462338 -0.1338530 -0.2791152

Largest  eigenvalues:
 [1] 99745942 95761893 89811844 85351340 85159813 82896329 82737409 80588156
 [9] 79647884 77657118

Smallest eigenvalues:
 [1]  0.29853507  0.25527026  0.24421619  0.23673835  0.15038527  0.13882399
 [7]  0.12645394  0.02038824 -0.11947001 -0.37218149

Largest  eigenvalues:
 [1] 98859117 97848875 90957788 86655989 86240604 84116248 83918632 81556170
 [9] 80358538 78391958

Smallest eigenvalues:
 [1]  0.373135740  0.364616979  0.353102074  0.337331571  0.270222883
 [6]  0.242042927  0.202188157  0.162763061 -0.005018144 -0.456501178

Largest  eigenvalues:
 [1] 98772103 94478806 88636212 84634983 83927568 82266229 81781790 80078692
 [9] 78626520 76820664

Smallest eigenvalues:
 [1]  0.40022422  0.37522604  0.37412534  0.35527681  0.29493933  0.18039555
 [7]  0.14180878  0.12389672 -0.02528634 -0.11756021

Largest  eigenvalues:
 [1] 100035885  96529283  89963471  86057691  85557221  83309737  82823923
 [8]  80821231  79664571  77824054

Smallest eigenvalues:
 [1]  0.22886423  0.20446361  0.19565306  0.15979919  0.13168703  0.07282501
 [7]  0.06773439  0.05458765 -0.07287387 -0.98799769

Largest  eigenvalues:
 [1] 98658511 96782287 90077766 86141917 85984971 83820536 83569788 81659254
 [9] 79784013 78330633

Smallest eigenvalues:
 [1]  0.27403230  0.24682704  0.23881421  0.20939585  0.13549206  0.10028434
 [7] -0.05113872 -0.05811827 -0.13349633 -0.25240867

Largest  eigenvalues:
 [1] 100494618  96114754  89715203  86428956  85337232  83775297  83045281
 [8]  80904438  80126143  77817060

Smallest eigenvalues:
 [1]  0.3798479  0.3688158  0.3364864  0.3303298  0.3272489  0.3162162
 [7]  0.1992480  0.1259659 -0.1398778 -0.3440427

Largest  eigenvalues:
 [1] 100410882  95396757  88751964  85551621  85523489  82527769  82090999
 [8]  80395773  78800558  77129034

Smallest eigenvalues:
 [1]  0.33297422  0.29790431  0.29286483  0.28843265  0.25235799  0.22673159
 [7]  0.21263566  0.19600496  0.19542258 -0.06945186

Largest  eigenvalues:
 [1] 98837058 97123615 89886140 86308816 84865807 84574869 82123122 81249554
 [9] 79580641 78345490

Smallest eigenvalues:
 [1]  0.355077112  0.350719211  0.326042181  0.296514661  0.208291617
 [6]  0.189387299  0.161544620  0.102807617  0.077319575 -0.001189006

Largest  eigenvalues:
 [1] 100476566  96798950  91026950  86171653  85485491  84370204  82689733
 [8]  81447276  80029234  78216619

Smallest eigenvalues:
 [1]  0.38835580  0.36551427  0.35402454  0.29785552  0.21562170  0.21157276
 [7]  0.17981580  0.12157408 -0.08894265 -0.08937981

Largest  eigenvalues:
 [1] 99460731 97427927 90684120 86734363 85572392 83707485 83369576 80970686
 [9] 80153589 78089272

Smallest eigenvalues:
 [1]  0.27768815  0.27614297  0.24100552  0.11418914  0.10189489  0.02029595
 [7] -0.02409096 -0.14590894 -0.18412974 -0.32071125

Largest  eigenvalues:
 [1] 100438388  94792822  89591775  85614689  84710004  82994653  82410232
 [8]  81137004  79061385  77677454

Smallest eigenvalues:
 [1]  0.3453203  0.3397317  0.3233700  0.3120832  0.2959284  0.1813801
 [7]  0.0192316 -0.1195605 -0.2008387 -0.3420154

Largest  eigenvalues:
 [1] 101743458  97013015  91185443  87005154  86364388  84297600  83431535
 [8]  81759283  80858983  78797023

Smallest eigenvalues:
 [1]  0.43650886  0.36076152  0.33759084  0.29757485  0.22891426  0.20259403
 [7]  0.18813998  0.05711445 -0.43878317 -0.79299022

Largest  eigenvalues:
 [1] 102500640  97062974  91394395  86936944  86672340  84427104  83425725
 [8]  81707388  80408492  78657733

Smallest eigenvalues:
 [1]  0.410386588  0.381209301  0.349629899  0.323425522  0.286472190
 [6]  0.256594317  0.210740097  0.101591392 -0.002145321 -0.198620150

Largest  eigenvalues:
 [1] 98348808 97535945 90524133 87179178 85127526 84475930 83523867 81460911
 [9] 80536335 78396110

Smallest eigenvalues:
 [1]  0.29651045  0.29356453  0.26481037  0.26069759  0.16710442  0.12839739
 [7]  0.11130759  0.09198345 -0.03437715 -0.33216658

Largest  eigenvalues:
 [1] 97735531 96710453 89789093 86520798 84310691 83303824 82935331 80645597
 [9] 79612318 77186769

Smallest eigenvalues:
 [1]  0.33984843  0.32673202  0.30049812  0.25743596  0.24022707  0.11653070
 [7]  0.04049596 -0.07248766 -0.68144113 -1.00090193

Largest  eigenvalues:
 [1] 100224721  96583178  90816691  86393696  85818164  84171253  83367723
 [8]  81615367  80343922  78501805

Smallest eigenvalues:
 [1]  0.4136193  0.4011755  0.3677415  0.3121629  0.2756345  0.2629066
 [7]  0.0394471 -0.2190153 -0.2527221 -0.7285935

Largest  eigenvalues:
 [1] 100047612  95239824  89660937  85294714  85252926  83022023  82581871
 [8]  80638899  79502001  77710669

Smallest eigenvalues:
 [1]  0.40839468  0.39874306  0.39242510  0.37805145  0.33232260  0.32985684
 [7]  0.28811633  0.23303703  0.10330107 -0.09094716

Largest  eigenvalues:
 [1] 99920097 95761768 89767763 85597931 85256643 82640229 82485340 80371137
 [9] 79358807 77271808

Smallest eigenvalues:
 [1]  0.45961726  0.40703058  0.39448133  0.37865704  0.37068883  0.27373200
 [7]  0.26225922  0.22040196  0.20106544 -0.06478495

Largest  eigenvalues:
 [1] 99473641 96127134 89231087 86246488 85487092 82988827 82206553 80180493
 [9] 79336506 77040230

Smallest eigenvalues:
 [1]  0.36595581  0.34903232  0.30691141  0.26846925  0.23379219  0.21200380
 [7]  0.15083474  0.09010609 -0.32297292 -0.57526093

Largest  eigenvalues:
 [1] 99273030 97166982 90932544 87166389 84974173 83357313 83194497 80603215
 [9] 80000309 77510943

Smallest eigenvalues:
 [1]  0.3851452  0.3818509  0.3426629  0.3245424  0.2641816  0.2208535
 [7]  0.1760051  0.1186726 -0.0736515 -0.1440016

Largest  eigenvalues:
 [1] 101024706  96609214  89835452  86425978  85679366  83785716  82723426
 [8]  81123755  79930253  77985604

Smallest eigenvalues:
 [1]  0.30920410  0.27671668  0.25686651  0.19981567  0.18665654  0.18423982
 [7]  0.16198289  0.06473794 -0.31880380 -0.39032891

Largest  eigenvalues:
 [1] 98885397 96726960 90846854 86643201 84929480 84044000 83294322 81110266
 [9] 80447717 78276114

Smallest eigenvalues:
 [1]  0.39838245  0.35036614  0.32766634  0.22231630  0.20469045  0.16577983
 [7]  0.09912122 -0.34726823 -0.42791126 -0.48356249

Largest  eigenvalues:
 [1] 101783620  97825931  91225498  87376845  86751437  84032473  83789608
 [8]  81763826  80532478  78700246

Smallest eigenvalues:
 [1]  0.42040981  0.36646895  0.35148799  0.33581034  0.29017098  0.24382018
 [7]  0.10913589  0.06364797  0.05196649 -1.03644202

Largest  eigenvalues:
 [1] 99183696 96667653 90524013 86984337 84353734 84188920 83192301 81747855
 [9] 80229049 78362409

Smallest eigenvalues:
 [1]  0.182744795  0.097649252  0.086594991  0.061893819  0.057781883
 [6] -0.007763881 -0.011758081 -0.323473398 -0.556873650 -3.093486907

Largest  eigenvalues:
 [1] 98399192 97328123 91161008 86824054 85043315 84196868 83707796 81356709
 [9] 80823293 78308159

Smallest eigenvalues:
 [1]  0.49664862  0.38861652  0.38490686  0.37964142  0.36688734  0.29506705
 [7]  0.20537207  0.09283510 -0.02305328 -0.19663247

Largest  eigenvalues:
 [1] 99538386 96697275 90867385 86634980 85116349 83496136 82969194 80824288
 [9] 80265036 77748292

Smallest eigenvalues:
 [1]  0.45764204  0.43522455  0.40738049  0.40663933  0.40575750  0.39548711
 [7]  0.30030275  0.23288669 -0.03119384 -0.10216182

Largest  eigenvalues:
 [1] 98636406 96078335 89843206 86388961 84214265 83234529 82815918 80948985
 [9] 79898731 77914697

Smallest eigenvalues:
 [1]  0.38020826  0.36753675  0.28338110  0.25377733  0.20129663  0.19264840
 [7]  0.18565038  0.09461722 -0.03626982 -0.04946334

Largest  eigenvalues:
 [1] 101838993  96756288  91169957  86382049  86148593  84748967  82988664
 [8]  81982233  80531681  79136495

Smallest eigenvalues:
 [1]  0.426044550  0.410347850  0.346535148  0.327959055  0.291376013
 [6]  0.223830945  0.138596016  0.008732714 -0.043980602 -0.313279641

Largest  eigenvalues:
 [1] 99847941 97026909 90541133 86800764 85684510 84102053 83394529 81539170
 [9] 80447749 78171220

Smallest eigenvalues:
 [1]  0.31350510  0.28915371  0.27987674  0.23052247  0.21965724  0.14746622
 [7]  0.11539168 -0.04531777 -0.24138083 -0.24578704

Largest  eigenvalues:
 [1] 99933756 96594597 89929089 86458027 84871533 84273391 82672712 81484442
 [9] 79936598 78273130

Smallest eigenvalues:
 [1]  0.2799180  0.2444111  0.2295801  0.2174750  0.1938087  0.1440567
 [7]  0.1356819 -0.2966907 -0.4874643 -1.0039626

Largest  eigenvalues:
 [1] 98198057 96973988 90197533 86245645 85054755 84136976 82180519 81155417
 [9] 79155553 78190695

Smallest eigenvalues:
 [1]  0.46066893  0.44394651  0.43858698  0.43055836  0.42919192  0.32624550
 [7]  0.28120610  0.22569189  0.09295630 -0.05083171

Largest  eigenvalues:
 [1] 100831147  96830649  90607187  86372222  85972076  83372078  82759171
 [8]  80874713  79708634  77627111

Smallest eigenvalues:
 [1]  0.42829647  0.40999005  0.39722576  0.35849593  0.34251641  0.30043016
 [7]  0.28943356  0.09552253  0.07680635 -0.13672731

Largest  eigenvalues:
 [1] 98621220 97086252 90344941 87141851 84485112 83825264 83147559 80724761
 [9] 80123649 77406472

Smallest eigenvalues:
 [1]  0.18389503  0.18372193  0.12822900  0.12504277  0.08795327  0.07601556
 [7]  0.06962724  0.03393597 -0.17476871 -0.21304736

Largest  eigenvalues:
 [1] 97054864 96267448 90271226 87015051 84342747 83583121 83479696 81762372
 [9] 80575122 78320702

Smallest eigenvalues:
 [1]  0.54647024  0.50914350  0.47300351  0.39829130  0.35744543  0.30066341
 [7]  0.21865488  0.15150680  0.10686805 -0.03764187

Largest  eigenvalues:
 [1] 100177717  97149296  90919394  86903117  85598857  83859986  83713001
 [8]  81314877  80531967  78210634

Smallest eigenvalues:
 [1]  0.36188095  0.33154497  0.28084677  0.27027198  0.25349816  0.23266924
 [7]  0.16157990 -0.08828979 -0.09259169 -0.15250096

Largest  eigenvalues:
 [1] 99508726 95689348 89370252 85700586 83901788 83123438 82806295 80739396
 [9] 79483378 77428633

Smallest eigenvalues:
 [1]  0.33630454  0.30777249  0.30537957  0.28594531  0.19288364  0.16615106
 [7]  0.09010590  0.05899619 -0.10405405 -0.34019080

Largest  eigenvalues:
 [1] 99332276 95920113 90030227 86067077 83662528 83536728 82451170 81046350
 [9] 79893757 77975274

Smallest eigenvalues:
 [1]  0.39276363  0.35040358  0.32994772  0.32001891  0.29454848  0.16857480
 [7]  0.12142075  0.07432521  0.01099322 -0.29693436

Largest  eigenvalues:
 [1] 100299555  96759039  90566330  86307629  85931863  83694099  83024913
 [8]  81075841  80356558  78067487

Smallest eigenvalues:
 [1]  0.21893762  0.19593698  0.18543051  0.14873324  0.14516919  0.13645890
 [7]  0.11023235 -0.02897616 -0.14211528 -0.16044410

Largest  eigenvalues:
 [1] 100431057  95961096  89341427  86642375  85186878  83183779  82061555
 [8]  80101802  79347220  77445793

Smallest eigenvalues:
 [1]  0.2602365  0.2570870  0.2388784  0.2053796  0.1995073  0.1046424
 [7] -0.1621127 -0.2250190 -0.2843639 -0.3168477

Largest  eigenvalues:
 [1] 99647172 96916163 90640776 86239395 85470397 83579807 83328086 80822148
 [9] 80163657 77952000

Smallest eigenvalues:
 [1]  0.40400429  0.36604617  0.30860037  0.28677286  0.28115367  0.22716540
 [7]  0.04393261 -0.05833318 -0.11548213 -0.47605436

Largest  eigenvalues:
 [1] 101649014  95522373  90100448  85653832  85473953  83194115  82216662
 [8]  81115959  79330155  77859028

Smallest eigenvalues:
 [1]  0.37558747  0.36683486  0.31083082  0.22741827  0.21773171  0.11644854
 [7]  0.07298194  0.07005614 -0.41328467 -0.65295298

Largest  eigenvalues:
 [1] 102148664  97614896  91630564  87671115  86884646  85794834  83672506
 [8]  83012664  80790557  79753091

Smallest eigenvalues:
 [1]  0.51971322  0.50236056  0.48731704  0.45929382  0.45197303  0.38667543
 [7]  0.37841139  0.33527757 -0.03335841 -0.08405912

Largest  eigenvalues:
 [1] 99655885 96744856 90161402 86840470 85157421 83588651 83260994 80827890
 [9] 80257875 77936108

Smallest eigenvalues:
 [1]  0.43942356  0.40974277  0.39342205  0.36772868  0.29667184  0.29486481
 [7]  0.13749098 -0.02550308 -0.18765960 -0.27126923

Largest  eigenvalues:
 [1] 100636001  96151021  90344495  86105475  85282811  83325189  82874150
 [8]  80650549  79995501  77380646

Smallest eigenvalues:
 [1]  0.43776415  0.38631081  0.29806117  0.29448067  0.28620525  0.28405758
 [7]  0.28110522  0.16351536 -0.04610377 -0.24788462

Largest  eigenvalues:
 [1] 99272851 96419933 90717019 86045286 85116829 84428760 82978278 81984611
 [9] 79943126 78876023

Smallest eigenvalues:
 [1]  0.5509046  0.5457060  0.5062425  0.4487377  0.4130501  0.3349153
 [7]  0.3257687  0.1665704  0.1453993 -0.1944866

Largest  eigenvalues:
 [1] 99710199 97256160 90470268 87257597 85442606 83810170 82954597 80691333
 [9] 80276279 77766906

Smallest eigenvalues:
 [1]  0.22922968  0.21369999  0.20204880  0.18203972  0.15649445  0.09370964
 [7] -0.04422377 -0.08416410 -0.08849072 -0.45506529

Largest  eigenvalues:
 [1] 99619219 96888235 91079179 86104055 84816616 83456118 83312997 80852636
 [9] 80289936 78000833

Smallest eigenvalues:
 [1]  0.393891474  0.368868367  0.365145559  0.330822180  0.264080828
 [6]  0.263617170  0.259932186  0.137141252  0.001561397 -0.344528383

Largest  eigenvalues:
 [1] 100970049  95705926  89944456  86153788  84956462  83054093  82572837
 [8]  80673284  79605524  77463145

Smallest eigenvalues:
 [1]  0.3113159  0.2756453  0.1911906  0.1798713  0.1717007  0.1586581
 [7]  0.1500908  0.1007756 -0.3973729 -0.7090370

Largest  eigenvalues:
 [1] 100207484  95748029  89844841  85332900  84837122  83780557  82282207
 [8]  81352604  79617378  77938945

Smallest eigenvalues:
 [1]  0.40223768  0.39144923  0.36552822  0.31730640  0.27804525  0.17950052
 [7]  0.16813610  0.11463871 -0.04986981 -0.32003184

Largest  eigenvalues:
 [1] 99596151 96556998 90134915 86154525 85877594 83598114 83105399 81157801
 [9] 80066606 78360035

Smallest eigenvalues:
 [1]  0.38516375  0.35856738  0.35664409  0.34413946  0.28296176  0.22722562
 [7]  0.18128588  0.12341308 -0.06084001 -0.57956965

Largest  eigenvalues:
 [1] 99943402 96453675 89793614 86457386 85402811 83129530 82427586 80566073
 [9] 79726739 77550637

Smallest eigenvalues:
 [1]  0.3761855  0.3746307  0.3255401  0.2959918  0.2527528  0.1944826
 [7]  0.1570679  0.1247068 -0.2664169 -0.6922870

Largest  eigenvalues:
 [1] 98606790 96276700 90175078 85858342 85118926 83127152 82596470 80645223
 [9] 79490738 77445099

Smallest eigenvalues:
 [1]  0.37924129  0.30634121  0.26664416  0.20665351  0.19501598  0.11445113
 [7]  0.02504388 -0.01858016 -0.36288679 -0.47341315

Largest  eigenvalues:
 [1] 100681860  96008258  90031237  86153295  86135000  84138442  83281297
 [8]  81845217  80091499  78713334

Smallest eigenvalues:
 [1]  0.42865001  0.38990625  0.36763473  0.35062993  0.28735282  0.26719084
 [7]  0.18972497  0.10848164  0.08819804 -0.25454027

Largest  eigenvalues:
 [1] 99766283 96853515 90420953 86632539 85688765 84137676 82793902 81313784
 [9] 79926007 78404812

Smallest eigenvalues:
 [1]  0.25595105  0.22639834  0.22466148  0.18638676  0.14432052  0.11389366
 [7]  0.06940228 -0.33635245 -0.58425217 -0.68676949

Largest  eigenvalues:
 [1] 99510124 96771213 90629724 86650092 85341574 84012763 83365452 81783816
 [9] 80174278 78695313

Smallest eigenvalues:
 [1]  0.4285852254  0.3997891407  0.3969092617  0.3712435518  0.3664479509
 [6]  0.3549069316  0.1300255951  0.0731919449  0.0380002154 -0.0006040823

Largest  eigenvalues:
 [1] 100364487  96160140  90431147  85580724  84944369  82997627  82528999
 [8]  80440018  79946214  77468090

Smallest eigenvalues:
 [1]  0.46776230  0.45988348  0.45474318  0.44117380  0.40999107  0.30586253
 [7]  0.24687362  0.20382624  0.08107048 -0.35598098

Largest  eigenvalues:
 [1] 99029449 97009562 90557522 86998871 85211551 83767014 83006087 80692745
 [9] 80284306 77657956

Smallest eigenvalues:
 [1]  0.34728103  0.33471874  0.30801816  0.29508497  0.22548739  0.12634063
 [7]  0.12631132  0.09962885 -0.12022322 -0.97869459

Largest  eigenvalues:
 [1] 100469475  95876078  89979992  85869378  84699315  83095235  82597882
 [8]  80831290  79884327  77675066

Smallest eigenvalues:
 [1]  0.44706944  0.39920568  0.38985087  0.38958923  0.25891558  0.18416717
 [7]  0.15265301  0.14701494  0.08483516 -0.12834914

Largest  eigenvalues:
 [1] 100271850  95025032  89019897  85345507  84621904  82838048  81581391
 [8]  80368487  78668508  77202431

Smallest eigenvalues:
 [1]  0.47215679  0.39479868  0.34281193  0.33326029  0.29871603  0.23902886
 [7]  0.20912750  0.20871301  0.08198655 -0.08068304

Largest  eigenvalues:
 [1] 99333755 96743208 90837950 86361918 84596958 84446254 82755116 81852648
 [9] 79799114 78791922

Smallest eigenvalues:
 [1]  0.35998541  0.24171326  0.23265200  0.23159816  0.17045843  0.15681433
 [7] -0.07185973 -0.25306503 -0.28851923 -0.51593553

Largest  eigenvalues:
 [1] 100212223  96788515  90527247  87568042  84999210  84115242  83754942
 [8]  81059640  80616070  77720318

Smallest eigenvalues:
 [1]  0.43752264  0.43465960  0.43031536  0.32962370  0.32276997  0.27011194
 [7]  0.16963925  0.08553073 -0.11178122 -0.20050478

Largest  eigenvalues:
 [1] 99138418 96584437 89887545 86572127 84646997 83243397 82991443 80473208
 [9] 80073227 77419974

Smallest eigenvalues:
 [1]  0.20043427  0.16173165  0.14849818  0.04248158  0.03502653 -0.02527992
 [7] -0.02737679 -0.10294468 -0.19073288 -0.48769691

Largest  eigenvalues:
 [1] 96965417 96822366 90658075 86010713 84167454 83493425 83065549 80584530
 [9] 79777801 77470917

Smallest eigenvalues:
 [1]  0.314275122  0.284166683  0.284143168  0.268311125  0.152286799
 [6]  0.141677021  0.119435624  0.111505918  0.003968222 -0.239445632

Largest  eigenvalues:
 [1] 98020104 96050530 89620544 85472708 83752495 83069269 82848614 80624445
 [9] 79517959 77406359

Smallest eigenvalues:
 [1]  0.26293799  0.22792776  0.18670991  0.16475471  0.14428839  0.12266500
 [7]  0.08996917 -0.20903127 -0.62081804 -1.45886878

Largest  eigenvalues:
 [1] 100657250  96917723  90829997  87242993  85322828  84391765  84028328
 [8]  81985538  80922661  78700272

Smallest eigenvalues:
 [1]  0.43378311  0.37363816  0.35481855  0.34296215  0.29283867  0.23132859
 [7]  0.18172462  0.08693672 -0.12029571 -0.24043411

Largest  eigenvalues:
 [1] 98294759 96319160 89798418 86356281 84383428 83157465 83028146 80636073
 [9] 79804024 77343655

Smallest eigenvalues:
 [1]  0.49396069  0.38615448  0.34757115  0.31180418  0.27055155  0.20844742
 [7]  0.17181707  0.11385935  0.01217052 -0.06995956

Largest  eigenvalues:
 [1] 101294337  95492743  89634942  85869682  85568152  83603315  82530069
 [8]  80906557  79686247  77812945

Smallest eigenvalues:
 [1]  0.1526260314  0.1311212752  0.1014911600  0.0979826409  0.0373865808
 [6]  0.0349146992 -0.0004025047 -0.0521226967 -0.4723957994 -0.7229358658

Largest  eigenvalues:
 [1] 101893790  97244837  90812424  87115832  86693676  85898778  82935662
 [8]  82444550  80784605  79199158

Smallest eigenvalues:
 [1]  0.14384739  0.08788012  0.08777941  0.02201911 -0.04388965 -0.23056977
 [7] -0.30866149 -0.52467144 -0.75183837 -0.90022854

Largest  eigenvalues:
 [1] 98023175 97487943 91364914 86462944 85372742 84248844 83734940 81182009
 [9] 80406336 78317018

Smallest eigenvalues:
 [1]  0.4530279  0.3534015  0.3061967  0.2845028  0.2399986  0.1968493
 [7]  0.1812347  0.1071914 -0.2455290 -0.3969593

Largest  eigenvalues:
 [1] 98975078 96608261 90288001 86348950 85085949 83305422 83109169 80795737
 [9] 79822024 77816369

Smallest eigenvalues:
 [1]  0.343317748  0.339378521  0.271306168  0.265682309  0.262015729
 [6]  0.254886949  0.163092072  0.083546179 -0.007327227 -0.453658290

Largest  eigenvalues:
 [1] 101186982  95847778  90160713  86656954  85252703  84153975  82222508
 [8]  81421827  79650678  78453483

Smallest eigenvalues:
 [1]  0.40731401  0.37668139  0.33959024  0.26674997  0.23655481  0.15124796
 [7]  0.13885303  0.06057001 -0.55934292 -0.63713510

Largest  eigenvalues:
 [1] 101268224  96547217  91192230  86637955  85882631  84559945  82962242
 [8]  82162655  80263228  79313609

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	19.50949	0.6735958	1821.112	0.05	2.281469	2.326024

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)/
             (GET_results[[5]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

HR ~ air pressure + noise

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- HR_fd
covariates <- list(air_pressure = airpressure_fd, 
                   noise = noise_fd
                  )
path_plot <- 'figures/model_HR_airpress_noise_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
                     air_pressure = list(nbetabasis = 90, norder = 4, lambda = 1e2),
                     noise = list(nbetabasis = 90, norder = 4, lambda = 1e2)
                    )

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, 
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 30.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 172 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Smallest eigenvalues:
 [1]  0.15845393  0.15456730  0.15323569  0.15309657  0.15263615  0.15138328
 [7]  0.15056304  0.07148425  0.07130301 -0.15743932

Largest  eigenvalues:
 [1] 18484502 18333396 18120823 18065769 17986287 17761297 17622487 17535008
 [9] 17467479 17328246

Smallest eigenvalues:
 [1]  0.17853850  0.17663013  0.17544969  0.17417858  0.17227721  0.17139890
 [7]  0.15289376  0.09391307  0.07861465 -0.11685164

Largest  eigenvalues:
 [1] 18497405 18345455 18101366 18048431 17963927 17857263 17678093 17601874
 [9] 17508740 17392413

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	8.784591	0.401951	6.733928	0.04	0.6636861	0.6926779

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

HR ~ air pressure + noise + air temp

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- HR_fd
covariates <- list(air_pressure = airpressure_fd, 
                   noise = noise_fd,
                   temperature = temperature_fd
                  )
path_plot <- 'figures/model_HR_airpress_noise_temp_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
                     air_pressure = list(nbetabasis = 90, norder = 4, lambda = 1e2),
                     noise = list(nbetabasis = 90, norder = 4, lambda = 1e2),
                     temperature = list(nbetabasis = 90, norder = 4, lambda = 1e2)
                    )

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, 
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 25.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 262 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Smallest eigenvalues:
 [1]  0.10049050  0.09870038  0.09683498  0.09604983  0.09565113  0.09325221
 [7]  0.09139448  0.05526609  0.04407148 -0.32047288

Largest  eigenvalues:
 [1] 16355053 16198674 16132178 15903323 15792269 15611790 15471286 15345177
 [9] 15263289 15199542

Smallest eigenvalues:
 [1]  0.10760275  0.10682632  0.10317115  0.10090800  0.09703859  0.09303815
 [7]  0.08418235  0.06159548  0.04931716 -1.22004555

Largest  eigenvalues:
 [1] 16361221 16100095 15977299 15853573 15809618 15699875 15574450 15511030
 [9] 15414523 15261930

Smallest eigenvalues:
 [1]  0.13587619  0.13276008  0.13207705  0.12912577  0.12441757  0.12243005
 [7]  0.09461737  0.07095360  0.06942470 -0.22605266

Largest  eigenvalues:
 [1] 16254373 16132921 16014237 15926807 15820685 15699559 15536213 15475377
 [9] 15326802 15241950

Smallest eigenvalues:
 [1]  0.082537385  0.081961386  0.079301818  0.078346931  0.076345831
 [6]  0.073700496  0.068863082  0.043700523  0.031455814 -0.009860154

Largest  eigenvalues:
 [1] 16404595 16215084 16190676 15860716 15797660 15695601 15490967 15395130
 [9] 15287997 15235032

Smallest eigenvalues:
 [1]  0.0579022118  0.0560362018  0.0546029674  0.0532622023  0.0514941030
 [6]  0.0510026453  0.0487051856  0.0471930905  0.0278328470 -0.0001433643

Largest  eigenvalues:
 [1] 16432027 16160121 16156371 15928699 15903793 15677388 15561430 15426807
 [9] 15346551 15292998

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	8.724708	0.4400124	9.678972	0.21	1.179298	0.9076917

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
            (GET_results[[3]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

HR ~ alt + n + acc + Sex

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- HR_fd
covariates <- list(altitude = altitude_fd, 
                   noise = noise_fd,
                   acceleration = acceleration_fd)
path_plot <- 'figures/model_HR_alt_noise_acc_Sex_N200'
basis_params <- list(beta_0 = list(nbetabasis = 60, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 60, norder = 4, lambda = 1e4),
                     noise = list(nbetabasis = 60, norder = 4, lambda = 1e4),
                     acceleration = list(nbetabasis = 60, norder = 4, lambda = 1e4),
                     Sex = list(nbetabasis = 60, norder = 4, lambda = 1e4))

factors <- list(Sex = participant_info$Sex |> as.factor())

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params,
                            factors = factors)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}
for (fact in names(factors)) {
    assign(fact, factors[[fact]][participant_info$ID %in% (model_1$common_IDs |> 
                                                           substr(4, 9))] |> as.numeric())
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, 
                            basis_params = basis_params, nperm = nperm, factors = factors, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        if(!is.na(factors[1])) {for (fact in names(factors)) {
            assign(paste0(fact, '_BS'), 
                   factors[[fact]][participant_info$ID %in% (model_1$common_IDs |> substr(4, 9))][BS_sample] |> 
                   as.numeric())}}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS'))
        if(!is.na(factors[1])) {for(nam in names(factors)) {formula_BS <- paste0(formula_BS, '+', nam, '_BS')}}
        formula_BS <- as.formula(formula_BS)
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 31.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 450 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Smallest eigenvalues:
 [1]  0.9688860  0.7923770  0.7839802  0.7089242  0.7061079  0.7004947
 [7]  0.5701982  0.4222949  0.4087865 -0.5678656

Largest  eigenvalues:
 [1] 135256038 131203586 122990816 117887683 114015726 113315527 113149768
 [8] 110015403 109084873 105696629

Smallest eigenvalues:
 [1]  0.9544816  0.9361034  0.8328902  0.8091576  0.7739644  0.7606454
 [7]  0.7575709  0.7553243  0.1693061 -1.5115225

Largest  eigenvalues:
 [1] 137501025 131427866 122889632 118097765 116624626 113193359 113001944
 [8] 110026587 108756610 105629481

Smallest eigenvalues:
 [1]  0.9614418  0.9225914  0.6914412  0.5924914  0.5497382  0.4885853
 [7]  0.4144111  0.3878296  0.1064785 -0.4911248

Largest  eigenvalues:
 [1] 137094604 131113312 123628899 116688854 116595749 114057268 112946378
 [8] 110814368 108618032 106607737

Smallest eigenvalues:
 [1]  1.1564350  1.1338316  1.0377003  1.0259619  0.9665639  0.9647546
 [7]  0.8127989  0.6185221  0.3791011 -0.7589908

Largest  eigenvalues:
 [1] 136164340 132656839 124259577 118533944 115847823 114388485 113266284
 [8] 110231758 109759032 105893395

Smallest eigenvalues:
 [1]  1.1505863  1.1160754  1.0165090  0.9922383  0.7094019  0.6516838
 [7]  0.6134164  0.6052341  0.5655830 -0.6573829

Largest  eigenvalues:
 [1] 133436218 130976030 122381334 118328235 114037347 112576615 112408328
 [8] 109260710 108780920 104773053

Smallest eigenvalues:
 [1]  1.1185887  1.0582716  1.0201250  0.9637271  0.7956847  0.7826604
 [7]  0.6542965  0.5654786  0.4072251 -2.3559232

Largest  eigenvalues:
 [1] 130885760 130852944 122800509 118881715 114030886 113204217 112216022
 [8] 109642554 109304156 105369724

Smallest eigenvalues:
 [1]  1.0545992  1.0354944  0.9779019  0.9233780  0.8905897  0.5518688
 [7]  0.4873694  0.4469574  0.3539931 -0.3402065

Largest  eigenvalues:
 [1] 137221285 132919786 123981982 118234497 117328678 113931463 113638093
 [8] 110702506 109484838 106761073

Smallest eigenvalues:
 [1]  1.2248888  1.1887652  1.0533451  0.9403865  0.9210631  0.9103510
 [7]  0.8423889  0.6573866  0.5516138 -0.1483955

Largest  eigenvalues:
 [1] 135967218 133801548 124451848 119797832 115847951 114282065 113843866
 [8] 110629861 110098930 106579426

Smallest eigenvalues:
 [1]  1.30813749  1.23787645  1.11359816  1.08186806  0.99086914  0.98551032
 [7]  0.74845577  0.74071083  0.73728535 -0.01505082

Largest  eigenvalues:
 [1] 134207169 132134609 124319846 119466943 113807668 113757586 113304155
 [8] 110364240 109728413 106183448

Smallest eigenvalues:
 [1]  0.9093957  0.8429204  0.8335873  0.7220211  0.6488800  0.6238243
 [7]  0.5957890  0.4801154  0.4549419 -0.2964439

Largest  eigenvalues:
 [1] 133564077 130973207 123187379 117847002 113721761 113522829 112256016
 [8] 109508175 109079325 104938910

Smallest eigenvalues:
 [1]  1.1379407  1.1350288  1.0406986  1.0160823  0.9563521  0.8142150
 [7]  0.7077676  0.5935217  0.5108063 -0.5471780

Largest  eigenvalues:
 [1] 135589123 131853370 123504640 118080264 115528579 113263608 112991338
 [8] 109711348 108986896 105540395

Smallest eigenvalues:
 [1]  0.9958364  0.9658244  0.9067076  0.6886484  0.6639905  0.6244460
 [7]  0.3789718  0.1823708 -0.1282827 -0.2723373

Largest  eigenvalues:
 [1] 135899280 131617753 122651526 117517101 117307561 113063232 112617621
 [8] 110270841 108429819 105988203

Smallest eigenvalues:
 [1]  1.2189650  1.1226973  1.0456972  0.9896847  0.9072902  0.8142459
 [7]  0.7862135  0.7627543  0.4311736 -0.3123060

Largest  eigenvalues:
 [1] 135784267 132040516 124005747 118895274 115183729 113834466 113179370
 [8] 110398891 109733851 106098447

Smallest eigenvalues:
 [1]  1.0673985  1.0276958  0.9202925  0.7714554  0.7674908  0.7567785
 [7]  0.6805751  0.5179251  0.4594829 -1.0889680

Largest  eigenvalues:
 [1] 136233676 131115345 123195429 117389036 116851635 114412764 113143992
 [8] 111196341 109291964 107197555

Smallest eigenvalues:
 [1]  1.0690837  0.9603471  0.9035975  0.8955947  0.8855373  0.8298453
 [7]  0.4307876  0.3166552  0.2495788 -0.3645691

Largest  eigenvalues:
 [1] 137555695 131472385 123296996 116795616 116522479 113675823 112757097
 [8] 110610289 108553828 106126259

Smallest eigenvalues:
 [1]  1.0245585  0.8950231  0.8644307  0.8083248  0.7798005  0.7499528
 [7]  0.7214333  0.6622987  0.3735917 -0.2413907

Largest  eigenvalues:
 [1] 135227207 132767734 124313537 118755259 115391844 114112100 113805937
 [8] 110217395 109610881 105566847

Smallest eigenvalues:
 [1]  1.0029995  0.9328319  0.9327370  0.7864304  0.7034891  0.6673939
 [7]  0.4594537  0.4216955  0.2183513 -1.0060318

Largest  eigenvalues:
 [1] 137521867 131754185 123571527 118107671 115551061 113946805 113279981
 [8] 111044078 109348892 106127866

Smallest eigenvalues:
 [1]  0.9994690  0.9923605  0.8979505  0.8552854  0.8415888  0.7673291
 [7]  0.7044542  0.5943836  0.2936434 -1.3660862

Largest  eigenvalues:
 [1] 135827267 131919435 123966458 118766214 115619043 113775048 112836485
 [8] 110178249 109410240 105749460

Smallest eigenvalues:
 [1]  1.0396130  0.9961151  0.9130125  0.9100908  0.7780031  0.6903398
 [7]  0.6894318  0.4253155  0.2656445 -0.9492245

Largest  eigenvalues:
 [1] 133952093 132103118 123966949 119337988 115274875 114228599 112678706
 [8] 110388789 109685854 105674388

Smallest eigenvalues:
 [1]  1.1463728  1.1153447  1.1106684  0.9843023  0.8711505  0.5423673
 [7]  0.4561904  0.4381777  0.1650653 -0.3194171

Largest  eigenvalues:
 [1] 135367953 132887135 124382054 119161115 115521159 114612291 113575311
 [8] 111124531 110241836 106783026

Smallest eigenvalues:
 [1]  0.9599534  0.9208488  0.7784240  0.7152306  0.6778071  0.6279480
 [7]  0.6182952  0.5785797  0.3802319 -2.1925345

Largest  eigenvalues:
 [1] 135813654 131088733 123695233 117728555 115143708 113937891 113646450
 [8] 110764971 109238901 106156772

Smallest eigenvalues:
 [1]  0.8289328  0.7574264  0.7193836  0.6006725  0.5094471  0.4480233
 [7]  0.4358892  0.3556260  0.1490550 -0.3459324

Largest  eigenvalues:
 [1] 136451616 133599516 125078740 119203866 116952202 115594046 114341390
 [8] 111603666 109920607 107468866

Smallest eigenvalues:
 [1]  0.9456964  0.8166213  0.7219202  0.6977297  0.6921685  0.6267455
 [7]  0.3664069  0.3627567  0.2819279 -1.7848098

Largest  eigenvalues:
 [1] 131782468 131683019 123643540 119056495 114902359 112664850 112160452
 [8] 109723501 109237765 104993065

Smallest eigenvalues:
 [1]  1.08574416  1.04379105  0.87243525  0.76919023  0.75698360  0.74917196
 [7]  0.71926067  0.55608833  0.32192858 -0.07440743

Largest  eigenvalues:
 [1] 137204189 133698370 123653770 118320912 115980438 114927605 113702543
 [8] 110894210 109558845 106495311

Smallest eigenvalues:
 [1]  1.05120787  1.04194036  1.01487272  0.84994413  0.82884007  0.73016267
 [7]  0.67209992  0.38022451  0.01509145 -0.55404841

Largest  eigenvalues:
 [1] 139545221 133719550 125097865 118921985 118548854 115112308 114227798
 [8] 111756446 110199741 108045089

Smallest eigenvalues:
 [1]  1.03882583  1.03589737  1.00296502  0.99136485  0.95654367  0.68156244
 [7]  0.56062695  0.48393081  0.06807012 -0.05950702

Largest  eigenvalues:
 [1] 134660729 132528232 123727535 118831674 115788801 113922877 113733353
 [8] 110572639 109714521 106738489

Smallest eigenvalues:
 [1]  1.0396135  0.9658589  0.9288576  0.8188947  0.7920223  0.5702712
 [7]  0.5405805  0.4809489  0.4721227 -0.7104762

Largest  eigenvalues:
 [1] 134391282 131590394 123112441 117596800 114973951 113143452 112762835
 [8] 109797770 108418449 105431644

Smallest eigenvalues:
 [1]  1.0985861  1.0472141  0.8957156  0.8647416  0.8581900  0.7825575
 [7]  0.7382876  0.5735613 -0.1684700 -1.5405825

Largest  eigenvalues:
 [1] 138094351 132871277 124701353 118682935 117156566 114227129 113443152
 [8] 110656295 109328286 106572389

Smallest eigenvalues:
 [1]  0.98827770  0.91802702  0.89916978  0.83174811  0.77879069  0.74220782
 [7]  0.45411217  0.42020081  0.09615512 -1.35473343

Largest  eigenvalues:
 [1] 137226580 129641131 122202867 116765239 116068150 112224765 111172666
 [8] 109438196 107429670 105315868

Smallest eigenvalues:
 [1]  1.0626611  1.0403723  0.9546409  0.8719927  0.8703990  0.8472838
 [7]  0.7625131  0.5842803  0.4190668 -0.5842997

Largest  eigenvalues:
 [1] 134865388 133264740 124233541 118695796 115644771 114050208 113853054
 [8] 110472404 109398206 106439372

Smallest eigenvalues:
 [1]  1.1326700  1.0922024  0.9600027  0.9551540  0.8502791  0.8476822
 [7]  0.5703527  0.4598740  0.2663142 -1.3852334

Largest  eigenvalues:
 [1] 134036097 131231871 122870296 117969399 115053098 114155375 112021342
 [8] 109643866 109089247 105379549

Smallest eigenvalues:
 [1]  0.9432775  0.9171678  0.8801126  0.6817939  0.6409919  0.5686675
 [7]  0.5499618  0.4847470  0.4839770 -0.3029676

Largest  eigenvalues:
 [1] 133336389 131671868 122921902 117829257 114511870 113480728 112057007
 [8] 109110659 108697995 104527953

Smallest eigenvalues:
 [1]  1.0441547  0.8622080  0.8376512  0.6449458  0.4220183  0.4127773
 [7]  0.3766716  0.2891900  0.2540777 -2.3349884

Largest  eigenvalues:
 [1] 135409978 130621350 123305525 116890769 115116988 112917597 111904457
 [8] 109522498 108680530 105452550

Smallest eigenvalues:
 [1]  1.1737463  1.0370897  1.0367004  1.0018156  0.9337256  0.5546521
 [7]  0.5498891  0.5392489  0.4780433 -0.1168439

Largest  eigenvalues:
 [1] 136678006 131110370 122902021 117295611 114960874 113692034 112107141
 [8] 110766592 108301375 105927461

Smallest eigenvalues:
 [1]  1.09287956  1.06839714  0.96582559  0.83378381  0.80879817  0.80785344
 [7]  0.76328510  0.75127011  0.09723270 -0.04897159

Largest  eigenvalues:
 [1] 134024766 132152890 123201687 118187585 114776757 113813751 113674088
 [8] 110447327 109389374 106170001

Smallest eigenvalues:
 [1]  1.0373517  0.9628217  0.8235005  0.7981366  0.7436669  0.7305748
 [7]  0.6893718  0.3580972  0.3278450 -0.2480008

Largest  eigenvalues:
 [1] 134068829 130328346 122216629 116461162 114767052 112616520 112410744
 [8] 109313265 108378882 105618944

Smallest eigenvalues:
 [1]  0.94239969  0.91631954  0.85648240  0.83564551  0.75669972  0.58620550
 [7]  0.57479169  0.06901803 -0.24964130 -0.92038140

Largest  eigenvalues:
 [1] 136697646 132135761 123686622 117715904 116929739 113115981 112892445
 [8] 109880688 108866536 105911807

Smallest eigenvalues:
 [1]  1.03191434  1.01720133  0.97081175  0.79336619  0.79227968  0.68027693
 [7]  0.64973896  0.58258275  0.31591576 -0.09416299

Largest  eigenvalues:
 [1] 135764860 133313011 124941669 119811243 116457258 114435615 113282294
 [8] 110689677 109964691 106310896

Smallest eigenvalues:
 [1]  1.0102334  1.0053290  0.9922848  0.9440762  0.9420984  0.7800463
 [7]  0.6185816  0.6145541  0.3906510 -0.1893042

Largest  eigenvalues:
 [1] 134168773 132413407 123483919 118725487 115450878 113973195 113267006
 [8] 110043069 109115099 106326255

Smallest eigenvalues:
 [1]  1.0382794  0.9507924  0.8870887  0.8596301  0.8197861  0.6592628
 [7]  0.4005770  0.3394154  0.2245226 -0.1000553

Largest  eigenvalues:
 [1] 133454860 133243296 123388221 118452104 114077892 113646217 112838495
 [8] 110064391 109218737 105580077

Smallest eigenvalues:
 [1]  1.0167987  1.0067789  0.9547590  0.8825125  0.7061137  0.5148236
 [7]  0.4051440  0.3832299  0.3774022 -0.6660513

Largest  eigenvalues:
 [1] 136470553 131583617 124097831 117671681 115680492 113881169 113251208
 [8] 110353641 109572124 106185007

Smallest eigenvalues:
 [1]  1.14044774  1.07652696  1.05616281  0.98110823  0.86910508  0.84694068
 [7]  0.75258935  0.74457466  0.02533093 -0.32940363

Largest  eigenvalues:
 [1] 134572855 131091376 123161126 118091908 113544916 113360274 113168853
 [8] 110228013 109265994 105826947

Smallest eigenvalues:
 [1]  1.0621701  0.9427645  0.9051551  0.7601148  0.7127552  0.6917281
 [7]  0.6727694  0.6178408  0.5034638 -0.3369336

Largest  eigenvalues:
 [1] 135478646 131436911 123378303 118212557 115176749 114316871 112839297
 [8] 110765987 109095546 106718081

Smallest eigenvalues:
 [1]  1.0812048  1.0747398  1.0736365  0.9934737  0.8520125  0.6980457
 [7]  0.5633948  0.5116939  0.4333273 -1.1274514

Largest  eigenvalues:
 [1] 135882265 131209793 122888194 117444421 114638127 112831917 112129557
 [8] 109628140 108460250 104829513

Smallest eigenvalues:
 [1]  1.03732870  1.00664470  0.84059559  0.77478882  0.76739547  0.67184545
 [7]  0.58217521  0.57531073  0.09229861 -0.05517217

Largest  eigenvalues:
 [1] 137095448 131407432 123822762 117517416 116024738 114572931 112648701
 [8] 110800203 109088975 106965861

Smallest eigenvalues:
 [1]  1.1185494  0.9618374  0.8826793  0.8400191  0.7787778  0.6220969
 [7]  0.5899111  0.3627868  0.3621359 -1.8165766

Largest  eigenvalues:
 [1] 137128564 132715349 124609803 119839915 116826845 114198047 113939538
 [8] 110891242 110178742 106996164

Smallest eigenvalues:
 [1]  1.0300828  1.0123090  0.9680805  0.9600012  0.8598882  0.7299005
 [7]  0.7035601  0.4769452  0.3803877 -0.3507494

Largest  eigenvalues:
 [1] 138199497 131383770 123316687 117794606 115208842 113152572 112741264
 [8] 110383742 108698402 105728821

Smallest eigenvalues:
 [1]  1.15855795  1.03425798  1.00420820  0.95886997  0.95464209  0.78459917
 [7]  0.76063053  0.70590603  0.15621349 -0.09697355

Largest  eigenvalues:
 [1] 136527333 133215622 124499265 119061136 116017097 114439462 113995372
 [8] 111017571 110179199 107271217

Smallest eigenvalues:
 [1]  1.0899275  0.9415549  0.8288436  0.7935858  0.7935681  0.6617445
 [7]  0.5165707  0.4647370  0.4446136 -1.1766939

Largest  eigenvalues:
 [1] 136813978 131908882 123877553 117981861 116710636 113872231 113408480
 [8] 110501043 109354994 106521405

Smallest eigenvalues:
 [1]  0.9798561  0.9364494  0.9043078  0.7296532  0.7047301  0.5731803
 [7]  0.4850737  0.3515605 -0.1347396 -0.7692006

Largest  eigenvalues:
 [1] 137165980 132241603 124655682 118218050 117543621 115257665 113489925
 [8] 111406701 109504037 107381322

Smallest eigenvalues:
 [1]  1.1299150  0.9825307  0.9790333  0.9624829  0.8022683  0.7206804
 [7]  0.6934415  0.6221411  0.3919681 -0.1552567

Largest  eigenvalues:
 [1] 137694879 131383995 123206519 116574538 116432181 113597009 112774664
 [8] 110386153 108939718 106362020

Smallest eigenvalues:
 [1]  0.9894955  0.8810198  0.8657774  0.7079470  0.6990686  0.6798601
 [7]  0.5330665  0.4387386  0.4039624 -2.5682382

Largest  eigenvalues:
 [1] 135216382 133459996 124724070 120336564 115554988 115366952 114665146
 [8] 111217857 110798478 106730976

Smallest eigenvalues:
 [1]  1.0029979  0.9894337  0.9657951  0.8931327  0.8164346  0.6385867
 [7]  0.5978628  0.4032887  0.1920436 -0.4420922

Largest  eigenvalues:
 [1] 137303389 133358960 124970971 119030667 117398001 114759806 114555708
 [8] 111195691 110457642 107281242

Smallest eigenvalues:
 [1]  1.1706722  1.1636130  1.0101147  0.9820114  0.7333357  0.6732234
 [7]  0.6613315  0.5527298  0.5316512 -0.4742273

Largest  eigenvalues:
 [1] 132158494 130575865 122426208 117641221 113374585 112834698 112040247
 [8] 109352560 108647544 105236386

Smallest eigenvalues:
 [1]  1.0713429  0.9447356  0.9297435  0.8098997  0.7529481  0.6839599
 [7]  0.5237067  0.5076790  0.1330335 -0.3192479

Largest  eigenvalues:
 [1] 138112927 132166960 124182609 117773864 117595566 113885243 113202295
 [8] 111378240 109075657 107139664

Smallest eigenvalues:
 [1]  1.0078198  0.9884496  0.8281396  0.8240012  0.7819829  0.7271506
 [7]  0.6248498  0.5160166  0.3270552 -0.6627981

Largest  eigenvalues:
 [1] 136172368 132725773 123921939 118333364 116155954 113587555 113447898
 [8] 110328728 108856619 105632767

Smallest eigenvalues:
 [1]  1.0803471  1.0787975  0.9374415  0.9142182  0.7968931  0.7776288
 [7]  0.7272637  0.3873496 -0.3064515 -0.3781777

Largest  eigenvalues:
 [1] 135214937 131037347 122740232 117913818 114517981 113125097 112252269
 [8] 109615174 108564016 104600437

Smallest eigenvalues:
 [1]  1.15468054  1.13827933  1.10157035  1.04311364  1.02172702  0.70618442
 [7]  0.65712530  0.65160852  0.47955042 -0.09350394

Largest  eigenvalues:
 [1] 139268878 131214833 123639789 118037519 116924485 114191276 112706295
 [8] 111163310 108946403 106738930

Smallest eigenvalues:
 [1]  1.1500913  1.0903491  1.0377948  1.0226323  0.9639596  0.8951181
 [7]  0.7722534  0.6654304  0.3544484 -0.7270938

Largest  eigenvalues:
 [1] 134807524 129555422 122004078 116805208 113507606 112732081 111911925
 [8] 109055639 108317510 104663642

Smallest eigenvalues:
 [1]  1.1705832  1.0630012  0.9594253  0.8926407  0.7998752  0.7619922
 [7]  0.7162435  0.6524585  0.5284527 -0.4569586

Largest  eigenvalues:
 [1] 135508113 131861201 124082315 118831952 115768962 114193954 113317044
 [8] 110673094 109547710 106682237

Smallest eigenvalues:
 [1]  1.1668380  1.0706558  0.9716204  0.8585883  0.8583195  0.7228779
 [7]  0.5798090  0.5079012  0.4785799 -0.6842266

Largest  eigenvalues:
 [1] 136679991 131923202 124405717 118085272 116062159 114726834 113626859
 [8] 110897825 109701668 106968195

Smallest eigenvalues:
 [1]  0.939367915  0.885596297  0.870563838  0.837719439  0.786857291
 [6]  0.621768854  0.565269996  0.411356303  0.073933769 -0.006983568

Largest  eigenvalues:
 [1] 139077174 132124672 123980267 118349442 118117583 114096803 113003819
 [8] 111077288 109107279 106815214

Smallest eigenvalues:
 [1]  1.11616284  1.09019475  0.95782270  0.93344345  0.76680151  0.76044917
 [7]  0.56072419  0.49844045  0.44558962 -0.06395638

Largest  eigenvalues:
 [1] 134037434 133412526 124965521 119618047 115376964 114849933 113401577
 [8] 110916067 110260571 106364627

Smallest eigenvalues:
 [1]  1.0638062  1.0204108  1.0201889  0.9741826  0.9173209  0.7768200
 [7]  0.7477912  0.6002204  0.3250965 -0.1614133

Largest  eigenvalues:
 [1] 137470031 132773397 124687420 118780808 116541311 114334022 114118409
 [8] 110909022 109786086 106460132

Smallest eigenvalues:
 [1]  1.161057641  1.139323340  1.119134342  1.077427176  0.951895774
 [6]  0.850399296  0.501310214  0.442614923  0.247149976 -0.007004209

Largest  eigenvalues:
 [1] 138114071 131246382 122993093 117257180 117232495 113249107 112317609
 [8] 110083531 108571560 106190741

Smallest eigenvalues:
 [1]  1.03379506  1.00044033  0.98587366  0.92724962  0.90234853  0.80694965
 [7]  0.43928140  0.41782564  0.35778457 -0.02320456

Largest  eigenvalues:
 [1] 136334834 132832534 124200620 118463890 116046464 114364309 113383480
 [8] 110862490 109141477 106925725

Smallest eigenvalues:
 [1]  1.0396085  0.9816794  0.9353829  0.8728415  0.7665449  0.7195809
 [7]  0.6814536  0.5571039  0.1449074 -0.9692659

Largest  eigenvalues:
 [1] 135364810 132251770 124065318 118426680 116119556 113825123 113576465
 [8] 110483721 109563995 106287467

Smallest eigenvalues:
 [1]  0.9254435  0.8949878  0.8869167  0.7865337  0.6624205  0.6541863
 [7]  0.6275214  0.5222385  0.1541507 -0.6593987

Largest  eigenvalues:
 [1] 138704012 133142230 124778197 118805116 118412541 114297735 113748114
 [8] 111209987 109654377 106805201

Smallest eigenvalues:
 [1]  0.9774613  0.9400363  0.9262829  0.7432793  0.7073598  0.6508125
 [7]  0.6235384  0.4389632 -0.0403218 -3.5779398

Largest  eigenvalues:
 [1] 135264930 133019006 124636691 118960397 115540945 114608832 113027163
 [8] 110340612 109921951 105900412

Smallest eigenvalues:
 [1]  1.1194456  0.9408376  0.9391890  0.9048962  0.9040624  0.5934157
 [7]  0.5779869 -0.1388906 -0.2294558 -0.2961695

Largest  eigenvalues:
 [1] 135351701 132503924 123840160 118485643 116001148 113942287 112821885
 [8] 110238416 108582737 106026739

Smallest eigenvalues:
 [1]  0.9733772  0.9475114  0.9039902  0.8221547  0.7985379  0.7923911
 [7]  0.7133250  0.2374300  0.1609382 -0.4256023

Largest  eigenvalues:
 [1] 138658952 133370194 124677304 118205339 117806051 114559949 113596193
 [8] 111127738 109909377 107218546

Smallest eigenvalues:
 [1]  1.1523276  1.0727685  0.9417707  0.8766789  0.8642186  0.6458429
 [7]  0.6127939  0.5895132  0.4473188 -0.1236023

Largest  eigenvalues:
 [1] 138442094 131847172 124019996 117443441 117308575 114539258 113032983
 [8] 111128537 109470399 107388397

Smallest eigenvalues:
 [1]  1.1489040  1.1019013  1.0462988  0.9444421  0.8721010  0.7637375
 [7]  0.5163876  0.4070077  0.1835515 -0.4694777

Largest  eigenvalues:
 [1] 136736763 131526730 122963932 118254279 115894535 113300732 112543831
 [8] 109973278 108793453 105357982

Smallest eigenvalues:
 [1]  1.1312476  1.0080637  1.0018752  0.9978000  0.9618659  0.7797975
 [7]  0.6260164  0.4672589  0.2929586 -0.1255885

Largest  eigenvalues:
 [1] 137588856 132736714 124211896 118623875 117267608 114148667 113529875
 [8] 110618015 109372782 106897298

Smallest eigenvalues:
 [1]  1.0185650  0.9224327  0.8358586  0.7332705  0.7184736  0.5636534
 [7]  0.4657152  0.1213703 -0.5094281 -0.6227698

Largest  eigenvalues:
 [1] 138104365 132748751 124292918 118005706 117389329 115911964 113983794
 [8] 111844393 109938123 107693840

Smallest eigenvalues:
 [1]  1.1389064  1.1194827  1.0602250  1.0239757  0.9224550  0.8925552
 [7]  0.6883756  0.5754431  0.4100234 -0.6709451

Largest  eigenvalues:
 [1] 135666698 132792273 124242028 118879952 115418687 114117573 113902735
 [8] 110496266 109938114 106402326

Smallest eigenvalues:
 [1]  1.140632608  1.092645038  1.090132805  0.947767067  0.860220262
 [6]  0.795300162  0.726303306  0.654235165  0.156476362 -0.009928531

Largest  eigenvalues:
 [1] 136056041 130440720 122097944 117164727 115859815 113418367 112512702
 [8] 110316008 108333230 105955024

Smallest eigenvalues:
 [1]  1.1626412  1.1377907  0.9018100  0.8872660  0.8651979  0.8102843
 [7]  0.7785115  0.5679260  0.3282432 -0.3858834

Largest  eigenvalues:
 [1] 134842687 130160538 121970545 116709344 114824686 112854681 111930818
 [8] 110049615 107825324 105688420

Smallest eigenvalues:
 [1]  0.9467027  0.9344285  0.9128206  0.8793134  0.8229584  0.7172003
 [7]  0.4629851  0.4395434  0.3896888 -0.2694351

Largest  eigenvalues:
 [1] 134584027 130636848 121809879 116876073 116032135 112804070 112179017
 [8] 109622442 108012773 105233956

Smallest eigenvalues:
 [1]  0.9920661  0.9556303  0.9429426  0.9273824  0.8202346  0.6476825
 [7]  0.6057444  0.5363126  0.5177233 -0.4422573

Largest  eigenvalues:
 [1] 135231824 131932056 124450265 118474375 115744029 114244324 113792893
 [8] 110906920 109500186 106756262

Smallest eigenvalues:
 [1]  0.9891930  0.9660190  0.8836175  0.8081286  0.7950407  0.7269758
 [7]  0.6339289  0.6085802  0.4587375 -1.0288509

Largest  eigenvalues:
 [1] 136760097 132539224 124927148 118607346 116438162 114816379 114585336
 [8] 111446077 110101114 107043899

Smallest eigenvalues:
 [1]  1.17805466  1.08685419  1.01508059  0.90591219  0.79288098  0.77678451
 [7]  0.70242775  0.69695614  0.39463342 -0.08891716

Largest  eigenvalues:
 [1] 136815119 131655007 123290803 118629720 115897039 113336981 113072924
 [8] 110238640 109122433 105906429

Smallest eigenvalues:
 [1]  1.1951818  1.1468847  1.1365253  0.9713300  0.8909258  0.7750622
 [7]  0.5643882  0.5238809  0.1732544 -0.3450903

Largest  eigenvalues:
 [1] 134550263 130386870 122775230 117400578 113470701 112950527 111617268
 [8] 109187017 108689410 104469553

Smallest eigenvalues:
 [1]  1.0734417  0.9908388  0.9189598  0.8508919  0.7110209  0.6407004
 [7]  0.5944665  0.3382000 -0.1875544 -0.2892285

Largest  eigenvalues:
 [1] 137386476 131938257 124076635 117534570 117226370 113532647 112661568
 [8] 110062268 109085950 106456943

Smallest eigenvalues:
 [1]  1.12448430  1.08428395  1.00088508  0.94199478  0.76755438  0.70106879
 [7]  0.61489198  0.59903763  0.30084487 -0.02584492

Largest  eigenvalues:
 [1] 136476153 131443483 123709735 117800125 114850395 113162448 112635437
 [8] 109832834 108946491 105662583

Smallest eigenvalues:
 [1]  1.04972246  1.02070746  0.99070188  0.97510889  0.86771419  0.83804821
 [7]  0.69861209  0.69429875  0.33455010 -0.09572964

Largest  eigenvalues:
 [1] 136410923 131233477 122772426 118234786 115965776 114024465 112638416
 [8] 110678158 108726545 106627176

Smallest eigenvalues:
 [1]  0.8870807  0.8350603  0.7537281  0.6871759  0.6801307  0.5319542
 [7]  0.5129123  0.4828997  0.2478617 -0.1038163

Largest  eigenvalues:
 [1] 136207429 132987934 123556191 118317096 117194264 114673331 114144973
 [8] 110729926 109780598 106688378

Smallest eigenvalues:
 [1]  1.0451253  1.0198112  0.9709212  0.8929643  0.7286408  0.7119554
 [7]  0.6767607  0.3768106  0.2641183 -0.3429396

Largest  eigenvalues:
 [1] 133330612 131423598 123327066 118010895 114919944 113881784 112757857
 [8] 109967866 109114314 105773268

Smallest eigenvalues:
 [1]  1.0251317  0.8462031  0.8286233  0.7594445  0.6191225  0.5088844
 [7]  0.3982119  0.3302044  0.0692134 -0.7669854

Largest  eigenvalues:
 [1] 136606330 132169759 123776772 118378432 116438924 114511608 113387366
 [8] 111132497 109158997 106186212

Smallest eigenvalues:
 [1]  1.1159767  1.0990815  0.9757286  0.9481750  0.8609663  0.7677819
 [7]  0.6912020  0.6865107  0.5992712 -0.0877039

Largest  eigenvalues:
 [1] 134296836 133342673 124668678 119947870 115297766 114666704 113803740
 [8] 110484060 109927542 106125472

Smallest eigenvalues:
 [1]  1.03136331  0.93132714  0.90225052  0.77323007  0.75986151  0.71989671
 [7]  0.59324172  0.40434595  0.09217178 -2.15644924

Largest  eigenvalues:
 [1] 136867281 131260557 123317783 117285307 115639016 113508969 112926740
 [8] 110841135 108777015 106256351

Smallest eigenvalues:
 [1]  1.0973832  1.0241306  0.8782204  0.8405039  0.8163045  0.7780373
 [7]  0.7372148  0.6885016  0.5990339 -1.3667574

Largest  eigenvalues:
 [1] 135863194 132574410 124625111 118614630 115902032 114766756 113979118
 [8] 111324725 109779369 106905766

Smallest eigenvalues:
 [1]  1.1230325  1.1047961  1.0752721  1.0207528  0.9992266  0.9191325
 [7]  0.7282923  0.6650337  0.3576889 -0.1807112

Largest  eigenvalues:
 [1] 136097531 130810524 122975854 117447009 115846513 113711003 112949949
 [8] 110384045 108991892 106356184

Smallest eigenvalues:
 [1]  1.0288400  1.0095087  1.0057071  0.9747426  0.7791183  0.6868027
 [7]  0.5204124  0.4368311  0.1049893 -0.5382668

Largest  eigenvalues:
 [1] 135624526 130367454 122735719 118211509 116205766 113588177 112576700
 [8] 110522025 108869951 106633052

Smallest eigenvalues:
 [1]  1.1674445  1.0240108  0.9640820  0.9590423  0.9284936  0.7813545
 [7]  0.6966257  0.5217715  0.3947093 -0.8671934

Largest  eigenvalues:
 [1] 135369181 132618799 123845043 119583023 115134503 114325934 113944121
 [8] 110623377 109903829 106508636

Smallest eigenvalues:
 [1]  1.1984974  1.1748076  1.1406129  1.0869761  1.0421804  0.9440269
 [7]  0.8823381  0.8298928  0.5048125 -0.2724884

Largest  eigenvalues:
 [1] 135228843 131001067 123172022 117407262 114724822 113525947 112395265
 [8] 110208998 108537676 105991114

Smallest eigenvalues:
 [1]  1.0884185  1.0326757  1.0155812  0.9271647  0.9078090  0.7644290
 [7]  0.7067695  0.5544309  0.4498260 -1.1355492

Largest  eigenvalues:
 [1] 132899651 130426270 122390315 118245434 113329684 112826955 112060763
 [8] 109428086 108925104 105054404

Smallest eigenvalues:
 [1]  0.9516667  0.7914653  0.7638693  0.7460755  0.7175364  0.6906613
 [7]  0.5071603  0.4262511  0.2476806 -0.1450733

Largest  eigenvalues:
 [1] 137734421 133570970 125429114 119062996 116812287 114499194 114263514
 [8] 111108704 110317877 107440074

Smallest eigenvalues:
 [1]  0.9721431  0.8012526  0.7359061  0.6706211  0.6601480  0.6252495
 [7]  0.5656663  0.3330420  0.2391079 -0.2682998

Largest  eigenvalues:
 [1] 133118204 129246232 121604393 116258335 113453271 112163743 112019736
 [8] 109121491 107799092 105220406

Smallest eigenvalues:
 [1]  1.02299413  0.92619474  0.84507185  0.76140619  0.67339652  0.52095106
 [7]  0.48050942 -0.04923667 -0.18329085 -0.91614320

Largest  eigenvalues:
 [1] 137119298 131287858 122838959 117123867 116618885 113575833 112897754
 [8] 110709801 108715514 106472629

Smallest eigenvalues:
 [1]  1.16444102  0.98223638  0.96022756  0.94234237  0.91371043  0.71855750
 [7]  0.68984883  0.67665249  0.33828438 -0.08746629

Largest  eigenvalues:
 [1] 134273581 131329145 123293412 117021129 113748904 113271704 112966340
 [8] 110752466 108898424 106024281

Smallest eigenvalues:
 [1]  1.065287179  1.041477481  0.998169554  0.984279234  0.810966236
 [6]  0.745708417  0.681727266  0.500262255  0.405207790 -0.005957367

Largest  eigenvalues:
 [1] 138264372 131625221 123165725 117337269 116907042 113579614 112390428
 [8] 110393190 108405828 106131073

Smallest eigenvalues:
 [1]  1.1013091  1.0018530  0.9878088  0.9433219  0.8061246  0.7666738
 [7]  0.7503725  0.6898731  0.4191194 -0.4062362

Largest  eigenvalues:
 [1] 136441308 132079017 123904208 118523120 115271083 114449921 113287499
 [8] 111230394 109382441 106887599

Smallest eigenvalues:
 [1]  1.1243010  1.0683696  0.9778119  0.9029492  0.8604403  0.8081882
 [7]  0.6770519  0.6295505  0.5576291 -0.1758463

Largest  eigenvalues:
 [1] 135819666 132069852 123502718 118365220 115281534 113303449 113108897
 [8] 110011170 108938363 105847620

Smallest eigenvalues:
 [1]  1.0834586  0.9339904  0.8307919  0.8274291  0.7797233  0.7457566
 [7]  0.5526795  0.5526047  0.4070128 -0.1907547

Largest  eigenvalues:
 [1] 135250675 132457856 124310215 118346890 114712484 114271673 113815785
 [8] 110824101 109908392 106746116

Smallest eigenvalues:
 [1]  1.0674725  1.0463354  0.9577353  0.9209438  0.7593151  0.6831467
 [7]  0.6489527  0.6238522  0.5595071 -0.8519290

Largest  eigenvalues:
 [1] 136562107 132264080 123935648 118411242 116178752 114770419 113568068
 [8] 111479767 109482573 106840688

Smallest eigenvalues:
 [1]  1.07471232  1.05422917  1.00280112  0.97110287  0.97018141  0.90518340
 [7]  0.66409443  0.65071087  0.52992902 -0.03140993

Largest  eigenvalues:
 [1] 135306596 133094840 124395524 119729185 115416436 115151230 114517802
 [8] 111544165 110561374 107596312

Smallest eigenvalues:
 [1]  1.0791689  1.0778712  1.0308044  0.9709707  0.8055795  0.7877484
 [7]  0.7823670  0.7549878  0.4521996 -0.6812339

Largest  eigenvalues:
 [1] 134593500 131166176 122401515 118536090 114771480 114034002 112249168
 [8] 109633479 109048214 105262744

Smallest eigenvalues:
 [1]  1.0874851  1.0123813  0.9746583  0.8677117  0.8027323  0.7816284
 [7]  0.6702468  0.4923499  0.4519261 -0.9243272

Largest  eigenvalues:
 [1] 135936453 133209744 124683858 118927807 115768401 114494334 113853301
 [8] 111043306 110025074 106402378

Smallest eigenvalues:
 [1]  1.0119422  0.9791951  0.7639759  0.7606874  0.7547262  0.6753445
 [7]  0.5382947  0.4630023  0.3518115 -0.9520252

Largest  eigenvalues:
 [1] 134236915 134167652 124681259 119672695 116041916 114981995 113609443
 [8] 110399201 109962014 105919794

Smallest eigenvalues:
 [1]  1.06562058  1.02892398  0.98292482  0.94893836  0.90037480  0.71464507
 [7]  0.68182895  0.66333554  0.38184958 -0.06201706

Largest  eigenvalues:
 [1] 133254037 130657142 123120104 117436445 113513428 113253508 112958400
 [8] 109736932 109214721 105951445

Smallest eigenvalues:
 [1]  0.9377315  0.9169039  0.9166504  0.8768386  0.6206026  0.6110003
 [7]  0.5853355  0.5578546 -0.1678941 -0.1946190

Largest  eigenvalues:
 [1] 137666164 131122123 123445549 117430348 117286391 115150476 113057360
 [8] 111373622 109290998 107618751

Smallest eigenvalues:
 [1]  0.97662034  0.95050752  0.92040757  0.78450358  0.70894762  0.70374400
 [7]  0.50616102  0.50264093  0.20342701 -0.07540777

Largest  eigenvalues:
 [1] 134928976 132132724 123219343 118282508 115533485 114044413 112906917
 [8] 110076155 108896279 105332906

Smallest eigenvalues:
 [1]  1.09686659  0.83797395  0.83724003  0.82588658  0.67891249  0.50850710
 [7]  0.49984932  0.34855186 -0.05394257 -0.19309521

Largest  eigenvalues:
 [1] 137751950 130312207 123066953 116733279 115916945 113016498 111273137
 [8] 109636828 107737729 105812548

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	8.668593	0.5548134	12.21568	0.195	1.257246	1.071169

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, sex = FALSE, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

GET_res <- GET_function(J = j+1, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, sex = TRUE, lenght_tt = lenght_tt)
GET_results[[j+1]] <- GET_res

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

HR ~ alt + speed + Sex

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- HR_fd
covariates <- list(altitude = altitude_fd, 
                   speed = speed_fd)
path_plot <- 'figures/model_HR_alt_speed_Sex_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     speed = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     Sex = list(nbetabasis = 80, norder = 4, lambda = 1e3))

factors <- list(Sex = participant_info$Sex |> as.factor())

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params,
                            factors = factors)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}
for (fact in names(factors)) {
    assign(fact, factors[[fact]][participant_info$ID %in% (model_1$common_IDs |> 
                                                           substr(4, 9))] |> as.numeric())
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, 
                            basis_params = basis_params, nperm = nperm, factors = factors, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        if(!is.na(factors[1])) {for (fact in names(factors)) {
            assign(paste0(fact, '_BS'), 
                   factors[[fact]][participant_info$ID %in% (model_1$common_IDs |> substr(4, 9))][BS_sample] |> 
                   as.numeric())}}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS'))
        if(!is.na(factors[1])) {for(nam in names(factors)) {formula_BS <- paste0(formula_BS, '+', nam, '_BS')}}
        formula_BS <- as.formula(formula_BS)
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 47.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Warning message in `^.fd`((outcome - yhatfd), 2):
"The maximum error exceeds the tolerance level."
Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 500 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Smallest eigenvalues:
 [1]  1.1781640  1.1346809  1.1146184  0.8654722  0.7578887  0.6003548
 [7]  0.5576528  0.5394753  0.4745520 -5.7280285

Largest  eigenvalues:
 [1] 149590000 141780953 134185261 129504683 127893292 124292907 121372067
 [8] 119917159 118139682 117320293

Smallest eigenvalues:
 [1]  1.3187540  1.2534301  1.1642820  1.0235925  0.9119360  0.9064681
 [7]  0.7091962  0.5859837  0.4572523 -7.0889327

Largest  eigenvalues:
 [1] 148160290 141296343 133762539 128975099 128516111 124927929 120378765
 [8] 119386591 118165962 117240667

Smallest eigenvalues:
 [1]  1.36405751  1.22228365  1.18786766  1.07988584  1.02677005  0.77947244
 [7]  0.77873041  0.68768944  0.49510563 -0.01505912

Largest  eigenvalues:
 [1] 149017513 142560121 134692549 130836886 128841489 124655181 120831532
 [8] 120696007 119676855 117503360

Smallest eigenvalues:
 [1]  1.18460164  1.11650549  1.07755792  0.93144211  0.90962915  0.80811594
 [7]  0.57973552  0.55787425  0.48535873 -0.04310089

Largest  eigenvalues:
 [1] 148297472 141175379 132341435 128248523 127778904 124436227 120213673
 [8] 118444663 118142425 116617546

Smallest eigenvalues:
 [1]  1.2945462  1.1691853  1.1622388  0.8758997  0.8595341  0.8106490
 [7]  0.7410779  0.7266192  0.4030367 -1.3535300

Largest  eigenvalues:
 [1] 149303155 141302696 133796017 130663810 128202506 124960250 120659543
 [8] 119738357 118180862 116318403

Smallest eigenvalues:
 [1]  1.6624388  1.4599492  1.2697815  1.1601602  0.9192361  0.9029982
 [7]  0.8854069  0.8695371  0.7843537 -0.2452722

Largest  eigenvalues:
 [1] 149389330 140579687 133410327 128283290 127854013 123567059 119814335
 [8] 119068707 117682411 116096158

Smallest eigenvalues:
 [1]  1.4054855  1.3187594  0.8976240  0.8742945  0.8008566  0.7547644
 [7]  0.6148409  0.3120185  0.2711259 -2.8259375

Largest  eigenvalues:
 [1] 147283928 142656542 133991712 128748635 128378003 125466443 120782776
 [8] 118443362 118308851 116891374

Smallest eigenvalues:
 [1]  1.1107011  0.8671631  0.8482472  0.8185048  0.6363300  0.5259692
 [7]  0.4595736  0.3374729  0.3083746 -2.9191520

Largest  eigenvalues:
 [1] 148216997 141543776 133306305 129361066 128307698 124582093 120404402
 [8] 119725084 118358360 116461766

Smallest eigenvalues:
 [1]  1.12287587  0.96214433  0.86950738  0.80735512  0.68341585  0.66271969
 [7]  0.47118475  0.44982958 -0.05296173 -2.91914208

Largest  eigenvalues:
 [1] 147946186 143143036 133385140 130553807 129040444 125374886 120971050
 [8] 120075677 119105695 117093054

Smallest eigenvalues:
 [1]  1.5155546  1.3898472  1.3875458  1.2195079  1.0167413  1.0006485
 [7]  0.9476630  0.7764376  0.6618371 -2.7221814

Largest  eigenvalues:
 [1] 148749372 142782114 134090142 129119629 128722738 124682308 120093595
 [8] 119386462 119071311 117071997

Smallest eigenvalues:
 [1]  1.2238397  1.1643391  1.0616039  1.0439030  1.0287803  0.7962047
 [7]  0.7639633  0.6588083  0.1679842 -2.0741316

Largest  eigenvalues:
 [1] 153070872 140862952 133102113 130030721 127978209 123526345 120866812
 [8] 119944728 119558285 117576209

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	8.265521	0.6803457	12.40876	0	0.7130665	1.890904

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, sex = FALSE, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

GET_res <- GET_function(J = j+1, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, sex = TRUE, lenght_tt = lenght_tt)
GET_results[[j+1]] <- GET_res

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

HR ~ alt + steps + Sex

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- HR_fd
covariates <- list(altitude = altitude_fd, 
                   steps = steps_fd)
path_plot <- 'figures/model_HR_alt_steps_Sex_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     steps = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     Sex = list(nbetabasis = 80, norder = 4, lambda = 1e3))

factors <- list(Sex = participant_info$Sex |> as.factor())

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params,
                            factors = factors)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}
for (fact in names(factors)) {
    assign(fact, factors[[fact]][participant_info$ID %in% (model_1$common_IDs |> 
                                                           substr(4, 9))] |> as.numeric())
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, 
                            basis_params = basis_params, nperm = nperm, factors = factors, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        if(!is.na(factors[1])) {for (fact in names(factors)) {
            assign(paste0(fact, '_BS'), 
                   factors[[fact]][participant_info$ID %in% (model_1$common_IDs |> substr(4, 9))][BS_sample] |> 
                   as.numeric())}}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS'))
        if(!is.na(factors[1])) {for(nam in names(factors)) {formula_BS <- paste0(formula_BS, '+', nam, '_BS')}}
        formula_BS <- as.formula(formula_BS)
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 39.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 396 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	8.308018	0.7106202	11.9561	0	0.7517159	2.119495

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, sex = FALSE, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

GET_res <- GET_function(J = j+1, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, sex = TRUE, lenght_tt = lenght_tt)
GET_results[[j+1]] <- GET_res

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

HR ~ alt + n + acc

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- HR_fd
covariates <- list(altitude = altitude_fd, 
                   noise = noise_fd,
                   acceleration = acceleration_fd)
path_plot <- 'figures/model_HR_alt_noise_acc_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     noise = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     acceleration = list(nbetabasis = 80, norder = 4, lambda = 1e3))

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, 
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 32.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 432 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Smallest eigenvalues:
 [1]  0.9739181  0.9070555  0.9044741  0.8227855  0.7871775  0.5797282
 [7]  0.5447441  0.5304211  0.1462120 -0.3233728

Largest  eigenvalues:
 [1] 107757898 102082451  95875388  93692545  92991159  90103538  87300144
 [8]  87123994  86805321  85850434

Smallest eigenvalues:
 [1]  0.9600672  0.7639749  0.7222864  0.6831188  0.5820995  0.4457554
 [7]  0.4429751  0.4157449  0.3607366 -0.3871306

Largest  eigenvalues:
 [1] 106461459 102714673  96523396  93752390  93550486  90720069  87770294
 [8]  87276932  86752277  85605894

Smallest eigenvalues:
 [1]  1.12144307  1.06242080  0.87649874  0.79347665  0.74439217  0.66350438
 [7]  0.60190233  0.55378957  0.51711597 -0.02045023

Largest  eigenvalues:
 [1] 105829349 103394034  97749405  93653001  93095508  91441423  88374627
 [8]  88050165  86682215  86102144

Smallest eigenvalues:
 [1]  0.9973730  0.8630682  0.8204420  0.7664982  0.7029154  0.5189685
 [7]  0.5145405  0.5063051  0.2355076 -1.1446937

Largest  eigenvalues:
 [1] 106262500 101803413  96408942  93325711  93038505  90436544  88368260
 [8]  87122424  86188854  85614843

Smallest eigenvalues:
 [1]  0.9380506  0.9057991  0.7974583  0.7854969  0.7488043  0.6271615
 [7]  0.6157394  0.5951337  0.4298249 -0.1027140

Largest  eigenvalues:
 [1] 105888788 103182592  97000905  93468480  93316605  91022840  88196838
 [8]  87249699  86366499  85750471

Smallest eigenvalues:
 [1]  0.9959630  0.9587178  0.8511334  0.7057276  0.6709490  0.6441068
 [7]  0.5804226  0.5782194  0.2786083 -1.2692560

Largest  eigenvalues:
 [1] 108097038 101658959  96210444  93879148  92044067  89873924  87499400
 [8]  87105833  86999861  85447673

Smallest eigenvalues:
 [1]  1.0602412  0.9374022  0.9279722  0.8926586  0.7895102  0.7717937
 [7]  0.7001134  0.5497410  0.4865444 -0.6337533

Largest  eigenvalues:
 [1] 105569136 102515039  96393532  93228582  92611669  90551635  87551044
 [8]  87399116  85880860  85533123

Smallest eigenvalues:
 [1]  1.0522998  0.9887746  0.9156795  0.8701023  0.8261606  0.7990901
 [7]  0.7593079  0.7167662  0.3340540 -0.5894481

Largest  eigenvalues:
 [1] 107082135 102200653  96209165  93509252  92524823  90588967  87853406
 [8]  87276167  86071986  85207164

Smallest eigenvalues:
 [1]  0.9342266  0.9163383  0.7692761  0.6682715  0.6471987  0.5963400
 [7]  0.5617708  0.4187039  0.1625168 -0.2475219

Largest  eigenvalues:
 [1] 106501411 101930061  95686593  93077685  92859929  90129501  87533204
 [8]  86946163  85672585  85317158

Smallest eigenvalues:
 [1]  0.9954587  0.9656373  0.8385163  0.8183769  0.7468686  0.6036963
 [7]  0.5662285  0.4359675  0.4074427 -0.1552247

Largest  eigenvalues:
 [1] 107088196  99984352  95383721  92982159  91605599  89076474  86263273
 [8]  86181958  85876111  84957046

Smallest eigenvalues:
 [1]  0.7824925  0.7510949  0.6095060  0.5779382  0.5731246  0.5522463
 [7]  0.4849424  0.4824695  0.1987788 -0.6091327

Largest  eigenvalues:
 [1] 106546940 102558831  96903721  93204445  92896778  90696179  88422239
 [8]  87555852  86250195  85709403

Smallest eigenvalues:
 [1]  0.93256259  0.78722467  0.74130118  0.73611676  0.69867149  0.58071432
 [7]  0.58037770  0.33130211  0.27698438 -0.08817705

Largest  eigenvalues:
 [1] 105273231 101492058  96093008  93039779  92595070  90284383  87895010
 [8]  87259920  86134106  85754897

Smallest eigenvalues:
 [1]  1.0254990  0.9100123  0.8884040  0.8660469  0.8539111  0.6463336
 [7]  0.5813533  0.4988011  0.2079018 -1.3079552

Largest  eigenvalues:
 [1] 107247314 101561558  96239419  93415521  92490345  90227034  87886485
 [8]  86957699  86542579  85578622

Smallest eigenvalues:
 [1]  0.8154282  0.7877572  0.6802313  0.6671185  0.5109802  0.4850972
 [7]  0.4836900  0.4629582  0.3260486 -0.7163060

Largest  eigenvalues:
 [1] 108469806 103343989  96547874  94687313  93766980  90407563  87987230
 [8]  87847784  87623981  86167216

Smallest eigenvalues:
 [1]  0.9456455  0.8984036  0.8866654  0.8832891  0.6631040  0.6600169
 [7]  0.5796109  0.5008270  0.2935479 -0.6530128

Largest  eigenvalues:
 [1] 109676154 102844716  96957559  94695928  93532279  90818974  88235819
 [8]  87967576  87890004  86409684

Smallest eigenvalues:
 [1]  1.0483063  0.8318142  0.8043516  0.7301932  0.7110074  0.6254776
 [7]  0.5638472  0.3718597  0.3240146 -0.1978363

Largest  eigenvalues:
 [1] 105316952 102459779  96476288  92681962  92509315  90220461  87594586
 [8]  86441673  85771783  84897398

Smallest eigenvalues:
 [1]  1.09141225  1.07669232  1.01665677  0.95552947  0.88231725  0.87835712
 [7]  0.67359767  0.63757596  0.60719812 -0.01507027

Largest  eigenvalues:
 [1] 106739727 102068652  96163577  93570663  92969149  90671731  87256747
 [8]  87163185  86163665  85607077

Smallest eigenvalues:
 [1]  1.1193088  1.1184372  1.0164019  0.8572574  0.8291404  0.7187604
 [7]  0.6574832  0.6528185  0.5952092 -0.4579073

Largest  eigenvalues:
 [1] 106539673 102642731  96460135  93646440  93437770  90865029  87464845
 [8]  87428334  86687024  85779571

Smallest eigenvalues:
 [1]  1.0188610  0.7415235  0.7170481  0.6089356  0.5346981  0.4727927
 [7]  0.3380275  0.2920763 -0.1335225 -0.8869777

Largest  eigenvalues:
 [1] 106558703 100221025  95320206  92834115  91450142  88326528  87130785
 [8]  86452796  86020181  85313657

Smallest eigenvalues:
 [1]  1.1361328  1.0545885  0.9298457  0.8439620  0.6850588  0.6830385
 [7]  0.5856037  0.5693867  0.4086119 -0.5385280

Largest  eigenvalues:
 [1] 107256592 101498566  96535298  94008026  92603884  90202423  87387895
 [8]  87069620  86620373  85870043

Smallest eigenvalues:
 [1]  0.6890101  0.6524320  0.6485062  0.5782830  0.5497101  0.3645368
 [7]  0.3133968  0.2086596 -0.2817090 -1.9828159

Largest  eigenvalues:
 [1] 108480312 100853582  96589590  93113610  92255329  89341376  87134928
 [8]  86562125  86355509  85727803

Smallest eigenvalues:
 [1]  1.0955902  1.0409376  0.9183825  0.8478418  0.7498295  0.6879591
 [7]  0.5251165  0.5117385  0.3928066 -0.2432927

Largest  eigenvalues:
 [1] 105371754 100416913  95027949  92137122  92118418  89287405  86990511
 [8]  86118875  85278386  84780001

Smallest eigenvalues:
 [1]  0.8654643  0.8501803  0.6557305  0.5953598  0.5876937  0.5624438
 [7]  0.3403873  0.3399493  0.2272461 -0.2142548

Largest  eigenvalues:
 [1] 108756210 102682611  97522858  95741999  93430264  90957393  88257961
 [8]  88173520  87932791  86326087

Smallest eigenvalues:
 [1]  0.9306975  0.8753051  0.7986481  0.7878632  0.7436808  0.5883950
 [7]  0.5191112  0.2534280  0.1071440 -0.2756760

Largest  eigenvalues:
 [1] 108704297 103010102  97278702  95999986  93890698  91396459  88522334
 [8]  88095321  87615291  86411240

Smallest eigenvalues:
 [1]  1.0399542  0.9155670  0.8671659  0.8337449  0.7370843  0.6036512
 [7]  0.5964418  0.5219686  0.2235807 -0.3133140

Largest  eigenvalues:
 [1] 106550292 101841994  96294820  93131214  92786668  90355335  88269321
 [8]  86948202  86243817  85548646

Smallest eigenvalues:
 [1]  1.1321073  1.0896680  1.0208217  0.9838445  0.8353567  0.8005417
 [7]  0.7259968  0.6940746  0.5083624 -0.6082429

Largest  eigenvalues:
 [1] 108733158 101307471  96119582  93759244  92736810  89999366  87644581
 [8]  87069819  86996291  86205278

Smallest eigenvalues:
 [1]  0.8549064  0.7923236  0.7761904  0.7292166  0.6752019  0.6499100
 [7]  0.5727572  0.5258840 -0.2340326 -0.6195309

Largest  eigenvalues:
 [1] 107800389 102038357  97031044  94184788  92623989  90196274  88117397
 [8]  87752913  87406320  86562664

Smallest eigenvalues:
 [1]  0.84665529  0.79642648  0.66157459  0.59468960  0.59095047  0.44760698
 [7]  0.43947429  0.41525945  0.29558469 -0.07780902

Largest  eigenvalues:
 [1] 107486780 102397613  96246139  94955101  92493242  90317269  87811284
 [8]  87600492  87218129  85772277

Smallest eigenvalues:
 [1]  1.0399587  1.0004180  0.7030955  0.6702356  0.6508857  0.6409989
 [7]  0.5537590  0.5534124  0.4161613 -0.9415906

Largest  eigenvalues:
 [1] 105226174 101384146  96207126  92667623  91916540  90129115  87578087
 [8]  86834390  85760947  85265229

Smallest eigenvalues:
 [1]  1.0740236  0.9699365  0.9257382  0.8976239  0.8814413  0.8189048
 [7]  0.7087698  0.5209375  0.4943526 -0.6475468

Largest  eigenvalues:
 [1] 105432599 101961961  96632200  93200940  92903891  90942382  88527626
 [8]  86921735  85813932  85438444

Smallest eigenvalues:
 [1]  0.9613563  0.8535764  0.8520412  0.8291887  0.7795163  0.6968560
 [7]  0.5084520  0.4892364  0.3059006 -0.0407415

Largest  eigenvalues:
 [1] 108389100 101563713  96232884  94956012  92782694  90057687  87408472
 [8]  87205428  86912569  85714317

Smallest eigenvalues:
 [1]  0.9539057  0.9133985  0.8185856  0.6942262  0.6925654  0.4889985
 [7]  0.4595531  0.4110463  0.1071997 -0.1582165

Largest  eigenvalues:
 [1] 109272464 102640614  96526103  95468141  93805268  90601919  88419732
 [8]  88145744  87126209  86505585

Smallest eigenvalues:
 [1]  0.8484347  0.6440976  0.6061702  0.5426354  0.5336470  0.4505841
 [7]  0.4443875  0.2906917 -0.3276361 -1.4825787

Largest  eigenvalues:
 [1] 108071369 102573761  96562558  94781465  92606132  90093096  87891813
 [8]  87851695  86869427  85747906

Smallest eigenvalues:
 [1]  1.02355361  0.96973626  0.90924679  0.89008064  0.83161944  0.72567351
 [7]  0.58141891  0.58048383  0.44611625 -0.08229867

Largest  eigenvalues:
 [1] 106467640 100899267  95673039  93050578  92103650  89236240  87316141
 [8]  87098983  86233727  85986087

Smallest eigenvalues:
 [1]  0.7859443  0.7827471  0.7658371  0.6862303  0.6082995  0.5313227
 [7]  0.5001402  0.4797584  0.4562193 -0.8163203

Largest  eigenvalues:
 [1] 106338183 101741941  96582443  92904785  92145666  90014135  86924138
 [8]  86333393  86194225  84856749

Smallest eigenvalues:
 [1]  1.070407878  0.933948588  0.898295072  0.860893853  0.810180977
 [6]  0.655686908  0.562261570  0.557175728  0.550095770 -0.001107183

Largest  eigenvalues:
 [1] 106724776 101722385  96206922  93328293  93124718  90456090  87294056
 [8]  86751106  86173386  85034085

Smallest eigenvalues:
 [1]  0.8775099  0.8684947  0.7630967  0.6250612  0.5756749  0.5541340
 [7]  0.3185507  0.3141688  0.1140295 -1.1804514

Largest  eigenvalues:
 [1] 105311288  99680273  94926540  91728595  90973605  88726663  86707190
 [8]  86238942  85344718  85008989

Smallest eigenvalues:
 [1]  1.0698727  0.9825964  0.9636048  0.7260857  0.6620844  0.6241240
 [7]  0.4912535  0.4525449  0.3955901 -2.3864842

Largest  eigenvalues:
 [1] 105085125 100817852  95057283  92591380  92386877  89547713  87597386
 [8]  85899385  85526899  84540699

Smallest eigenvalues:
 [1]  1.0582997  1.0423215  0.9252621  0.9156458  0.8376192  0.8134114
 [7]  0.7389213  0.6342170  0.5806265 -0.6904383

Largest  eigenvalues:
 [1] 106831057 102251934  96516194  93007097  92784583  90216579  87734029
 [8]  86941752  86198545  85166290

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	8.588232	0.5394108	9.702973	0.115	0.8661495	0.6864926

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

HR ~ alt + n + speed

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- HR_fd
covariates <- list(altitude = altitude_fd, 
                   noise = noise_fd,
                   speed = speed_fd)
path_plot <- 'figures/model_HR_alt_noise_speed_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 90, norder = 4, lambda = 1e4),
                     noise = list(nbetabasis = 90, norder = 4, lambda = 1e4),
                     speed = list(nbetabasis = 90, norder = 4, lambda = 1e4))

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, 
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 39.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Warning message in `^.fd`((outcome - yhatfd), 2):
"The maximum error exceeds the tolerance level."
Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 544 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Smallest eigenvalues:
 [1]  0.7617205  0.7477865  0.7148203  0.6362117  0.6162146  0.5815881
 [7]  0.4405483  0.4055886  0.3600405 -1.1965898

Largest  eigenvalues:
 [1] 116195483 111748288 104405966 103957144 101468990  98773121  97195470
 [8]  96652661  94691486  94210649

Smallest eigenvalues:
 [1]  1.3277775  1.2388246  1.1172145  0.9280693  0.8347739  0.8189306
 [7]  0.7396110  0.5954559  0.4854317 -0.1209143

Largest  eigenvalues:
 [1] 117031665 110973293 105196308 102837568 102040803  99426680  96859116
 [8]  96308938  95242173  94478992

Smallest eigenvalues:
 [1]  1.1823724  1.1108130  1.0793316  0.8427276  0.7413642  0.7232134
 [7]  0.6714152  0.6341284  0.4915158 -0.4899471

Largest  eigenvalues:
 [1] 116016852 110373411 104330249 102880584 101093227  98753164  95712715
 [8]  95535870  93438738  92535885

Smallest eigenvalues:
 [1]  1.3060250  1.1933808  1.1234077  0.8447658  0.8172104  0.8119259
 [7]  0.7403245  0.6913732  0.4060425 -0.8774854

Largest  eigenvalues:
 [1] 116006302 110127656 104729619 102547274 101106888  98319509  95913736
 [8]  95617937  93720703  92832685

Smallest eigenvalues:
 [1]  1.0454655  1.0143675  0.7880554  0.6915586  0.5744043  0.5365012
 [7]  0.4478798  0.4113546  0.3630624 -0.4475338

Largest  eigenvalues:
 [1] 116542938 111400603 105761488 103844782 102185038  99622962  96861277
 [8]  96527788  95739488  94112863

Smallest eigenvalues:
 [1]  1.0071717  0.9666416  0.8214861  0.8111498  0.7295765  0.6971859
 [7]  0.5772700  0.4873467  0.4853716 -0.3726666

Largest  eigenvalues:
 [1] 118069780 110500665 105037548 103894359 101778252  98702108  96927996
 [8]  96550989  94040509  93565290

Smallest eigenvalues:
 [1]  1.0008711  0.8523772  0.8399589  0.8079212  0.7063454  0.6960455
 [7]  0.6703585  0.5626612  0.5393766 -0.1002940

Largest  eigenvalues:
 [1] 116516685 110204796 104193436 104059149 100961974  98821671  96797762
 [8]  95451787  93945153  92469406

Smallest eigenvalues:
 [1]  1.0112000  0.9618017  0.9064340  0.8582519  0.6792072  0.6680352
 [7]  0.6153928  0.5642197  0.5199594 -0.2248893

Largest  eigenvalues:
 [1] 116927792 111808947 104805722 103778860 102053412  99321668  96978883
 [8]  96642421  94435142  93401997

Smallest eigenvalues:
 [1]  0.94540766  0.94382542  0.81604349  0.69587258  0.66378513  0.60491167
 [7]  0.59868370  0.56132766  0.19148445 -0.00150778

Largest  eigenvalues:
 [1] 118205206 110717090 105044120 104933350 101210560  98764973  97528989
 [8]  95862060  94996876  93353379

Smallest eigenvalues:
 [1]  1.0273973  1.0232075  0.9348405  0.8387037  0.7966725  0.6588555
 [7]  0.6273982  0.6228426  0.4017236 -0.6066088

Largest  eigenvalues:
 [1] 117574604 111401120 104723078 103775184 102040651  99638705  96911850
 [8]  96578545  94416633  93560895

Smallest eigenvalues:
 [1]  1.35408259  1.21672034  1.07850898  1.01682658  0.73816501  0.70915603
 [7]  0.59119856  0.58812883  0.54719432 -0.02990621

Largest  eigenvalues:
 [1] 114859831 110649623 104172487 102050223 101168907  98680257  95964751
 [8]  94817062  92990487  92530528

Smallest eigenvalues:
 [1]  1.25613265  1.16853182  1.01505033  1.01502712  0.91905730  0.78134201
 [7]  0.77978246  0.63800900  0.58140982 -0.06894696

Largest  eigenvalues:
 [1] 114186660 110262741 104280233 101813294 101443436  98903388  96142401
 [8]  95356358  94268113  93270392

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	8.373718	0.760873	12.6287	0	0.8301466	2.496647

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

HR ~ alt + n + steps

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- HR_fd
covariates <- list(altitude = altitude_fd, 
                   noise = noise_fd,
                   steps = steps_fd)
path_plot <- 'figures/model_HR_alt_noise_steps_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 90, norder = 4, lambda = 1e3),
                     noise = list(nbetabasis = 90, norder = 4, lambda = 1e3),
                     steps = list(nbetabasis = 90, norder = 4, lambda = 1e3))

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, 
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 32.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 440 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Smallest eigenvalues:
 [1]  1.1183631  1.0176210  0.9297772  0.8452723  0.7416317  0.7239285
 [7]  0.6755437  0.6392289  0.4596060 -7.0519949

Largest  eigenvalues:
 [1] 97342625 89767749 85927968 85393823 82761422 80416058 79617758 77874284
 [9] 77830476 76648885

Smallest eigenvalues:
 [1]  0.8210996  0.7967740  0.7775604  0.6622976  0.5964201  0.4700285
 [7]  0.3924557  0.3526923  0.2299710 -1.9672223

Largest  eigenvalues:
 [1] 97687654 91789160 86679747 86363060 83441144 81363035 81221010 79222884
 [9] 77766615 76801490

Smallest eigenvalues:
 [1]  0.7809085  0.7613850  0.7280797  0.6448397  0.6044466  0.5885938
 [7]  0.3637156 -0.3397471 -0.4689503 -0.9617772

Largest  eigenvalues:
 [1] 94616108 92014319 87189576 84496714 83900342 82116066 79681349 78839727
 [9] 78226421 77210041

Smallest eigenvalues:
 [1]   0.8790409   0.8762651   0.8668854   0.8083423   0.6172791   0.4986781
 [7]   0.4639298   0.4487909   0.3879823 -83.8401403

Largest  eigenvalues:
 [1] 95013428 90569749 85918908 84249953 83632789 81235229 79313667 79022815
 [9] 77538099 77432421

Smallest eigenvalues:
 [1]  0.8182690  0.6401740  0.5501843  0.5120892  0.4566674  0.4324881
 [7]  0.3822173  0.3785554  0.3085159 -0.2504592

Largest  eigenvalues:
 [1] 96966908 91255816 86770080 85821377 83067470 81559868 80487231 78717159
 [9] 77957178 76823548

Smallest eigenvalues:
 [1]  0.8443321452  0.7014341727  0.5375279694  0.4550888811  0.4201822598
 [6]  0.4051580069  0.3375296354  0.1761667111  0.0007127554 -0.0165973187

Largest  eigenvalues:
 [1] 96806438 91300290 86815235 86162579 83218191 81217851 80537921 78963757
 [9] 78268287 77282901

Smallest eigenvalues:
 [1]  0.9823531  0.8947998  0.8728813  0.8447557  0.8135737  0.6899906
 [7]  0.6732836  0.5242621  0.4675930 -1.3404609

Largest  eigenvalues:
 [1] 95451019 91570758 86104006 85195379 83155760 80992776 79440481 78670863
 [9] 78018942 76633417

Smallest eigenvalues:
 [1]   1.0390931   0.9529703   0.9339237   0.8237270   0.7792322   0.7282763
 [7]   0.6451593   0.5112481   0.3376959 -28.3220241

Largest  eigenvalues:
 [1] 95834393 90947640 85769393 83874098 83688641 81565216 78836824 78824626
 [9] 77592514 76924571

Smallest eigenvalues:
 [1]  1.0335811  0.9599569  0.8353745  0.7895177  0.7619191  0.6985246
 [7]  0.6390835  0.5487342  0.3134193 -0.1837513

Largest  eigenvalues:
 [1] 96205870 90409373 85933555 85664122 83076060 80855113 80097453 78266143
 [9] 77974082 76646107

Smallest eigenvalues:
 [1]  0.8848091  0.8357054  0.8175768  0.6723973  0.6027441  0.5282721
 [7]  0.4208806  0.3864270 -0.5034857 -1.3005486

Largest  eigenvalues:
 [1] 96600178 90314570 84956974 84778438 83021410 81098185 79706643 77985859
 [9] 77523600 76252610

Smallest eigenvalues:
 [1]  0.9727185  0.8713698  0.8211615  0.8076140  0.7866359  0.5450408
 [7]  0.4848952  0.3819790  0.3526645 -0.6073986

Largest  eigenvalues:
 [1] 98159840 91550927 86406960 85948383 83750655 81535491 80511086 79445043
 [9] 78057025 76963392

Smallest eigenvalues:
 [1]  0.7994454  0.7980990  0.7727976  0.7306752  0.6654204  0.5804071
 [7]  0.4938032  0.4620601  0.3854601 -5.2689323

Largest  eigenvalues:
 [1] 96236424 89930310 85186737 85037654 82927329 80801786 79964170 78108661
 [9] 76365710 75632436

Smallest eigenvalues:
 [1]   0.9987405   0.8282154   0.7820841   0.7083499   0.7068107   0.6720074
 [7]   0.6550574   0.5963241   0.3904962 -26.0125030

Largest  eigenvalues:
 [1] 95897137 90277161 86094230 85415539 83015600 80970027 79298922 78717499
 [9] 77342657 76535222

Smallest eigenvalues:
 [1]  0.9106482  0.8725599  0.8068087  0.7525102  0.6446547  0.5736019
 [7]  0.5572219  0.4385993  0.3041376 -0.1036589

Largest  eigenvalues:
 [1] 94785674 89700105 84956515 84689601 81917125 80247314 79217789 77990231
 [9] 76801161 76283336

Smallest eigenvalues:
 [1]  0.8493593  0.7656852  0.7633727  0.6794515  0.6147809  0.5883757
 [7]  0.4586596  0.4099439  0.2995486 -0.2556937

Largest  eigenvalues:
 [1] 94698839 89899913 85030277 83892467 82941184 80746361 78672462 77918520
 [9] 77092099 76206674

Smallest eigenvalues:
 [1]  0.7597501  0.7359965  0.6113205  0.5533182  0.4643636  0.4331087
 [7]  0.4169669  0.2676231 -1.2904106 -7.4245328

Largest  eigenvalues:
 [1] 96694596 90550331 85791487 85504495 83231538 81174834 80138656 78776778
 [9] 77743858 76746502

Smallest eigenvalues:
 [1]  0.8096768  0.8080229  0.6192397  0.5808576  0.5696829  0.5216424
 [7]  0.4242342  0.3107008  0.2545836 -4.0480507

Largest  eigenvalues:
 [1] 97234301 91336989 87023326 86981303 83801467 81663531 80789482 79297968
 [9] 78308457 76932022

Smallest eigenvalues:
 [1]  0.8345835  0.7678830  0.7280397  0.6273266  0.6126059  0.5681748
 [7]  0.4992526  0.4169739  0.2130704 -1.1686863

Largest  eigenvalues:
 [1] 97173752 91673607 87080868 86734701 84034652 82325471 81185718 79060794
 [9] 78263298 76991975

Smallest eigenvalues:
 [1]  0.70745480  0.63708534  0.62267342  0.52474762  0.49496496  0.41734368
 [7]  0.40898477  0.32801835  0.09583426 -2.29334387

Largest  eigenvalues:
 [1] 92521415 89854653 85216031 82706697 82653520 81250894 78875544 76959270
 [9] 76841184 76474316

Smallest eigenvalues:
 [1]  0.9656954  0.9408413  0.8876182  0.7705218  0.7403162  0.6023363
 [7]  0.5968584  0.2868750  0.2190016 -0.2576864

Largest  eigenvalues:
 [1] 97038967 89604736 85449932 85242478 82450162 79980244 79463271 78075041
 [9] 76964527 76154970

Smallest eigenvalues:
 [1]  0.8880987  0.8879066  0.8675313  0.7690868  0.6384597  0.5964105
 [7]  0.5667384  0.4505765  0.4454542 -6.3000596

Largest  eigenvalues:
 [1] 97086238 90234362 85995703 85770637 83112879 81081677 81039049 78791957
 [9] 77757862 76853844

Smallest eigenvalues:
 [1]  0.8777975  0.8357658  0.7048800  0.6263099  0.5689071  0.5550204
 [7]  0.4405208  0.4316264  0.4193840 -0.1576789

Largest  eigenvalues:
 [1] 96700338 92147228 86839380 86180997 83471622 81246164 80646263 79252846
 [9] 78243911 77133471

Smallest eigenvalues:
 [1]  0.7569901  0.6930407  0.6167104  0.5166723  0.4608167  0.3336871
 [7]  0.2862939  0.1773101 -0.2638416 -1.8712947

Largest  eigenvalues:
 [1] 97862004 91019788 86122981 85669038 83412634 81367364 80406622 78584223
 [9] 78086890 76877454

Smallest eigenvalues:
 [1]  1.006842016  0.803337527  0.760850995  0.742796120  0.711957733
 [6]  0.682263884  0.532263495  0.398594162  0.001300631 -0.056494873

Largest  eigenvalues:
 [1] 93189303 91116267 85755306 83621079 82556698 81711333 78863027 77549826
 [9] 77484557 76886579

Smallest eigenvalues:
 [1]   0.9254361   0.8677790   0.6952662   0.6213181   0.5171152   0.4233124
 [7]   0.4127589   0.3896964   0.3616560 -20.0647939

Largest  eigenvalues:
 [1] 97517421 90887275 86741133 86308801 83738187 81727076 80767522 79247290
 [9] 78308366 77071954

Smallest eigenvalues:
 [1]  0.9221112  0.6273579  0.6017540  0.5419971  0.4840735  0.3566440
 [7]  0.3321478  0.3161846  0.2590900 -5.8431321

Largest  eigenvalues:
 [1] 98336627 90609523 86826911 86802791 83156548 80831082 80515045 78748336
 [9] 77845632 76744263

Smallest eigenvalues:
 [1]  1.0152904  0.9485014  0.8074888  0.7356652  0.7132664  0.5698418
 [7]  0.5522237  0.5110457  0.3421706 -1.6223099

Largest  eigenvalues:
 [1] 96436714 90775402 86565474 85370198 83043566 80878595 80146647 79007926
 [9] 78213492 77122380

Smallest eigenvalues:
 [1]  0.6262398  0.6030298  0.5897837  0.5417284  0.4639333  0.4227664
 [7]  0.3858953  0.1800709  0.1686028 -0.1691043

Largest  eigenvalues:
 [1] 96109951 91196818 85990241 85785450 82846540 81125703 80281543 78891487
 [9] 77473128 76810432

Smallest eigenvalues:
 [1]  0.9225509  0.9007225  0.8430807  0.7667531  0.7384909  0.6761920
 [7]  0.6278637  0.4378571  0.4051111 -0.4958256

Largest  eigenvalues:
 [1] 94926675 90415114 85419204 84769461 82684548 80510406 79162966 78518963
 [9] 77207221 76592112

Smallest eigenvalues:
 [1]  0.89785602  0.79423905  0.65984252  0.64846354  0.59898882  0.51796339
 [7]  0.44763014  0.32853625  0.23615514 -0.09008767

Largest  eigenvalues:
 [1] 96760475 91025403 85965696 85347750 83328351 81417932 80083727 78734951
 [9] 76977323 76886583

Smallest eigenvalues:
 [1]   0.8579348   0.8448779   0.7492269   0.6510432   0.5938614   0.5244255
 [7]   0.4847245   0.4549396   0.2810066 -10.8838739

Largest  eigenvalues:
 [1] 96582844 91841933 86374739 85300909 83113508 81140530 79398771 78749502
 [9] 77522302 76396169

Smallest eigenvalues:
 [1]  0.9813092  0.8430597  0.6818274  0.5987037  0.5922118  0.5200347
 [7]  0.4079037  0.3899331  0.3627472 -0.1262698

Largest  eigenvalues:
 [1] 94178693 88700630 84615615 83088373 81502142 79580880 77815670 77771354
 [9] 76629914 75973029

Smallest eigenvalues:
 [1]  0.8986536  0.8660044  0.7985145  0.7141116  0.6439741  0.5981077
 [7]  0.4698929  0.4130062  0.1723396 -0.4823159

Largest  eigenvalues:
 [1] 94888908 91178708 85724452 84807081 83789787 81504809 79743807 79626801
 [9] 77364800 77146917

Smallest eigenvalues:
 [1]   0.8245662   0.8212721   0.7058040   0.5876186   0.5287688   0.4516459
 [7]   0.3917832   0.3289544   0.3176127 -54.4242583

Largest  eigenvalues:
 [1] 95537133 88814399 84941291 83430609 82419458 80144807 77745157 77230520
 [9] 77136002 76392147

Smallest eigenvalues:
 [1]  0.7935410  0.7711320  0.7223435  0.5948197  0.5520337  0.5169339
 [7]  0.5151069  0.3901845  0.3163592 -3.5536421

Largest  eigenvalues:
 [1] 94931478 91268911 85460407 85458955 83142289 81245998 79212731 78801384
 [9] 77537339 77066987

Smallest eigenvalues:
 [1]  0.738303921  0.718467994  0.696675291  0.657685616  0.563580808
 [6]  0.449522496  0.374952228  0.258969352  0.186110053 -0.004662431

Largest  eigenvalues:
 [1] 95568795 92218054 87347682 85337592 84414188 82440341 80068791 79232920
 [9] 78757811 77819859

Smallest eigenvalues:
 [1]  0.83487953  0.80007875  0.65175969  0.61502176  0.58914868  0.54243355
 [7]  0.50488690  0.22633978  0.16764347 -0.01283282

Largest  eigenvalues:
 [1] 97871149 90012619 86656062 85658486 82504679 80649890 80352807 78139276
 [9] 77199974 76007852

Smallest eigenvalues:
 [1]   0.9063662   0.8437767   0.6882514   0.6507760   0.5958862   0.4931903
 [7]   0.4465234   0.4002606   0.2787049 -11.0352552

Largest  eigenvalues:
 [1] 95831899 91329581 86490907 85397769 83382993 81706383 80070057 79095968
 [9] 77735560 76838843

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	8.555006	0.7180601	11.37672	0	0.9351964	2.043492

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

HR ~ alt + n + acc + PM25

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- HR_fd
covariates <- list(altitude = altitude_fd, 
                   noise = noise_fd,
                   acceleration = acceleration_fd,
                   pollution = pollution25_fd)
path_plot <- 'figures/model_HR_alt_noise_acc_PM25_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 80, norder = 4, lambda = 1e4),
                     noise = list(nbetabasis = 80, norder = 4, lambda = 1e4),
                     acceleration = list(nbetabasis = 80, norder = 4, lambda = 1e4),
                     pollution = list(nbetabasis = 80, norder = 4, lambda = 1e4))

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, 
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 19.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Warning message in `^.fd`((outcome - yhatfd), 2):
"The maximum error exceeds the tolerance level."
Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 642 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Smallest eigenvalues:
 [1]  0.3572400  0.3241591  0.3175724  0.2539564  0.2211844  0.1429275
 [7]  0.1386985 -0.1192288 -0.1583929 -4.0563352

Largest  eigenvalues:
 [1] 64057025 60144807 57579659 55680452 55075247 53420479 52147618 51727274
 [9] 51700094 51150786

Smallest eigenvalues:
 [1]  0.20815480  0.19527708  0.13001476  0.07394004  0.05268478 -0.02520543
 [7] -0.03022643 -0.04639147 -0.18712336 -2.86933727

Largest  eigenvalues:
 [1] 63362686 61063658 57705778 55877424 55340792 53945203 52744004 52432708
 [9] 51874744 51619834

Smallest eigenvalues:
 [1]  0.320485037  0.308484457  0.294083995  0.287061731  0.236586395
 [6]  0.161861584  0.032725122 -0.005492232 -0.144953778 -0.522917077

Largest  eigenvalues:
 [1] 64171547 61147712 58395964 55891118 55767221 54364253 53237999 52349784
 [9] 52116894 51922555

Smallest eigenvalues:
 [1]  0.4918629799  0.4834773366  0.4230672504  0.3498649743  0.3391757226
 [6]  0.2622011103  0.2493391868  0.0006027109 -0.0047136550 -0.0656738895

Largest  eigenvalues:
 [1] 61992275 60517246 57617107 55854646 54975045 54089904 52470477 52433817
 [9] 51229294 51014200

Smallest eigenvalues:
 [1]  0.3364004  0.3289831  0.2962855  0.2262138  0.2071379  0.1997672
 [7]  0.1718978  0.1221774 -0.3798499 -2.5629421

Largest  eigenvalues:
 [1] 65213933 59900563 57366967 56070586 54801621 53236418 52165572 52027160
 [9] 51510823 51178965

Smallest eigenvalues:
 [1]  0.43960886  0.40739004  0.38036940  0.29119135  0.28331892  0.15010614
 [7]  0.04677086 -0.03605983 -0.10474583 -0.32354130

Largest  eigenvalues:
 [1] 64395757 60692182 57313959 56079725 55705692 53907634 52786711 52051200
 [9] 51774711 51464929

Smallest eigenvalues:
 [1]  0.2763762  0.2154392  0.1824499  0.1802923  0.1437914  0.1125075
 [7] -0.2037908 -0.2308594 -0.3786692 -0.4594503

Largest  eigenvalues:
 [1] 65043228 61026199 57678547 56174052 55510518 53897637 52985881 52156865
 [9] 52064095 51786866

Smallest eigenvalues:
 [1]  0.35130208  0.32195043  0.25929832  0.21560677  0.19993165 -0.06684521
 [7] -0.12772567 -0.30386030 -0.42230894 -0.56429931

Largest  eigenvalues:
 [1] 64887832 59884269 56538136 56494640 54526093 52725113 52491518 52190857
 [9] 51718398 51256374

Smallest eigenvalues:
 [1]  0.50100352  0.43554188  0.41233819  0.30676249  0.28168009  0.23034198
 [7]  0.20108541  0.07812386 -0.00289683 -0.14461111

Largest  eigenvalues:
 [1] 63905801 59824571 57232425 55822166 54696749 53191030 52245752 51787068
 [9] 51659209 51048402

Smallest eigenvalues:
 [1]  0.38226613  0.36936228  0.36840363  0.34104063  0.22871764  0.22722070
 [7]  0.21700001  0.13023772  0.07185889 -0.01500420

Largest  eigenvalues:
 [1] 64551889 60467163 58052828 55668533 55378222 54135552 52760185 52159002
 [9] 51911737 51745547

Smallest eigenvalues:
 [1]  0.44454890  0.39600696  0.35937368  0.33392174  0.20398786  0.06862949
 [7] -0.43067560 -0.45885425 -1.07110227 -3.59165125

Largest  eigenvalues:
 [1] 64721302 60074629 57264269 55818235 55237105 53021585 52213272 51976403
 [9] 51734457 51260959

Smallest eigenvalues:
 [1]  0.36073040  0.32762768  0.32553822  0.28244905  0.27152783  0.17385777
 [7]  0.12877348  0.02402656 -0.26864776 -1.67871407

Largest  eigenvalues:
 [1] 63336801 59899788 57139555 55231761 54844198 53644892 52169184 52061273
 [9] 51363479 51023299

Smallest eigenvalues:
 [1]  0.38919150  0.38198269  0.35993389  0.27814312  0.27361771  0.21880853
 [7]  0.21064366 -0.04733215 -0.22615366 -1.18213899

Largest  eigenvalues:
 [1] 64876586 59738225 57167871 56545952 54793387 53322920 52552913 52191143
 [9] 51496041 50778932

Smallest eigenvalues:
 [1]  0.56599589  0.51522001  0.49716308  0.42173562  0.37622006  0.37414837
 [7]  0.26249298  0.21907298  0.15529848 -0.01614275

Largest  eigenvalues:
 [1] 65044260 59528686 56804412 55982911 54935764 53289992 52171507 51972175
 [9] 51898375 51231592

Smallest eigenvalues:
 [1]  0.48076328  0.38622990  0.37523225  0.32448140  0.23316474  0.21960765
 [7]  0.14829284  0.09201754 -0.09826087 -0.11605853

Largest  eigenvalues:
 [1] 66301320 59326859 57246433 56655941 54051276 53267548 52561339 51334121
 [9] 51137182 50525665

Smallest eigenvalues:
 [1]  0.5181210  0.5010810  0.4883916  0.4406659  0.4190410  0.3673086
 [7]  0.2696495  0.1548473 -0.1228540 -0.2300485

Largest  eigenvalues:
 [1] 63366952 60111230 56810156 55261569 55002375 53483030 52025304 51386874
 [9] 50856721 50536505

Smallest eigenvalues:
 [1]  0.3934942  0.2690784  0.2653280  0.2518613  0.2162878  0.1790993
 [7]  0.1593644  0.1175771 -0.1392969 -0.5375719

Largest  eigenvalues:
 [1] 66530749 60558415 57877572 57276985 55065660 53399490 53207130 52953137
 [9] 51671805 51516286

Smallest eigenvalues:
 [1]  0.47095992  0.41151151  0.39009730  0.23555497  0.22889025  0.12739543
 [7]  0.11521296  0.08318608  0.06435559 -0.78822906

Largest  eigenvalues:
 [1] 65784661 60536220 56993951 56779371 55145628 53496493 52748314 52261602
 [9] 52051702 51288186

Smallest eigenvalues:
 [1]  0.49795664  0.49293705  0.46341960  0.39675058  0.34727816  0.27428560
 [7]  0.16133323  0.02520763 -0.08061078 -0.67548394

Largest  eigenvalues:
 [1] 63446078 59919192 57098632 55394866 54909682 53829454 52461465 51827299
 [9] 51013573 50912857

Smallest eigenvalues:
 [1]  0.4059169  0.3553364  0.3515291  0.3078905  0.2967307  0.2566029
 [7]  0.2360790  0.1652289  0.1104114 -0.0558672

Largest  eigenvalues:
 [1] 64299467 61503460 58102473 56629090 55669088 54037930 52798274 52541105
 [9] 52485403 51789855

Smallest eigenvalues:
 [1]  0.4460437  0.4370955  0.3816666  0.3473450  0.3281377  0.3055509
 [7]  0.2611311  0.2450317  0.1088500 -0.1154320

Largest  eigenvalues:
 [1] 64841249 61117481 58031276 56429263 56429118 54727577 53077512 52603011
 [9] 52328076 51720325

Smallest eigenvalues:
 [1]  0.29172716  0.26705452  0.16475462  0.11652670  0.09431992  0.01559144
 [7] -0.10874491 -0.10925043 -0.44551949 -1.44650426

Largest  eigenvalues:
 [1] 64767110 60244226 57025007 55944094 54913161 53357316 52009406 51944806
 [9] 51579422 50906645

Smallest eigenvalues:
 [1]  0.36347944  0.29839340  0.29050353  0.27232831  0.27195074  0.24277733
 [7]  0.19766683  0.09278354 -0.46095206 -0.47329183

Largest  eigenvalues:
 [1] 63926626 59805241 57282049 55213482 54470430 53013311 51953515 51381162
 [9] 51152429 51105799

Smallest eigenvalues:
 [1]  0.33389114  0.28761147  0.25725293  0.24741809  0.23223098  0.21213310
 [7]  0.20080965  0.08105087 -0.15044906 -0.24208737

Largest  eigenvalues:
 [1] 65795003 60475623 57891783 56764538 55158152 53459724 53025740 52786711
 [9] 52031389 51942040

Smallest eigenvalues:
 [1]  0.4327472  0.3712711  0.3592195  0.3255310  0.2916081  0.2505628
 [7]  0.1975630  0.1294015  0.1226310 -1.0956320

Largest  eigenvalues:
 [1] 65018324 59900371 57227164 56061496 55095751 53287288 52129538 52095714
 [9] 51571133 51184690

Smallest eigenvalues:
 [1]  0.49976091  0.44936337  0.35862225  0.35276438  0.34221020  0.29944621
 [7]  0.27312165  0.15231482 -0.06882362 -0.99085301

Largest  eigenvalues:
 [1] 63552092 59153520 57013572 55547625 54473665 52932118 51610368 51507431
 [9] 51463963 50580109

Smallest eigenvalues:
 [1]  0.44000755  0.39221958  0.32075230  0.31369847  0.26194793  0.21126722
 [7] -0.04150861 -0.04166315 -0.04180957 -0.26528260

Largest  eigenvalues:
 [1] 61138081 59059968 56149375 54859398 54134902 52952757 51834903 50853739
 [9] 50135535 49964435

Smallest eigenvalues:
 [1] -0.2384820 -0.3236995 -0.3343005 -0.3601049 -0.4290560 -0.5295021
 [7] -0.5546944 -0.9277185 -1.1302971 -1.2198926

Largest  eigenvalues:
 [1] 64898588 61095112 58239056 55669635 55579062 54249523 52480127 52006758
 [9] 51696025 51445370

Smallest eigenvalues:
 [1]  0.284032075  0.269374108  0.243847802  0.228442778  0.185862668
 [6]  0.037836381  0.008364788 -0.257175665 -0.420003497 -0.881523873

Largest  eigenvalues:
 [1] 64854170 61072067 57743302 56639843 55610572 54015814 52784207 52606800
 [9] 52385667 51809985

Smallest eigenvalues:
 [1]  0.39745675  0.30378715  0.28698407  0.26038800  0.21561967  0.12034930
 [7]  0.09870136 -0.08735814 -1.11663102 -1.26942154

Largest  eigenvalues:
 [1] 64523575 60174634 56672842 56286533 55328894 53334607 52575618 52264961
 [9] 52213394 51231045

Smallest eigenvalues:
 [1]  0.465164853  0.381467739  0.338419493  0.285814524  0.255618713
 [6]  0.189508223  0.141939371 -0.007267245 -0.668396315 -1.002118380

Largest  eigenvalues:
 [1] 64041823 58837004 56494584 55832043 54013667 52296979 51760999 51300462
 [9] 51038577 49991980

Smallest eigenvalues:
 [1]  0.42135977  0.33064526  0.24581927  0.22783270  0.22315299  0.19639218
 [7]  0.17289158  0.12267540  0.04686315 -5.31312804

Largest  eigenvalues:
 [1] 61838534 59832243 56893230 55076043 54672635 53480740 52126963 51470915
 [9] 50730290 50528299

Smallest eigenvalues:
 [1]  0.28167814  0.22157573  0.21288895  0.19779428  0.07514761  0.05132728
 [7] -0.11726279 -0.18719471 -1.32155859 -2.87728671

Largest  eigenvalues:
 [1] 66521296 60602632 57417818 56450468 55360607 53713243 52566459 52437993
 [9] 51819287 51677782

Smallest eigenvalues:
 [1]  0.43084282  0.36104450  0.34359855  0.34209815  0.26088381  0.24825747
 [7]  0.22729943  0.19323460  0.06281628 -0.05721952

Largest  eigenvalues:
 [1] 64606593 60791818 58246345 55827890 55634400 54284458 52799172 52472818
 [9] 51810122 51555398

Smallest eigenvalues:
 [1]  0.31737948  0.29517252  0.28227197  0.22005093  0.21848316  0.17054747
 [7]  0.09857276 -0.16891386 -0.20307817 -2.19901137

Largest  eigenvalues:
 [1] 65092502 60587247 57765907 55910841 55845101 54172541 52449565 52256703
 [9] 52217606 51368550

Smallest eigenvalues:
 [1]  0.38163167  0.37451189  0.29926363  0.28470765  0.20351932  0.09792982
 [7]  0.04525726 -0.12321008 -0.19859943 -1.45050876

Largest  eigenvalues:
 [1] 63906345 59932378 57057508 55237595 55061015 53491821 52205040 51514534
 [9] 51373076 51216214

Smallest eigenvalues:
 [1]  0.46659129  0.38597616  0.35789100  0.32751038  0.32706560  0.31221075
 [7]  0.25349908  0.01068126 -0.01013948 -0.07940873

Largest  eigenvalues:
 [1] 65265428 60401834 57500936 56436683 54876402 53095347 52565577 52149870
 [9] 51327532 50910693

Smallest eigenvalues:
 [1]  0.37669338  0.36404481  0.34189170  0.26190141  0.24874713  0.20737541
 [7]  0.05400449 -0.02976017 -0.09473307 -2.55934522

Largest  eigenvalues:
 [1] 63181444 59833074 56975787 55162188 55000313 53385834 51720296 51676789
 [9] 51154527 50900452

Smallest eigenvalues:
 [1]  0.49248639  0.40960297  0.38621108  0.36023736  0.25673056  0.21464356
 [7]  0.19234884  0.12075105  0.04248594 -0.74549449

Largest  eigenvalues:
 [1] 65248302 59959049 57181583 57138421 54533561 53101756 52865862 52025574
 [9] 51921307 51080228

Smallest eigenvalues:
 [1]  0.39334122  0.33047064  0.32629501  0.19379635  0.16812416  0.13090414
 [7] -0.05477706 -0.18408445 -0.58098414 -0.73843717

Largest  eigenvalues:
 [1] 65099505 61015316 58085042 56802595 55375841 53431849 53031496 52679607
 [9] 51855798 51724354

Smallest eigenvalues:
 [1]  0.30548339  0.24554368  0.23642478  0.15987535  0.12703925  0.09378831
 [7] -0.01922214 -0.04353630 -0.76229442 -0.80612734

Largest  eigenvalues:
 [1] 64876948 60619630 58099614 56431443 55108354 53540208 52736423 52490566
 [9] 52120586 51811918

Smallest eigenvalues:
 [1]  0.32426554  0.28197256  0.27470200  0.22563615  0.14239162  0.02433923
 [7] -0.10797768 -0.37291393 -0.37486837 -1.13147897

Largest  eigenvalues:
 [1] 64183660 59619217 56887479 54899471 54800085 53098550 51321536 51264428
 [9] 51136247 50515792

Smallest eigenvalues:
 [1]  0.40126316  0.25364061  0.22030842  0.21609708  0.17124851 -0.02436149
 [7] -0.03301147 -0.03839447 -0.14124017 -1.71023636

Largest  eigenvalues:
 [1] 63345061 59846669 56972690 55212679 54762249 53165915 51686538 51499515
 [9] 51314190 50892958

Smallest eigenvalues:
 [1]  0.5420560  0.5337247  0.4513997  0.4431111  0.4387204  0.3984351
 [7]  0.3288936  0.3042720  0.2969365 -0.1362922

Largest  eigenvalues:
 [1] 64190092 60453721 57603505 55851775 55388324 53681934 51747159 51708031
 [9] 51587499 50661375

Smallest eigenvalues:
 [1]  0.55073374  0.54297222  0.51082963  0.41523274  0.37805263  0.34798850
 [7]  0.21287291  0.10695564  0.02502659 -0.30731463

Largest  eigenvalues:
 [1] 62155485 59563751 56678418 55281099 54357100 53446897 51731277 51612997
 [9] 50474959 50330190

Smallest eigenvalues:
 [1]  0.45152808  0.34221015  0.30429844  0.20070174  0.14375819  0.13941621
 [7]  0.08835044  0.07877502 -0.05718764 -1.53016412

Largest  eigenvalues:
 [1] 63522551 59582375 56789777 55303776 55069116 53402280 52399364 51864767
 [9] 51457574 51231107

Smallest eigenvalues:
 [1]  0.5290067  0.5073476  0.4420684  0.3898846  0.3662684  0.3397274
 [7]  0.3302179  0.2940417  0.2693324 -0.3899703

Largest  eigenvalues:
 [1] 63840064 59665589 57254705 55531452 54728658 52972436 51716648 51544130
 [9] 51094943 50413086

Smallest eigenvalues:
 [1]  0.38186404  0.31882138  0.28269268  0.26221908  0.20873195  0.15620325
 [7] -0.02502617 -0.30825898 -0.31270897 -1.12140298

Largest  eigenvalues:
 [1] 64256357 60086955 57105046 56034737 55098977 53576186 52434184 51980495
 [9] 51940992 51457099

Smallest eigenvalues:
 [1]  0.39110953  0.34511263  0.31179453  0.27568164  0.22779465  0.19631693
 [7]  0.19355203  0.04445829 -0.11891403 -0.22965545

Largest  eigenvalues:
 [1] 64839947 61068909 58364751 56124469 55809464 54409762 52478759 52320824
 [9] 52033838 51550025

Smallest eigenvalues:
 [1]  0.35694152  0.34963105  0.34781769  0.31988503  0.31902393  0.28779090
 [7]  0.22480478  0.01865781 -0.21348169 -0.30714021

Largest  eigenvalues:
 [1] 65504655 60510141 57714234 56596733 55246141 53717935 52512222 52195935
 [9] 52006730 51271604

Smallest eigenvalues:
 [1]  0.4909675452  0.4701221131  0.4694390051  0.3028352919  0.2452801542
 [6]  0.2434072671  0.2156807159  0.1587221503  0.1034061497 -0.0001388593

Largest  eigenvalues:
 [1] 62734711 59648912 56895573 55276388 54848491 53646421 52111196 52070200
 [9] 51026420 50847040

Smallest eigenvalues:
 [1]  0.48689541  0.48576490  0.42829449  0.42401995  0.34528136  0.34205796
 [7]  0.28160503  0.25025727  0.22272704 -0.02304821

Largest  eigenvalues:
 [1] 65413861 60757798 57982157 56637338 56053608 54461964 52624305 52393563
 [9] 52307239 51374075

Smallest eigenvalues:
 [1]  0.3527634  0.3377088  0.2587051  0.2288362  0.2127325  0.1806885
 [7]  0.1418255 -0.5672442 -0.7168194 -0.8473275

Largest  eigenvalues:
 [1] 66350945 60730408 57995685 57153080 55114805 53539171 53286408 52343010
 [9] 51910982 51533345

Smallest eigenvalues:
 [1]  0.339633151  0.310616532  0.291608181  0.277225532  0.252504765
 [6]  0.169082446  0.162774847  0.001912881 -0.319071006 -0.434709805

Largest  eigenvalues:
 [1] 63904353 60530472 57176519 55799468 55759682 54076998 52933246 52229310
 [9] 51972024 51712235

Smallest eigenvalues:
 [1]  0.46803290  0.40007338  0.39735059  0.38421421  0.28975389  0.25730761
 [7]  0.23455695  0.20195783  0.06326498 -0.10195046

Largest  eigenvalues:
 [1] 64926444 59584366 57024175 56457057 54213155 52691044 52451666 51421785
 [9] 51182888 50350749

Smallest eigenvalues:
 [1]  0.489624709  0.476595477  0.442252616  0.426693886  0.366338445
 [6]  0.304354167  0.286983162  0.071696970 -0.009922337 -0.447757310

Largest  eigenvalues:
 [1] 65282066 60214595 57649067 56349320 55503948 53486895 52614501 52116710
 [9] 51764200 51074615

Smallest eigenvalues:
 [1]  0.26667410  0.26436845  0.22151618  0.19676606  0.16215809  0.03159199
 [7] -0.14277823 -0.42581091 -0.60823173 -5.49263649

Largest  eigenvalues:
 [1] 66280509 60867634 57250468 57233839 55635451 53794764 53255816 52423911
 [9] 52234572 51477171

Smallest eigenvalues:
 [1]  0.28709078  0.20331330  0.20177601  0.12799313  0.07467996 -0.13078776
 [7] -0.28376289 -0.37779122 -1.02675664 -1.90156009

Largest  eigenvalues:
 [1] 64433506 60553778 57915879 56646316 55549939 53877112 52605303 52435448
 [9] 52267266 51276730

Smallest eigenvalues:
 [1]  0.16609193  0.09717454 -0.02646772 -0.07053619 -0.20321858 -0.27499109
 [7] -0.60901198 -1.23618886 -1.32677766 -1.47023854

Largest  eigenvalues:
 [1] 66253058 60130437 57946127 55909172 54888313 53086936 52370053 51736024
 [9] 51309271 50971911

Smallest eigenvalues:
 [1]  0.46975502  0.43519165  0.37942305  0.36708858  0.27975748  0.23585324
 [7]  0.19380726  0.15939322  0.05698807 -0.11427379

Largest  eigenvalues:
 [1] 65529438 61280097 58090169 56867114 55920524 54308978 53501979 52863928
 [9] 52407450 52105472

Smallest eigenvalues:
 [1]  0.30493520  0.30361421  0.25118172  0.23662969  0.18855208  0.13848131
 [7]  0.12401362  0.02835327 -0.79716026 -2.16432190

Largest  eigenvalues:
 [1] 63520605 59810322 56988333 55559966 54828332 53227450 51975931 51770147
 [9] 51535491 50967707

Smallest eigenvalues:
 [1]  0.30810328  0.29251766  0.28242599  0.25433050  0.24175884  0.21017416
 [7]  0.13656731  0.09620963 -0.05430687 -4.88009646

Largest  eigenvalues:
 [1] 63371756 60622385 57209715 55854883 54924041 53937623 51970148 51808118
 [9] 51042825 50743218

Smallest eigenvalues:
 [1]  0.32692241  0.29829005  0.27990019  0.20355077  0.17774474  0.12937465
 [7]  0.12499896  0.09147319 -0.02837267 -1.63256340

Largest  eigenvalues:
 [1] 65896751 60994812 58298313 56665523 55690281 54023518 53070445 52622140
 [9] 52504727 52218025

Smallest eigenvalues:
 [1]  0.29123360  0.25552098  0.24744107  0.18772308  0.14368051  0.13594990
 [7]  0.08102463 -0.01648910 -1.26516585 -1.66643920

Largest  eigenvalues:
 [1] 66363864 60452546 57785218 56830800 55104627 53950293 52662443 52521438
 [9] 52403732 51841080

Smallest eigenvalues:
 [1]  0.3176570  0.2599552  0.2206302  0.1857760  0.1767845  0.1608564
 [7] -0.1829376 -0.2739934 -0.3076590 -0.9759104

Largest  eigenvalues:
 [1] 66225723 59997228 57408594 56895546 54695757 53083737 52883697 52487458
 [9] 51680595 51629488

Smallest eigenvalues:
 [1]  0.28363349  0.21716033  0.17639894  0.14059422  0.08211850 -0.02726647
 [7] -0.07456445 -0.45684450 -0.46106893 -0.66625631

Largest  eigenvalues:
 [1] 63988847 60206749 57672892 55438938 54789217 53584650 51631636 51550552
 [9] 51538830 50952331

Smallest eigenvalues:
 [1]  0.42425696  0.38013073  0.37781261  0.32415938  0.23073376  0.22262037
 [7]  0.15176636  0.08159191  0.08022446 -0.18023148

Largest  eigenvalues:
 [1] 64625430 60376646 57509574 56341473 55326289 53849102 52404494 52394558
 [9] 52196673 51321110

Smallest eigenvalues:
 [1]  0.5191467  0.4686153  0.4516688  0.3730825  0.3441009  0.3229599
 [7]  0.3111210  0.1283469  0.1048464 -0.1217506

Largest  eigenvalues:
 [1] 64787356 59680482 57150602 55766186 54922128 53520921 51937823 51870435
 [9] 51333616 50441071

Smallest eigenvalues:
 [1]  0.37900607  0.37579912  0.27173130  0.21796658  0.19640719 -0.01881112
 [7] -0.02828844 -0.05670632 -0.06603805 -1.09931498

Largest  eigenvalues:
 [1] 64317344 60501775 57312053 55711535 55517062 53842750 52919276 52012859
 [9] 51925415 51669765

Smallest eigenvalues:
 [1]  0.50712127  0.48934228  0.45347655  0.41772840  0.31821041  0.31608375
 [7]  0.25888299  0.21728037  0.21681046 -0.05002221

Largest  eigenvalues:
 [1] 64251988 59601604 57278581 55460939 54652246 53099431 51707945 51415652
 [9] 51329183 50664169

Smallest eigenvalues:
 [1]  0.3815020  0.3807990  0.3111092  0.2517962  0.2453625  0.2000132
 [7]  0.1690091 -0.3948289 -0.6721841 -1.5067667

Largest  eigenvalues:
 [1] 62652338 59239403 56794264 55101152 54862422 53183050 51910360 51763619
 [9] 50959454 50629579

Smallest eigenvalues:
 [1]  0.60482897  0.59706653  0.55296030  0.44912071  0.40053895  0.35550987
 [7]  0.28081158  0.22796525  0.13531928 -0.01172452

Largest  eigenvalues:
 [1] 62827970 60198068 57100827 55800015 54823978 54143832 52473105 52220781
 [9] 51084783 50859672

Smallest eigenvalues:
 [1]  0.28537640  0.27041960  0.25421609  0.25285332  0.21962138  0.14971529
 [7]  0.04060564 -0.64100655 -0.89371618 -1.60482220

Largest  eigenvalues:
 [1] 64845499 60310134 57853417 56182016 55183337 53355559 52475901 52174561
 [9] 52123980 51625946

Smallest eigenvalues:
 [1]  0.4340012  0.3854872  0.3431338  0.3090682  0.2976295  0.1498647
 [7]  0.1238922  0.1113390 -0.1564700 -1.0322496

Largest  eigenvalues:
 [1] 65537564 60563339 57489206 56242934 55155758 53406753 52397355 52341330
 [9] 51946283 51357532

Smallest eigenvalues:
 [1]  0.05972360  0.05200599 -0.04472271 -0.16168531 -0.16186883 -0.24938951
 [7] -0.37060917 -0.50403192 -0.69908135 -1.45177859

Largest  eigenvalues:
 [1] 63057342 59950075 57158487 55183252 54773629 53154759 52203185 51393303
 [9] 51172907 50947017

Smallest eigenvalues:
 [1]  0.45780726  0.41737971  0.39189471  0.34565040  0.33201705  0.32925516
 [7]  0.27582942  0.26857818  0.22532502 -0.02481878

Largest  eigenvalues:
 [1] 61730421 59149979 56795635 54872641 54315883 53110801 51467664 51098763
 [9] 50403432 50107821

Smallest eigenvalues:
 [1]  0.3833729  0.2971821  0.2509440  0.2385454  0.2273118  0.1989267
 [7]  0.1780260  0.1460718 -0.1974149 -0.2472994

Largest  eigenvalues:
 [1] 64559982 60233243 57646543 56378330 54917363 53389939 52527544 51636354
 [9] 51499126 50476047

Smallest eigenvalues:
 [1]  0.3646963  0.3595078  0.3072282  0.2735260  0.2448138  0.2367198
 [7]  0.1456193  0.1061710 -0.4978399 -0.7282223

Largest  eigenvalues:
 [1] 65333194 60302100 58379970 55608168 55542254 54454931 52877525 52716338
 [9] 51870592 51565797

Smallest eigenvalues:
 [1]  0.39905585  0.34746703  0.33720530  0.29311411  0.22012125  0.16280442
 [7]  0.14794924  0.09903528 -0.24700643 -0.40767001

Largest  eigenvalues:
 [1] 63695027 59342693 57346795 55885049 54196878 52875004 51793667 51721753
 [9] 51423784 50701111

Smallest eigenvalues:
 [1]  0.434026699  0.420192491  0.371494212  0.358349883  0.347354950
 [6]  0.346054388  0.288792083  0.260117823 -0.003616318 -5.376752724

Largest  eigenvalues:
 [1] 64232300 60079341 57133128 55612150 55126506 53351497 52136211 51729628
 [9] 51640725 50865858

Smallest eigenvalues:
 [1]  0.4585522  0.3856040  0.3708957  0.3625370  0.3149726  0.2731110
 [7]  0.2052727  0.1783903  0.1507486 -0.1390350

Largest  eigenvalues:
 [1] 64071662 59743549 57114570 55988912 54757544 53261189 52106801 51859210
 [9] 51843735 50950023

Smallest eigenvalues:
 [1]  0.52550429  0.45846857  0.42359247  0.36130431  0.35432233  0.27856730
 [7]  0.25876853  0.17755187  0.04585812 -0.02392554

Largest  eigenvalues:
 [1] 61461227 59847398 56981738 56081301 54131884 53957016 52768555 51638564
 [9] 50771560 50680765

Smallest eigenvalues:
 [1]  0.50990672  0.46278808  0.41709809  0.35218117  0.32965894  0.31780317
 [7]  0.30296146  0.28301839  0.18501853 -0.00942292

Largest  eigenvalues:
 [1] 63736727 60732480 57344755 55938129 55842612 54144641 52561228 52046197
 [9] 51892779 51503323

Smallest eigenvalues:
 [1]  0.45191564  0.40166766  0.37066922  0.36635833  0.34610321  0.30301743
 [7]  0.26437871  0.22812645  0.08560410 -0.04506491

Largest  eigenvalues:
 [1] 61841680 60861022 57523438 55652906 55024490 53882842 52145718 52133906
 [9] 51249343 50993076

Smallest eigenvalues:
 [1]  0.35778838  0.32313732  0.28070710  0.23478564  0.18571347  0.17820559
 [7]  0.08602546 -0.09724300 -0.44512864 -0.61094981

Largest  eigenvalues:
 [1] 64625903 61385440 58300290 56597975 55845160 54012351 53779061 52835131
 [9] 52238935 52088055

Smallest eigenvalues:
 [1]  0.4258179  0.4123385  0.4066811  0.3173327  0.2935820  0.2873354
 [7]  0.2741114  0.2036702 -0.1543384 -3.3223935

Largest  eigenvalues:
 [1] 64939930 60522264 57799431 56325991 55224145 53740974 52412394 52134671
 [9] 52080729 51217120

Smallest eigenvalues:
 [1]  0.270139743  0.258125051  0.203855010  0.077238656 -0.001353699
 [6] -0.053471372 -0.118071092 -0.423497535 -0.585571198 -1.222890407

Largest  eigenvalues:
 [1] 64910131 59792874 56955673 55471984 54675711 53020805 51973689 51656018
 [9] 51318182 51136891

Smallest eigenvalues:
 [1]  0.39030630  0.36431513  0.36048649  0.33081098  0.32275195  0.30510288
 [7]  0.30134017  0.19091043  0.13860613 -0.08821795

Largest  eigenvalues:
 [1] 65305567 60809308 57448752 57138166 55260736 53667722 52883231 52679282
 [9] 52342210 51421750

Smallest eigenvalues:
 [1]  0.4336938  0.3811972  0.3025028  0.2152404  0.2143854  0.2104441
 [7]  0.1731974 -0.0584411 -0.5365725 -0.6975240

Largest  eigenvalues:
 [1] 65336805 61045320 57411766 56236779 56023012 54133555 53072179 52554321
 [9] 52224186 51677922

Smallest eigenvalues:
 [1]  0.5561153  0.4781759  0.4731293  0.4199611  0.3779361  0.3670875
 [7]  0.3379363  0.3342902  0.2321161 -0.1889379

Largest  eigenvalues:
 [1] 64128295 60229662 57354590 56035765 55393982 53533497 52070744 51986858
 [9] 51783110 50818410

Smallest eigenvalues:
 [1]  0.31847471  0.27490608  0.23103712  0.22072614  0.18654000  0.15055378
 [7]  0.13807697  0.05449083  0.04996715 -0.14503993

Largest  eigenvalues:
 [1] 62145682 58953799 56457959 54823954 54766718 53069711 52032662 51514143
 [9] 50725101 50484234

Smallest eigenvalues:
 [1]  0.54542371  0.54113868  0.48147653  0.43825609  0.40116155  0.39243073
 [7]  0.36925263  0.22188467  0.13469984 -0.06763395

Largest  eigenvalues:
 [1] 63989765 60064953 56688317 55432189 55317750 53611973 52250079 51468344
 [9] 51428732 50599410

Smallest eigenvalues:
 [1]  0.357807286  0.349088475  0.306174172  0.277724705  0.261292687
 [6]  0.173233031  0.162480802  0.025775202  0.003066232 -0.123847602

Largest  eigenvalues:
 [1] 64934958 59195924 56706974 56383183 54608310 53050491 52425423 51637283
 [9] 50773408 50214397

Smallest eigenvalues:
 [1]  0.38691058  0.37914400  0.33736700  0.31413882  0.29839175  0.22319961
 [7]  0.03296122 -0.21851472 -0.23160158 -2.89636509

Largest  eigenvalues:
 [1] 65486301 60407178 57524222 56061381 55528873 53988543 52680697 52180972
 [9] 52000827 51801406

Smallest eigenvalues:
 [1]  0.191085559  0.065989762  0.008864738 -0.183355908 -0.232380493
 [6] -0.334767617 -0.398897637 -0.657233726 -0.801103140 -4.031988330

Largest  eigenvalues:
 [1] 62467877 59642617 56815956 55395970 54469087 53479396 52096444 51827825
 [9] 51053428 50696642

Smallest eigenvalues:
 [1]  0.4398407  0.4306110  0.3948517  0.3484145  0.2794921  0.2648174
 [7]  0.1589810  0.1463925  0.1036701 -1.7050408

Largest  eigenvalues:
 [1] 63980535 60398989 57544343 55407189 55338956 53847128 52225912 52135617
 [9] 51542032 51339157

Smallest eigenvalues:
 [1]  0.4169138  0.3747850  0.3499980  0.3279687  0.2570091  0.2533887
 [7]  0.1829724  0.1039144 -0.3099311 -0.4348086

Largest  eigenvalues:
 [1] 63146644 60498559 56882123 55837653 54962582 53275487 52182459 51720406
 [9] 51549935 50745190

Smallest eigenvalues:
 [1]  0.3863383  0.3725693  0.3402612  0.3273823  0.2639087  0.2452811
 [7]  0.2289172  0.1238991 -0.1618517 -1.8142402

Largest  eigenvalues:
 [1] 61949083 59617663 56877805 54958154 54410347 53058589 51373009 51229911
 [9] 50626749 50419702

Smallest eigenvalues:
 [1]  0.46990848  0.40559481  0.35611387  0.34376946  0.32571544  0.30474885
 [7]  0.28793421  0.19319505  0.14470277 -0.02924618

Largest  eigenvalues:
 [1] 64953733 59868091 57465829 56072246 54744131 53119010 52212536 51873610
 [9] 51791675 51033031

Smallest eigenvalues:
 [1]  0.54957838  0.54463200  0.54083681  0.49891923  0.44485620  0.32740063
 [7]  0.19661494  0.12678108  0.06429228 -0.11750755

Largest  eigenvalues:
 [1] 63577287 60261787 57455345 55593772 55191894 53664021 52175088 51940753
 [9] 51687081 51055238

Smallest eigenvalues:
 [1]  0.4709673  0.4291171  0.4028882  0.3893349  0.3609741  0.1549805
 [7]  0.1294421  0.1147023 -0.2065128 -1.2897480

Largest  eigenvalues:
 [1] 64544441 59253113 56768190 54881410 54868360 53166589 52188223 51313191
 [9] 51236105 50625199

Smallest eigenvalues:
 [1]  0.45164240  0.44019667  0.40313259  0.37379501  0.29893470  0.17303321
 [7]  0.15966312  0.10582758  0.04361385 -1.57612389

Largest  eigenvalues:
 [1] 64465797 60173534 56910177 55991850 55341440 53346972 52389483 52067523
 [9] 51626043 51233134

Smallest eigenvalues:
 [1]  0.27477744  0.19467440  0.15954488  0.13991501  0.04603371  0.03438404
 [7] -0.14440284 -0.35007133 -0.71840349 -1.00148048

Largest  eigenvalues:
 [1] 64265707 60898864 57567800 55670013 55293760 53592729 52122966 51866676
 [9] 51558509 51228311

Smallest eigenvalues:
 [1]  0.4639443  0.3820820  0.3295740  0.3076395  0.2967086  0.2568272
 [7]  0.2402834  0.2292922 -0.1798325 -1.5247088

Largest  eigenvalues:
 [1] 63195149 60080687 57331128 55870705 54715203 53362558 52176900 51718922
 [9] 51652835 51199680

Smallest eigenvalues:
 [1]  0.39226084  0.37562998  0.29721386  0.25695495  0.22287605  0.21889827
 [7]  0.03522171 -0.01706078 -0.08423336 -4.77415802

Largest  eigenvalues:
 [1] 63384454 59723997 56753544 55135280 55009229 52935019 51489509 51476458
 [9] 51242597 50468580

Smallest eigenvalues:
 [1]  0.48214799  0.39204477  0.37424865  0.30111249  0.27718006  0.19968578
 [7]  0.19933059  0.17981972  0.04870542 -0.95063877

Largest  eigenvalues:
 [1] 64958122 59814991 57656939 55931689 54641361 53469264 52223894 51709642
 [9] 51491801 50804445

Smallest eigenvalues:
 [1]  0.34432973  0.33329624  0.26655716  0.25276806  0.21523261  0.21465369
 [7]  0.16558935  0.09561748 -0.20705440 -0.78292764

Largest  eigenvalues:
 [1] 62475151 60265280 57299132 55650530 55076418 53513444 52320094 52193170
 [9] 51463215 50825775

Smallest eigenvalues:
 [1]  0.22849935  0.18694592  0.18098389  0.16741839  0.07950545  0.06576836
 [7] -0.09110808 -0.30732187 -1.42761057 -1.49394263

Largest  eigenvalues:
 [1] 63628570 59499789 56996636 54843240 54713184 53246776 51625543 51142830
 [9] 51003266 50462528

Smallest eigenvalues:
 [1]  0.35787283  0.35011015  0.24563930  0.20501641  0.17293359  0.10539791
 [7]  0.02451984 -0.04600245 -0.27117584 -3.61089959

Largest  eigenvalues:
 [1] 64993769 59728540 56948551 56312540 54900219 53180784 52474433 52270809
 [9] 51783391 51276052

Smallest eigenvalues:
 [1]  0.31604271  0.19673866  0.15549241  0.13863547 -0.02487789 -0.06897950
 [7] -0.08343397 -0.21110623 -1.12848267 -2.62019299

Largest  eigenvalues:
 [1] 65900523 59804408 57078015 56628833 54590583 53078528 52673395 52198791
 [9] 51430489 51405360

Smallest eigenvalues:
 [1]  0.45523176  0.35999222  0.22123303  0.19836564  0.16940852  0.15057724
 [7]  0.12738629 -0.06692745 -0.36537776 -1.64320673

Largest  eigenvalues:
 [1] 63838185 59446151 56371291 55103399 54663391 52965884 51742312 51303359
 [9] 51148867 50390962

Smallest eigenvalues:
 [1]  0.39787487  0.35098284  0.25080461  0.21356840  0.06106247  0.02017161
 [7]  0.00824589 -0.05994448 -0.06769519 -0.61758956

Largest  eigenvalues:
 [1] 63377372 59462491 56783258 54808869 54550405 53042371 51706114 51281312
 [9] 51090453 50666183

Smallest eigenvalues:
 [1]  0.48339463  0.40487813  0.39380319  0.37767780  0.31110870  0.29576419
 [7]  0.28300147 -0.04288057 -0.04937407 -2.30489085

Largest  eigenvalues:
 [1] 64330203 60638336 57010518 55710863 55589969 53647643 52214285 52008904
 [9] 51837158 51149013

Smallest eigenvalues:
 [1]  0.255264366  0.254990769  0.217688954  0.035840286  0.004374647
 [6] -0.135924345 -0.439217037 -0.712485014 -1.004096669 -1.462425588

Largest  eigenvalues:
 [1] 65916877 59557708 56872477 56268542 54426004 53022054 52329167 51769053
 [9] 51385268 50961594

Smallest eigenvalues:
 [1]  0.31873412  0.31250610  0.21958598  0.19047078  0.12456352  0.04217012
 [7] -0.31752076 -0.84956313 -1.54931113 -1.85553762

Largest  eigenvalues:
 [1] 66480855 60451398 58477588 56962582 55166767 53218412 52907259 52235169
 [9] 51819266 51494708

Smallest eigenvalues:
 [1]  0.398368541  0.375293894  0.353760776  0.348714132  0.324237684
 [6]  0.297573747  0.259491607  0.190384594  0.188742215 -0.007200348

Largest  eigenvalues:
 [1] 64560412 60759659 58180807 55842189 55725554 54407633 52470706 52086613
 [9] 51948297 51214153

Smallest eigenvalues:
 [1]  0.09924339  0.09212016 -0.07674742 -0.11192897 -0.11770956 -0.30974467
 [7] -0.32442439 -0.41295500 -0.75624235 -1.25053246

Largest  eigenvalues:
 [1] 66174916 60425722 58000364 57270357 54879815 53398413 53127546 52816238
 [9] 51907206 51546062

Smallest eigenvalues:
 [1]  0.39169404  0.35807565  0.34137348  0.30946762  0.30397442  0.20935081
 [7]  0.10948453 -0.08906589 -0.16411154 -1.18168583

Largest  eigenvalues:
 [1] 63649704 60295657 57417707 56285869 55031440 53359681 52534598 52075870
 [9] 51845050 51345187

Smallest eigenvalues:
 [1]  0.49899881  0.44947993  0.44740584  0.41504017  0.32800306  0.28183749
 [7]  0.23949415  0.20376783  0.06009082 -0.05709857

Largest  eigenvalues:
 [1] 66277567 60079407 57790439 57107823 54888753 53599572 53206689 51950193
 [9] 51774331 51002716

Smallest eigenvalues:
 [1]  0.38366071  0.34406182  0.32912277  0.28789686  0.27037455  0.21597467
 [7]  0.19302749  0.06957620 -0.01169218 -0.39114228

Largest  eigenvalues:
 [1] 64975846 60161970 57064134 56596868 54936164 53341354 52572077 52522065
 [9] 52017910 51569705

Smallest eigenvalues:
 [1]  0.20658819  0.20612932  0.16018438  0.13353185 -0.08180843 -0.25074857
 [7] -0.49105292 -1.44979331 -1.64269705 -1.80304536

Largest  eigenvalues:
 [1] 65304738 60312398 57707210 56519668 54775305 53442200 52649438 52170833
 [9] 51628495 51359821

Smallest eigenvalues:
 [1]  0.5460028  0.5302948  0.5084107  0.4437580  0.3605250  0.3539121
 [7]  0.1820593  0.1637137  0.1177607 -0.2146693

Largest  eigenvalues:
 [1] 64230436 59313733 56643170 55582984 54401178 52349863 51640310 51166093
 [9] 51136973 50298500

Smallest eigenvalues:
 [1]  0.54698461  0.50663764  0.44033516  0.41707953  0.35626267  0.29646196
 [7]  0.26599981  0.04527109 -0.35341494 -4.01554427

Largest  eigenvalues:
 [1] 65509740 59852530 56857360 56455643 54578768 52577185 52279191 51489216
 [9] 51446201 50655796

Smallest eigenvalues:
 [1]  0.21512081  0.14906591  0.11011256 -0.02687004 -0.04432804 -0.11844368
 [7] -0.12821064 -0.75861408 -1.07331104 -1.88364080

Largest  eigenvalues:
 [1] 66346754 60430127 57394352 57201277 55015751 53289194 53142123 52837674
 [9] 51867902 51817783

Smallest eigenvalues:
 [1]  0.3710866  0.3508347  0.3330107  0.2301228  0.1937342  0.1514765
 [7]  0.1155636 -0.1839370 -0.3467024 -0.9801734

Largest  eigenvalues:
 [1] 64161091 59907824 56932779 55163755 54732640 53146760 51799713 51708517
 [9] 51315252 51075084

Smallest eigenvalues:
 [1]  0.40675491  0.39034868  0.37854384  0.31899379  0.24789933  0.21148566
 [7]  0.18662655  0.06834084  0.04751032 -1.39155705

Largest  eigenvalues:
 [1] 64636119 60346324 56880739 56056506 55420205 53660458 51922999 51808036
 [9] 51730717 50887629

Smallest eigenvalues:
 [1]  0.37560935  0.32417452  0.28600191  0.17181566  0.16361341  0.10896189
 [7]  0.07418611  0.04317457  0.01693225 -1.98185328

Largest  eigenvalues:
 [1] 64017903 60209294 57307816 55527122 55100499 53941130 52052588 51609549
 [9] 51137565 50816590

Smallest eigenvalues:
 [1]  0.23822468  0.15785225  0.07970109  0.03502709 -0.02867249 -0.03180909
 [7] -0.04859561 -0.14190216 -0.35951790 -0.80680108

Largest  eigenvalues:
 [1] 66185362 60797860 58203730 56379951 55293550 53795333 52608526 52301710
 [9] 51941995 51468308

Smallest eigenvalues:
 [1]  0.45419461  0.44368857  0.43370536  0.34804360  0.27836663  0.25406331
 [7]  0.05162261  0.03380550 -0.05274366 -2.24685353

Largest  eigenvalues:
 [1] 65335127 60115805 57124621 56485791 55228878 53740399 52397571 52154837
 [9] 51986445 51282511

Smallest eigenvalues:
 [1]  0.48826024  0.44528091  0.39528801  0.37821865  0.37242237  0.31592848
 [7]  0.29375195  0.18116860  0.12910893 -0.07278919

Largest  eigenvalues:
 [1] 64465138 59851261 56568612 55876383 54725508 53134958 51928974 51899398
 [9] 51459432 50812873

Smallest eigenvalues:
 [1]  0.34388338  0.31470295  0.28232951  0.22163303  0.21047650 -0.05258964
 [7] -0.09257466 -0.17995696 -0.55886801 -2.94081634

Largest  eigenvalues:
 [1] 65528265 60800537 57441141 55909013 55398441 53481114 52024662 51925550
 [9] 51660791 51175536

Smallest eigenvalues:
 [1]  0.42191337  0.40200855  0.38913334  0.34370348  0.31553045  0.31497820
 [7]  0.27415048  0.25952143  0.22060993 -0.07022526

Largest  eigenvalues:
 [1] 64195125 60152331 57304196 55463690 55434272 53799107 51926986 51583696
 [9] 51343087 50445553

Smallest eigenvalues:
 [1]  0.4103166  0.3596281  0.3257396  0.2889494  0.2519206  0.1794170
 [7]  0.1181834 -0.0274441 -0.1130602 -0.1458673

Largest  eigenvalues:
 [1] 65764229 60379872 57456948 56463180 55395999 53968774 52502043 52023538
 [9] 51853948 50636427

Smallest eigenvalues:
 [1]  0.30003658  0.27514071  0.17844680  0.15536466  0.12801314  0.11383686
 [7]  0.03036235 -0.76134313 -1.02306789 -1.02501568

Largest  eigenvalues:
 [1] 65345324 59863669 57682632 55964107 55052907 53777348 52565652 52048010
 [9] 52036139 51682016

Smallest eigenvalues:
 [1]  0.47415951  0.37584902  0.36955926  0.36509014  0.34253408  0.28984457
 [7]  0.26700710  0.23295508  0.17400323 -0.03047848

Largest  eigenvalues:
 [1] 65451957 60215216 57924912 56724194 54828496 53211681 52742956 52001688
 [9] 51813755 51223775

Smallest eigenvalues:
 [1]  0.142281911  0.101247008  0.058590347 -0.001330423 -0.018051874
 [6] -0.165937088 -0.235156334 -0.324502851 -0.873190654 -1.518822952

Largest  eigenvalues:
 [1] 63612917 60497610 57801040 55150393 54997608 53777524 51966738 51895853
 [9] 51181740 50962162

Smallest eigenvalues:
 [1]  0.44430905  0.42370743  0.39945639  0.38466041  0.31193506  0.28184779
 [7]  0.26945890  0.19909868  0.08485923 -0.02049831

Largest  eigenvalues:
 [1] 65151204 60334609 58049947 55760301 55419529 53694643 52455348 52100206
 [9] 51983032 51506661

Smallest eigenvalues:
 [1]  0.35826086  0.24687905  0.24497400  0.18758641  0.13949461  0.04921253
 [7]  0.02583006 -0.04954255 -0.18359965 -0.53091826

Largest  eigenvalues:
 [1] 66211298 60601066 57991016 56631218 55032931 53636523 52696588 52642256
 [9] 51961725 51793681

Smallest eigenvalues:
 [1]  0.36911374  0.36687346  0.35853611  0.27108959  0.23069233  0.16791281
 [7]  0.16721935  0.10432921  0.02927506 -0.42260927

Largest  eigenvalues:
 [1] 66573956 61037979 57893578 57292566 56070603 54380361 53325296 53235505
 [9] 52422433 52016380

Smallest eigenvalues:
 [1]  0.4190735  0.4070922  0.3405512  0.3072790  0.2964792  0.2503843
 [7]  0.1807682  0.1407221  0.1123483 -0.6553671

Largest  eigenvalues:
 [1] 65495821 59565246 57296642 56802713 54631670 53355384 52744751 51886134
 [9] 51510542 51004241

Smallest eigenvalues:
 [1]  0.56463874  0.48159187  0.47784485  0.41365549  0.37551443  0.26991481
 [7]  0.25479935  0.22357007 -0.07050388 -3.82438333

Largest  eigenvalues:
 [1] 64843447 60121967 57418202 56099220 55146568 53460555 52210715 51970094
 [9] 51943783 50976876

Smallest eigenvalues:
 [1]  0.45303443  0.44804797  0.41963693  0.39024844  0.34455935  0.25551341
 [7]  0.24148828  0.09942670  0.06185218 -3.53302476

Largest  eigenvalues:
 [1] 63805044 60644696 57912325 56030931 55706527 54414673 52713698 52670737
 [9] 51886899 51591819

Smallest eigenvalues:
 [1]  0.4578711  0.3773066  0.3653459  0.3542151  0.3523558  0.3166131
 [7]  0.2718408  0.2593948  0.1147047 -0.4169546

Largest  eigenvalues:
 [1] 64253743 60372200 57746910 55665604 55563209 54205803 52588849 52325706
 [9] 51650457 51142665

Smallest eigenvalues:
 [1]  0.44713283  0.42137137  0.38632405  0.29865266  0.20458295  0.18679541
 [7]  0.09734140  0.05745541  0.01992097 -1.39667907

Largest  eigenvalues:
 [1] 63035420 60100239 56982329 55403538 54676248 53660700 51811384 51729271
 [9] 50947612 50846655

Smallest eigenvalues:
 [1]  0.51203841  0.46721205  0.43036363  0.38347410  0.36912243  0.35571560
 [7]  0.34827207  0.14763799  0.10701455 -0.06605479

Largest  eigenvalues:
 [1] 65203605 61313877 57696881 56611895 56318921 54595251 53459840 52595437
 [9] 52313518 51842000

Smallest eigenvalues:
 [1]  0.44892974  0.42565504  0.38195828  0.37610479  0.33296835  0.28640749
 [7]  0.26135775 -0.03768478 -0.18366181 -0.77853612

Largest  eigenvalues:
 [1] 64156328 60460528 57654175 56136977 55415842 53872704 52373780 52179905
 [9] 51819921 51193054

Smallest eigenvalues:
 [1]   0.31731585   0.21097395   0.20436093   0.18989051   0.12797501
 [6]   0.08474374   0.02840311  -0.22049051  -0.29987531 -22.45608441

Largest  eigenvalues:
 [1] 65886530 59829752 57773321 56119051 54976959 53811668 52505007 52310217
 [9] 52004167 51444084

Smallest eigenvalues:
 [1]  0.4421756  0.4001940  0.3461679  0.2436915  0.2121544  0.1651616
 [7]  0.1135466 -0.2049093 -0.2953542 -0.7346995

Largest  eigenvalues:
 [1] 65775083 60449279 57675268 56924751 54877346 52924646 52865527 52450857
 [9] 51750396 51548305

Smallest eigenvalues:
 [1]  0.5660133  0.5591972  0.4488088  0.4276763  0.3074990  0.2735265
 [7]  0.2437631  0.2436161 -0.2092905 -0.2403396

Largest  eigenvalues:
 [1] 65518084 60770237 57694984 56663045 55505105 53769933 52798593 52618856
 [9] 51982966 51418190

Smallest eigenvalues:
 [1]  0.39201828  0.36607785  0.35204663  0.32680014  0.28956974  0.22437456
 [7]  0.14268699  0.12509449  0.03413339 -2.99073803

Largest  eigenvalues:
 [1] 63731433 59913220 57537649 55585139 54967054 53503923 51893813 51760078
 [9] 51578795 50913673

Smallest eigenvalues:
 [1]  0.34244869  0.24713111  0.22917031  0.21855827  0.12267815  0.02799559
 [7] -0.09435156 -0.25574024 -0.63660542 -1.31597273

Largest  eigenvalues:
 [1] 65188942 60609757 57885515 56226885 55318100 53900123 52354358 52096839
 [9] 51809490 51127977

Smallest eigenvalues:
 [1]  0.41227613  0.40870052  0.33616820  0.33362906  0.28079421  0.23104931
 [7]  0.19895556  0.12086652  0.05272953 -0.39137290

Largest  eigenvalues:
 [1] 65176525 60286508 57729669 56397156 55140153 53515113 53259637 52595000
 [9] 51885942 51641438

Smallest eigenvalues:
 [1]  0.5008149  0.4216607  0.3996957  0.3841024  0.3261405  0.3150002
 [7]  0.2412383  0.2055896 -0.1503619 -0.1628951

Largest  eigenvalues:
 [1] 64503744 60436940 57293888 55935278 55144083 53420476 51923137 51838316
 [9] 51810506 50910026

Smallest eigenvalues:
 [1]  0.6144951  0.5285018  0.5217817  0.5196151  0.4470148  0.3437827
 [7]  0.2999062  0.2523786  0.2484838 -0.6737067

Largest  eigenvalues:
 [1] 64546214 59863211 57068038 55710816 55048166 53609544 52170113 51846223
 [9] 51643171 50809190

Smallest eigenvalues:
 [1]  0.37222354  0.37165058  0.31668573  0.28685235  0.27794986  0.18920346
 [7]  0.18072816  0.17747899  0.13493871 -0.06034644

Largest  eigenvalues:
 [1] 65832347 60698452 58366800 56387753 55512010 53945062 52598967 52453114
 [9] 52357428 51818851

Smallest eigenvalues:
 [1]  0.35770525  0.33293579  0.32768492  0.30300358  0.25719724  0.20680826
 [7]  0.19959926  0.09582846 -0.49196518 -3.15240362

Largest  eigenvalues:
 [1] 65449561 59860469 57142189 56774543 54882509 52878486 52661818 52447356
 [9] 51871090 51498949

Smallest eigenvalues:
 [1]  0.4517968  0.4144365  0.3300266  0.3087105  0.2581300  0.2437867
 [7]  0.2334273  0.1675006  0.1075077 -0.5933252

Largest  eigenvalues:
 [1] 61990273 59495261 56169635 54830368 54810776 53084656 51980907 51963983
 [9] 50881904 50687090

Smallest eigenvalues:
 [1]  0.3506319230  0.2758619363  0.2657261017  0.2395028654  0.1649213441
 [6]  0.0811668969  0.0003459881 -0.1449473441 -0.5231058413 -0.8660665085

Largest  eigenvalues:
 [1] 65291053 61470136 58265204 57253097 55376675 53682057 53391601 52686558
 [9] 52297482 51450792

Smallest eigenvalues:
 [1]  0.4793136  0.4583449  0.4146647  0.3706613  0.3250721  0.2587679
 [7]  0.2264628  0.1974565  0.1659534 -0.5557488

Largest  eigenvalues:
 [1] 62927075 59428130 56917992 54832712 54746405 53274805 51958205 51216053
 [9] 50862840 50480673

Smallest eigenvalues:
 [1]  0.2412614  0.2390749  0.1992416  0.1908809  0.1331087  0.0116919
 [7] -0.1018362 -0.2505629 -0.3093319 -1.0932292

Largest  eigenvalues:
 [1] 64095374 59974165 57551797 55743796 54854443 53577597 51806523 51776650
 [9] 51717979 50834386

Smallest eigenvalues:
 [1]  0.41544694  0.37910818  0.23492621  0.07291494  0.07267453  0.04956870
 [7] -0.05042230 -0.06958034 -0.30108024 -2.05870162

Largest  eigenvalues:
 [1] 63849817 60299918 57457323 55643758 55519229 53803956 52656806 51852855
 [9] 51754879 51311383

Smallest eigenvalues:
 [1]  0.2246526516  0.1942011844  0.1937623025  0.1659102309  0.1623246554
 [6]  0.1610865035  0.0879658289 -0.0009876474 -0.2353104174 -0.3403656520

Largest  eigenvalues:
 [1] 63603903 59327103 56393229 55541008 54790499 53096645 51785774 51502903
 [9] 50837448 50204772

Smallest eigenvalues:
 [1]  0.50770215  0.39444190  0.37925689  0.37911256  0.33363794  0.29753137
 [7]  0.20674451  0.17236082 -0.08702109 -0.34161654

Largest  eigenvalues:
 [1] 64556946 60777383 57801352 55956468 55380047 53784533 52804492 52188723
 [9] 52119033 51895624

Smallest eigenvalues:
 [1]  0.3858945  0.3357381  0.3322148  0.2991350  0.2648856  0.2166075
 [7]  0.2097733  0.1959674 -0.1248980 -1.5621686

Largest  eigenvalues:
 [1] 64988000 60744097 58054952 55793758 55714057 54257483 52254240 52026348
 [9] 51952737 51354732

Smallest eigenvalues:
 [1]  0.22561415  0.16207596  0.15719959  0.07536898  0.03632150 -0.06279389
 [7] -0.35865122 -0.37470584 -1.38351044 -1.73710540

Largest  eigenvalues:
 [1] 64611910 59590608 56910221 55998848 54675695 53070642 52256865 52004935
 [9] 51630179 51039778

Smallest eigenvalues:
 [1]  0.44767823  0.40929841  0.31800547  0.29323309  0.24793446  0.23712671
 [7]  0.17928678  0.16993373 -0.04305723 -1.19057602

Largest  eigenvalues:
 [1] 64459967 60581001 57233205 56274291 55618530 53983003 52254222 52103640
 [9] 51949071 51065380

Smallest eigenvalues:
 [1]  0.29175891  0.23391803  0.17408246  0.15674499  0.13489617  0.03069871
 [7] -0.08542268 -0.29960155 -0.49240463 -1.15718716

Largest  eigenvalues:
 [1] 65011155 60446753 57391949 56561354 54868283 53567535 52497609 52424645
 [9] 51804319 51659271

Smallest eigenvalues:
 [1]  0.28625032  0.23514710  0.20044846  0.12233990  0.07800716 -0.17761160
 [7] -0.25776908 -0.35657178 -0.52667098 -1.41482632

Largest  eigenvalues:
 [1] 64139926 59265630 57053193 55480737 54299754 53206194 51861387 51672562
 [9] 51475812 50955437

Smallest eigenvalues:
 [1]  0.22936969  0.21020719  0.17412006  0.16857077  0.14773110 -0.04124600
 [7] -0.04524443 -0.13908801 -0.19386815 -1.60214300

Largest  eigenvalues:
 [1] 64827179 60849185 57772424 56091366 55686590 54345296 52699600 52619501
 [9] 52033152 51844209

Smallest eigenvalues:
 [1]   0.412687187   0.378728427   0.329309738   0.315846639   0.309482282
 [6]   0.260399031   0.258287998   0.004449181  -0.127375454 -10.241339447

Largest  eigenvalues:
 [1] 64424604 59948334 57293836 55663979 55086637 53523884 52232847 51767244
 [9] 51558272 50970216

Smallest eigenvalues:
 [1]  0.36599217  0.35035789  0.33298055  0.24896675  0.20065789  0.16959265
 [7]  0.13564926  0.13228616  0.07244268 -0.05980429

Largest  eigenvalues:
 [1] 62703934 60077912 57137338 55468784 55142718 53363255 52450982 52300059
 [9] 51319769 51097271

Smallest eigenvalues:
 [1]  0.3801999  0.3482936  0.2911245  0.2376649  0.2114886  0.2042119
 [7]  0.1396087 -0.1238492 -0.3356010 -1.5960486

Largest  eigenvalues:
 [1] 65509902 60152591 57115971 56687346 55225618 53671732 52595198 52389513
 [9] 52049240 51614870

Smallest eigenvalues:
 [1]  0.40036700  0.34391822  0.33329054  0.27999331  0.18251816  0.15645880
 [7]  0.04867742 -0.37491944 -0.43668209 -5.08273853

Largest  eigenvalues:
 [1] 65539086 60222540 57388358 56269213 55131641 53232074 52490064 52041479
 [9] 51631253 51249262

Smallest eigenvalues:
 [1]  0.1954337  0.1900241  0.1856947 -0.1009354 -0.1317049 -0.2657994
 [7] -0.3685551 -0.3867340 -0.4988534 -1.0059088

Largest  eigenvalues:
 [1] 65078229 61302853 57667033 56408164 56335387 54364814 53902332 52580335
 [9] 52210065 51853661

Smallest eigenvalues:
 [1]  0.4477225  0.3848476  0.3436877  0.3162659  0.2796636  0.2688860
 [7]  0.2687305  0.1863084 -0.1544271 -0.4701790

Largest  eigenvalues:
 [1] 64188783 60775878 58101977 56181014 55269762 53746974 52018781 51951917
 [9] 51867480 50942808

Smallest eigenvalues:
 [1]  0.29422165  0.19777063  0.10466091  0.09802734  0.08529111 -0.01484967
 [7] -0.03153301 -0.07522498 -0.08202590 -2.15647362

Largest  eigenvalues:
 [1] 65018490 59874004 57597808 56494080 55166656 53943434 52963395 52339654
 [9] 52293857 51909023

Smallest eigenvalues:
 [1]  0.4571294  0.4331764  0.3556075  0.3295324  0.3015585  0.2531303
 [7]  0.1890027 -0.0762550 -0.2423593 -2.0077737

Largest  eigenvalues:
 [1] 65594600 59761014 56750503 56303172 54397133 52641892 52325120 51402736
 [9] 51157988 50646589

Smallest eigenvalues:
 [1]  0.4646382  0.4500035  0.4326764  0.3553120  0.3421914  0.2759485
 [7]  0.2269887  0.1665191  0.1383409 -0.3495080

Largest  eigenvalues:
 [1] 64765642 59847766 57466185 55416579 55326091 53851506 51752952 51621365
 [9] 51513030 50756216

Smallest eigenvalues:
 [1]  0.54077236  0.45580438  0.39245221  0.36618302  0.32701812  0.25522995
 [7]  0.17374478  0.09220614  0.02697602 -0.18929149

Largest  eigenvalues:
 [1] 64297809 60192559 57326812 55886898 55741257 54169291 52391068 52339491
 [9] 51817913 51719604

Smallest eigenvalues:
 [1]   0.28795199   0.27277850   0.20074329   0.18314525   0.07810581
 [6]   0.07390435  -0.14078310  -0.23773276  -0.81091645 -19.99259512

Largest  eigenvalues:
 [1] 63386915 60157856 57630136 55396973 55059110 53740049 52612356 51764476
 [9] 51217132 50971375

Smallest eigenvalues:
 [1]  0.44495994  0.43756862  0.40479803  0.36700433  0.29030394  0.28358212
 [7]  0.20101780  0.16501665  0.06417002 -0.60855837

Largest  eigenvalues:
 [1] 65777865 59744112 57271941 56758633 54656306 53142956 52658067 52156304
 [9] 51650234 51153478

Smallest eigenvalues:
 [1]  0.5600320259  0.5197066362  0.4716906350  0.4274944451  0.3802579594
 [6]  0.3145297440  0.1539205452  0.0993539107  0.0449715190 -0.0008183772

Largest  eigenvalues:
 [1] 64622130 60260555 57568973 55499532 55270147 53859864 52528099 52187523
 [9] 51608209 51386552

Smallest eigenvalues:
 [1]  0.38680342  0.38043602  0.29153600  0.24563297  0.23429306  0.18889191
 [7]  0.01685479 -0.06894029 -0.25638247 -0.99896044

Largest  eigenvalues:
 [1] 64469025 59751953 56836436 56087082 54973882 53396839 52174809 52118878
 [9] 51635719 51052704

Smallest eigenvalues:
 [1]  0.46791424  0.42696534  0.40733922  0.29847974  0.27113267  0.26420213
 [7]  0.22380461  0.19868696  0.03986304 -1.18350445

Largest  eigenvalues:
 [1] 63467451 59614210 57326320 55294604 54774928 53569594 52225269 51868355
 [9] 51462107 51049675

Smallest eigenvalues:
 [1]  0.43702356  0.42604157  0.39079303  0.34412615  0.33467068  0.30929347
 [7]  0.21153955  0.05084477 -0.07964505 -0.36445304

Largest  eigenvalues:
 [1] 62826830 59678675 57072272 55577700 54873055 53217787 51617413 51517158
 [9] 51454822 50419893

Smallest eigenvalues:
 [1]  0.48176879  0.47590168  0.45135691  0.35256321  0.29979562  0.24374336
 [7]  0.18477920  0.15047625  0.04436969 -0.31178165

Largest  eigenvalues:
 [1] 64051732 60470592 57314570 55920693 55677193 53961064 52688454 52333781
 [9] 52084407 51491467

Smallest eigenvalues:
 [1]  0.5016051  0.4968539  0.4371616  0.3619396  0.2849206  0.2823763
 [7]  0.2764347  0.2168504 -0.4795734 -0.9207457

Largest  eigenvalues:
 [1] 63668237 59487438 56679394 55383196 54760833 52965982 52505702 51419262
 [9] 51258260 50827519

Smallest eigenvalues:
 [1]  0.41912095  0.41569188  0.38103989  0.35351037  0.32666803  0.15140703
 [7]  0.10824039  0.04329408  0.01489731 -0.63925734

Largest  eigenvalues:
 [1] 65886826 59762903 57373163 56081924 54784273 53253947 52266660 51992319
 [9] 51872940 50786459

Smallest eigenvalues:
 [1]  0.43595765  0.39682051  0.39075055  0.33381001  0.29843423  0.27807291
 [7]  0.08690499  0.06523444 -0.02987169 -0.15160563

Largest  eigenvalues:
 [1] 64742431 59808026 57082245 55931053 55223080 53601270 51979427 51713581
 [9] 51200746 50160068

Smallest eigenvalues:
 [1]  0.40488521  0.33661461  0.31488626  0.30953580  0.20523401  0.19087398
 [7]  0.12114293 -0.04880466 -0.21783977 -1.20261650

Largest  eigenvalues:
 [1] 63223035 60261246 57197895 55536047 54634545 53602041 51867519 51650129
 [9] 51020678 50782355

Smallest eigenvalues:
 [1]  0.4849433275  0.4841665497  0.3777428439  0.3416971499  0.2464414420
 [6]  0.1714379744  0.1662778665  0.1268239945  0.0005470483 -0.7292119221

Largest  eigenvalues:
 [1] 62227487 59472121 56301950 54810892 54627139 52990412 51981668 51350084
 [9] 50758495 50592550

Smallest eigenvalues:
 [1]  0.56944125  0.56092355  0.53088372  0.38999585  0.37768531  0.33125085
 [7]  0.14577636  0.07204877 -0.01303944 -0.08134181

Largest  eigenvalues:
 [1] 65509212 59707801 56930931 56801415 54693907 52846224 52825664 51613132
 [9] 51241242 50563950

Smallest eigenvalues:
 [1]  0.45139495  0.33014890  0.32141809  0.24491037  0.20517283  0.06123890
 [7]  0.05308619 -0.11056516 -0.41556868 -1.78319977

Largest  eigenvalues:
 [1] 65090916 61286284 57576899 57017512 56036583 54061194 53642363 52598580
 [9] 52562384 52037266

Smallest eigenvalues:
 [1]  0.37826796  0.26562021  0.22840776  0.21147742  0.10750055  0.08870933
 [7] -0.07661383 -0.57303159 -0.72562523 -1.43752797

Largest  eigenvalues:
 [1] 66099606 59632397 56959965 56639559 54271809 52790293 52774600 51948815
 [9] 51194509 51138006

Smallest eigenvalues:
 [1]  0.49795328  0.48946833  0.37090172  0.34569614  0.34364666  0.24733095
 [7]  0.23063347  0.03688379 -0.06018632 -0.07092340

Largest  eigenvalues:
 [1] 64304716 59211940 56646151 55378824 54553727 52950678 51749212 51337080
 [9] 51010538 50350073

Smallest eigenvalues:
 [1]  0.57828218  0.43946131  0.43929519  0.43191753  0.32229192  0.26328218
 [7]  0.25870389  0.15465279 -0.01163865 -0.17573346

Largest  eigenvalues:
 [1] 63856256 59434670 56599109 55565201 54294527 52741153 51592902 51416187
 [9] 50854223 49980333

Smallest eigenvalues:
 [1]  0.32262618  0.28155888  0.26583075  0.25263305  0.18970866  0.18448297
 [7]  0.14260862  0.06096392  0.02455327 -0.61564965

Largest  eigenvalues:
 [1] 65520186 60717282 58313241 56814197 55276033 54077777 52758127 52422198
 [9] 52209834 51323013

Smallest eigenvalues:
 [1]  0.26260530  0.21686847  0.19140481  0.18325633  0.15980163  0.06528655
 [7]  0.03317500 -0.01989466 -0.02473640 -1.32647737

Largest  eigenvalues:
 [1] 65137609 59739526 56861443 55352361 54609599 53063802 51844055 51464858
 [9] 51354641 50984481

Smallest eigenvalues:
 [1]  0.49605156  0.47801544  0.38649387  0.32656970  0.29630198  0.29523228
 [7]  0.27247007  0.23548578 -0.01054134 -4.59470119

Largest  eigenvalues:
 [1] 65458625 60933445 58171282 56502806 55889848 54203623 52785493 52380574
 [9] 52298581 51335343

Smallest eigenvalues:
 [1]  0.46684321  0.36387549  0.27705717  0.25738809  0.18158818  0.17546580
 [7]  0.11212597  0.09262325 -0.04820603 -2.14074394

Largest  eigenvalues:
 [1] 64472340 59723600 56643172 55327342 54632084 53111796 51594997 51417633
 [9] 51103578 50351645

Smallest eigenvalues:
 [1]  0.12619207  0.11150809 -0.02642782 -0.11883213 -0.20232777 -0.26620876
 [7] -0.29929589 -0.33377198 -0.40606544 -2.12884828

Largest  eigenvalues:
 [1] 65215394 60451497 57823944 55590231 55242169 53697723 52268919 51749697
 [9] 51616911 51551837

Smallest eigenvalues:
 [1]  0.5134272  0.4424175  0.4241758  0.4106739  0.2890797  0.2725983
 [7]  0.2428147  0.1979289  0.1501808 -0.3316823

Largest  eigenvalues:
 [1] 65618110 60382275 57637651 56388302 54993976 53577224 52547187 51891132
 [9] 51701511 51075420

Smallest eigenvalues:
 [1]  0.59023219  0.58918366  0.47027725  0.45783010  0.32727309  0.31447231
 [7]  0.26417584  0.23580021  0.09613169 -0.19109745

Largest  eigenvalues:
 [1] 66106226 60462707 57873612 56510852 55256661 53910668 52629003 52425409
 [9] 51906728 51459859

Smallest eigenvalues:
 [1]  0.45392489  0.37648662  0.36913566  0.34349880  0.27966157  0.22471334
 [7]  0.19231751  0.15185063 -0.04310512 -0.54915024

Largest  eigenvalues:
 [1] 65138793 60799831 58083511 56522591 55289786 54000798 52439949 52299768
 [9] 52066025 51152576

Smallest eigenvalues:
 [1]  0.4809745  0.4590980  0.4387196  0.3687736  0.3483114  0.3247535
 [7]  0.2592652  0.2098659  0.1649771 -0.2093161

Largest  eigenvalues:
 [1] 64917145 59591691 56585076 56403815 54415806 52955504 52227002 51755799
 [9] 51457858 50476682

Smallest eigenvalues:
 [1]  0.5524188  0.5253289  0.5077754  0.4161437  0.3520868  0.3513292
 [7]  0.2103284  0.2087082  0.1859932 -0.1284037

Largest  eigenvalues:
 [1] 63837922 60245945 57035962 55380949 55326319 53792924 52322533 52050087
 [9] 51476482 51299291

Smallest eigenvalues:
 [1]  0.34254222  0.33927761  0.31655651  0.28933653  0.25041960  0.14760181
 [7]  0.14038325  0.10272106  0.09726858 -0.04434161

Largest  eigenvalues:
 [1] 62043686 60363468 57442009 55964839 55030812 54198462 52667039 52376837
 [9] 51524088 51024495

Smallest eigenvalues:
 [1]  0.5968017  0.5715338  0.5118664  0.4725151  0.4217953  0.4008595
 [7]  0.3050661  0.2051502  0.1252929 -0.6374712

Largest  eigenvalues:
 [1] 64160435 60688682 57059963 55706722 55619054 54010276 52354304 52204999
 [9] 51551473 51087770

Smallest eigenvalues:
 [1]  0.43921422  0.42016738  0.35638344  0.30966081  0.26502777  0.24474031
 [7]  0.18751967  0.10361093  0.09089492 -0.24473658

Largest  eigenvalues:
 [1] 65926783 60097564 57534009 57235572 54874892 53467654 53210909 52079431
 [9] 52018865 51148221

Smallest eigenvalues:
 [1]  0.4080132  0.3844416  0.3041990  0.2304309  0.1596702  0.1284254
 [7]  0.1103804 -0.1029656 -0.4918004 -6.7413261

Largest  eigenvalues:
 [1] 65643124 60330007 57714685 56891546 55069589 53498821 52869298 52499837
 [9] 52343252 51841262

Smallest eigenvalues:
 [1]  0.41389349  0.40761232  0.40226160  0.31894818  0.22299817  0.21388907
 [7]  0.16096874  0.03526162 -0.25323135 -0.37868853

Largest  eigenvalues:
 [1] 63486960 60336516 56992318 55336170 54965194 53270669 52033524 51574922
 [9] 51378816 51136791

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	7.557765	0.6677545	15.21572	0.375	2.885361	1.556578

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

HR ~ alt + n + speed + PM25

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- HR_fd
covariates <- list(altitude = altitude_fd, 
                   noise = noise_fd,
                   speed = speed_fd,
                   pollution = pollution25_fd)
path_plot <- 'figures/model_HR_alt_noise_speed_PM25_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     noise = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     speed = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     pollution = list(nbetabasis = 80, norder = 4, lambda = 1e3))

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, 
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 23.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Warning message in `^.fd`((outcome - yhatfd), 2):
"The maximum error exceeds the tolerance level."
Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 690 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Smallest eigenvalues:
 [1]  0.55555842  0.52728829  0.48163769  0.38049995  0.33141926  0.29894736
 [7]  0.15965511  0.14236862 -0.04375265 -0.09781512

Largest  eigenvalues:
 [1] 77852605 72468147 69543549 68101339 66340210 64604095 63247805 62692695
 [9] 62497944 61172405

Smallest eigenvalues:
 [1]  0.5495996  0.5415181  0.4532786  0.4462895  0.4052362  0.3679991
 [7]  0.3150882  0.2862877  0.2657705 -1.0512943

Largest  eigenvalues:
 [1] 76791680 73355541 69298167 67145218 67094572 65290569 62731881 62659850
 [9] 62210397 61176086

Smallest eigenvalues:
 [1]  0.5287191  0.4501140  0.4010844  0.3486700  0.3344508  0.2989247
 [7]  0.2611175  0.1993226  0.1569827 -0.2345939

Largest  eigenvalues:
 [1] 78487818 72662850 69727729 68466144 66817225 64840737 63957329 63618776
 [9] 62883583 62484279

Smallest eigenvalues:
 [1]  0.37290417  0.33637153  0.33445878  0.30001438  0.26563984  0.21833416
 [7]  0.14231247  0.03603118 -0.31116181 -2.34291591

Largest  eigenvalues:
 [1] 77177249 73888194 69789260 67689470 67261042 65988562 63684124 63346254
 [9] 62368724 62251599

Smallest eigenvalues:
 [1]  0.50705809  0.47539858  0.46162774  0.36896469  0.36028970  0.25692534
 [7]  0.15870346  0.15055635 -0.09623954 -0.81247184

Largest  eigenvalues:
 [1] 79298236 73628230 69295200 68914308 67151106 64899163 63840280 63447333
 [9] 63160977 62179685

Smallest eigenvalues:
 [1]  0.39101450  0.32199371  0.28225693  0.16372635  0.14477794  0.11132128
 [7]  0.04426752 -0.22348952 -0.26570912 -1.63083493

Largest  eigenvalues:
 [1] 75485883 71611387 68181468 66444781 66052529 64357156 62739515 61672432
 [9] 61300782 60822809

Smallest eigenvalues:
 [1]  0.5855252  0.5518508  0.4540662  0.4431510  0.4140982  0.3866626
 [7]  0.3376545  0.2628605  0.2476326 -0.9894454

Largest  eigenvalues:
 [1] 77293387 72188881 68415783 67610783 65719518 63658321 62638646 62461536
 [9] 61816972 60770744

Smallest eigenvalues:
 [1]  0.5799460  0.5603298  0.5003988  0.4458324  0.4356506  0.4286793
 [7]  0.4080188  0.3490708  0.1878189 -3.5536556

Largest  eigenvalues:
 [1] 75988914 72913043 68994841 67156631 66138065 64785145 62214828 61963332
 [9] 61562863 60875733

Smallest eigenvalues:
 [1]  0.69883501  0.61440128  0.59767830  0.49739299  0.49347247  0.36916433
 [7]  0.30936676  0.28456154  0.08151468 -2.47153780

Largest  eigenvalues:
 [1] 78015835 73849266 69612006 67790544 67127512 65036639 62908451 62852151
 [9] 62704195 61519853

Smallest eigenvalues:
 [1]  0.5490136  0.5397547  0.4695575  0.4457312  0.3864518  0.3399353
 [7]  0.3348434  0.2520170  0.1731115 -0.2825974

Largest  eigenvalues:
 [1] 77069210 73391676 69401683 67693519 66707140 64851361 63589978 62831081
 [9] 62616327 62192082

Smallest eigenvalues:
 [1]  0.5844980  0.5528689  0.5503917  0.4718512  0.4049323  0.3946117
 [7]  0.2342542  0.1777444 -0.4862035 -0.7585808

Largest  eigenvalues:
 [1] 78398351 73106463 69009886 68609684 66461426 64616292 63507885 63044836
 [9] 62492222 61536088

Smallest eigenvalues:
 [1]  0.6194306  0.5779876  0.4874307  0.4630778  0.4264805  0.3411356
 [7]  0.2928617  0.2079465  0.1335055 -0.4620508

Largest  eigenvalues:
 [1] 77994146 72893271 69065832 68580585 65999183 64310120 63471605 62837147
 [9] 62569495 61810980

Smallest eigenvalues:
 [1]  0.45788074  0.42309971  0.40090862  0.38221236  0.34828864  0.21213767
 [7]  0.19372156  0.14505021  0.07888568 -0.80880130

Largest  eigenvalues:
 [1] 78146310 72600696 69221140 67608841 66740406 64991234 62979454 62790393
 [9] 62660626 61452409

Smallest eigenvalues:
 [1]  0.6168094  0.5572084  0.5374052  0.5251353  0.5249124  0.5046800
 [7]  0.4569474  0.4548913  0.2314360 -0.6945941

Largest  eigenvalues:
 [1] 76235526 72335723 68519846 66469621 66441775 64209451 62098185 61780148
 [9] 61720044 60736950

Smallest eigenvalues:
 [1]  0.5314646  0.5099513  0.5099080  0.4973050  0.4577089  0.4410357
 [7]  0.3009149  0.2989683  0.2120361 -0.0138035

Largest  eigenvalues:
 [1] 79452910 73776748 70185105 68787719 67174984 65385856 63998128 63960675
 [9] 63326930 62997863

Smallest eigenvalues:
 [1]  0.62493210  0.54725729  0.54327818  0.50156730  0.45121646  0.34538651
 [7]  0.32638782  0.31876276  0.29815584 -0.04555588

Largest  eigenvalues:
 [1] 76618357 72487579 69004664 67951299 66017218 64202249 62834942 62588284
 [9] 62184932 61286842

Smallest eigenvalues:
 [1]  0.44078897  0.39139843  0.33659465  0.32896347  0.32197906  0.30968785
 [7]  0.11162296  0.06384558  0.05809202 -1.05255301

Largest  eigenvalues:
 [1] 77407628 71770446 68246119 67127652 66071967 64285362 62335156 62233380
 [9] 61208716 60215649

Smallest eigenvalues:
 [1]  0.5263925  0.5188747  0.4577213  0.4524209  0.3546828  0.2752125
 [7]  0.2539063  0.1666805  0.1617368 -0.2107332

Largest  eigenvalues:
 [1] 76711786 72676320 69540517 67083898 66554204 64794139 62998451 62932216
 [9] 62310847 61733304

Smallest eigenvalues:
 [1]  0.66481263  0.61482009  0.57523772  0.55175464  0.46494013  0.46226408
 [7]  0.32666906  0.28826360  0.27784328 -0.06359557

Largest  eigenvalues:
 [1] 76521100 72639045 68714086 67330102 66794859 64609065 63215306 62511510
 [9] 62277628 61739928

Smallest eigenvalues:
 [1]  0.4986982  0.4279475  0.3961460  0.3905884  0.3350755  0.2597042
 [7]  0.1955783  0.1518725 -0.3811265 -0.5243261

Largest  eigenvalues:
 [1] 75980370 72551792 68500084 67136245 66173454 64407744 62346993 62125441
 [9] 62114673 61126146

Smallest eigenvalues:
 [1]  0.5808036  0.5080080  0.3713764  0.3603891  0.3017764  0.2743892
 [7]  0.2127487  0.1965267  0.1487910 -0.6944401

Largest  eigenvalues:
 [1] 76897584 73355126 69750655 67473435 67302867 65417179 63246915 63028098
 [9] 62431583 62004429

Smallest eigenvalues:
 [1]  0.3771406  0.3759812  0.3213990  0.2888245  0.2797256  0.2491324
 [7]  0.1762963  0.1723401  0.1589532 -0.6173631

Largest  eigenvalues:
 [1] 79046323 73295252 69607209 68381300 66840258 65095784 63559949 62856547
 [9] 62628734 61455322

Smallest eigenvalues:
 [1]  0.53528264  0.53149011  0.48608870  0.43012781  0.41347810  0.31394941
 [7]  0.21785592  0.20878756  0.06146585 -5.46813623

Largest  eigenvalues:
 [1] 76290469 73070718 69381249 67298033 67046798 65215680 62928557 62867289
 [9] 62205344 61657154

Smallest eigenvalues:
 [1]  0.66250390  0.61385810  0.55137979  0.54938417  0.50297337  0.45324812
 [7]  0.37913765  0.33659068 -0.05761271 -0.12206886

Largest  eigenvalues:
 [1] 75592215 72518838 68660255 66959070 66251459 64584417 62484978 61647906
 [9] 61471263 60833785

Smallest eigenvalues:
 [1]  0.5849314  0.4373744  0.4091513  0.4010794  0.3815045  0.3560443
 [7]  0.3373346  0.2877986  0.1450914 -1.4198170

Largest  eigenvalues:
 [1] 77479604 73441696 69777301 68088435 66966636 65381673 63032728 62979445
 [9] 62903511 61936537

Smallest eigenvalues:
 [1]  0.60557911  0.58484716  0.49393627  0.40280653  0.33287795  0.28972098
 [7]  0.26601656  0.24841782  0.16388638 -0.05441307

Largest  eigenvalues:
 [1] 77082156 73877017 69702471 68344600 67663697 66092828 63402700 63373197
 [9] 62717161 61882140

Smallest eigenvalues:
 [1]  0.4889054  0.4871352  0.3191644  0.2962206  0.2906382  0.2786933
 [7]  0.1662760  0.1265456  0.0657774 -0.3544348

Largest  eigenvalues:
 [1] 78569694 73081345 69818041 68048219 66503846 64869983 63294435 63183628
 [9] 62831383 62356103

Smallest eigenvalues:
 [1]  0.4756273  0.3934981  0.3874914  0.3440475  0.3134588  0.2927338
 [7]  0.2740950  0.1973614  0.1959956 -0.3160029

Largest  eigenvalues:
 [1] 77439127 73783931 69275346 68176072 67167841 65524213 63069362 62965066
 [9] 62665077 61691586

Smallest eigenvalues:
 [1]  0.5063435  0.4917570  0.4443741  0.4362320  0.3029285  0.2605324
 [7]  0.2520872  0.2459957  0.1044600 -0.1443511

Largest  eigenvalues:
 [1] 76116027 72872160 68817488 66406472 66359732 64599828 62610965 61860263
 [9] 61567110 61029715

Smallest eigenvalues:
 [1]  0.5290909  0.5083187  0.4665687  0.4234332  0.3736429  0.3054960
 [7]  0.2335567  0.2270453  0.2116457 -0.1592977

Largest  eigenvalues:
 [1] 77921759 72857949 69052171 68007068 66626653 64708125 63111426 63000426
 [9] 62408304 61906800

Smallest eigenvalues:
 [1]  0.36661552  0.30929603  0.30742536  0.21494456  0.18134182  0.15057450
 [7]  0.06002734  0.03195828 -0.06611011 -1.45526277

Largest  eigenvalues:
 [1] 76614154 73331755 68923567 67435126 66884221 65180317 62888520 62602797
 [9] 62060557 61622212

Smallest eigenvalues:
 [1]  0.4921167  0.3874164  0.3865490  0.2996914  0.2818525  0.2649377
 [7]  0.1665864  0.1424315  0.0240136 -0.7258130

Largest  eigenvalues:
 [1] 78149782 73620717 68703441 68392940 66734943 64560462 63457569 63002285
 [9] 62769086 61616213

Smallest eigenvalues:
 [1]  0.54133226  0.47939196  0.47529224  0.44698848  0.43490710  0.40855642
 [7]  0.28605858  0.28576910  0.21836058 -0.08238886

Largest  eigenvalues:
 [1] 78220876 74062695 69384709 68038257 66855810 65067828 63037285 62984362
 [9] 62490232 61693400

Smallest eigenvalues:
 [1]  0.5545459  0.5000074  0.4829989  0.3590129  0.3401603  0.3179716
 [7]  0.2719059  0.2441626  0.2057473 -0.5421030

Largest  eigenvalues:
 [1] 80489112 73477164 70392565 69607600 66787882 64862544 64811689 63843984
 [9] 62815333 62305029

Smallest eigenvalues:
 [1]  0.65726321  0.63372687  0.62915262  0.47337714  0.36342521  0.34084810
 [7]  0.28821564  0.23414021  0.20009144 -0.02142219

Largest  eigenvalues:
 [1] 78984721 73516919 70004593 68436413 67120176 65214460 63637020 63605769
 [9] 63086170 62326939

Smallest eigenvalues:
 [1]  0.6459865  0.6007240  0.5837996  0.5317114  0.4840707  0.3975918
 [7]  0.3432262  0.2752723  0.2365726 -0.1149224

Largest  eigenvalues:
 [1] 76186298 73137106 68662707 66929907 66904385 64778314 62789313 62429628
 [9] 62029782 60954814

Smallest eigenvalues:
 [1]  0.41601355  0.40500918  0.39312189  0.34230354  0.33862652  0.29660024
 [7]  0.27296627  0.19984604  0.03709052 -0.17789021

Largest  eigenvalues:
 [1] 78788366 72220314 68704634 67920490 66241584 64367501 63094008 62782935
 [9] 62401740 61739598

Smallest eigenvalues:
 [1]  0.4936840  0.4768644  0.4601447  0.4373802  0.4011646  0.3905537
 [7]  0.3675231  0.2256587 -0.1364966 -1.2221878

Largest  eigenvalues:
 [1] 78593286 72934108 69437870 68095433 66465923 64960650 63188327 62788460
 [9] 62576967 61757346

Smallest eigenvalues:
 [1]  0.4427556  0.3518684  0.3170674  0.3041950  0.2530347  0.2177461
 [7]  0.2037026  0.1886076 -0.1033008 -1.1603044

Largest  eigenvalues:
 [1] 76391608 73948022 69751440 67659569 67414929 65901792 63651543 62837766
 [9] 62616337 61748303

Smallest eigenvalues:
 [1]  0.51237604  0.49206066  0.42232257  0.39542546  0.35375987  0.33764933
 [7]  0.31305289  0.21888474  0.15278400 -0.01144459

Largest  eigenvalues:
 [1] 75144808 73235910 68655099 66743099 66149355 64965577 62722694 61580772
 [9] 61120192 60692607

Smallest eigenvalues:
 [1]  0.4718915  0.4598640  0.4319729  0.3033941  0.2813592  0.2106465
 [7]  0.2040379  0.1973647 -0.0501652 -1.6833649

Largest  eigenvalues:
 [1] 79821936 74845410 70953182 69269966 67812576 66210710 64150178 64086565
 [9] 63886077 62979316

Smallest eigenvalues:
 [1]  0.42923111  0.36939278  0.36411000  0.35084460  0.32337498  0.17725018
 [7]  0.15312291  0.14547620  0.03321482 -0.07061571

Largest  eigenvalues:
 [1] 76073107 73012740 69030440 66710402 66659338 65163082 62804458 62267529
 [9] 61809913 61291701

Smallest eigenvalues:
 [1]  0.50733233  0.47407655  0.46170365  0.36481024  0.31770505  0.31603493
 [7]  0.28670603  0.26559821  0.04709938 -0.60327226

Largest  eigenvalues:
 [1] 77863969 72762349 69513834 67509929 66626572 65084528 62970628 62654396
 [9] 62627947 61482228

Smallest eigenvalues:
 [1]  0.4665780  0.4438761  0.4409078  0.3138097  0.2494724  0.1996239
 [7] -0.1891409 -0.2778360 -0.4473761 -1.9112227

Largest  eigenvalues:
 [1] 77991741 72283868 68669492 68609516 65712985 63333096 63292635 62854444
 [9] 62063437 61703054

Smallest eigenvalues:
 [1]  0.5457786  0.4659359  0.4465208  0.3980604  0.3579039  0.3550848
 [7]  0.3425942  0.2554771  0.1533031 -0.5294102

Largest  eigenvalues:
 [1] 77621762 73654559 70065271 67491687 66765709 65450796 63064068 62740847
 [9] 62469800 61944286

Smallest eigenvalues:
 [1]  0.5093040  0.4525158  0.4406104  0.4210410  0.3436718  0.3380359
 [7]  0.3199728  0.2061646  0.1537153 -0.9838352

Largest  eigenvalues:
 [1] 77918892 72386125 69177196 68384773 66365883 64763653 63389419 62616996
 [9] 62416252 61399950

Smallest eigenvalues:
 [1]  0.6005685  0.5557356  0.5551947  0.4810680  0.4710201  0.4104045
 [7]  0.2809539  0.2286925  0.1828317 -0.4757996

Largest  eigenvalues:
 [1] 76818195 72104379 68087691 67910726 65571185 63535607 62680589 62070470
 [9] 62052357 60720316

Smallest eigenvalues:
 [1]  0.53121934  0.52352207  0.50841272  0.48808474  0.39277930  0.25357988
 [7]  0.24704683  0.19446601 -0.06669131 -0.07913099

Largest  eigenvalues:
 [1] 78199046 73507287 70170876 68808368 66975482 65333991 63562747 63415115
 [9] 63378020 62075535

Smallest eigenvalues:
 [1]  0.54297918  0.41536686  0.37949719  0.36946249  0.34984323  0.33575353
 [7]  0.31270920  0.28567660  0.06091615 -0.21260932

Largest  eigenvalues:
 [1] 78163149 72798593 69570441 67243097 66506638 64878269 62498275 62481980
 [9] 62355956 61550046

Smallest eigenvalues:
 [1]  0.37033329  0.35583734  0.26322290  0.25305384  0.21991260  0.11218478
 [7]  0.09794139  0.06167154 -0.11005096 -0.45499641

Largest  eigenvalues:
 [1] 76903246 72382656 68527707 67514262 66378832 64507244 62786897 62743626
 [9] 62458906 61739738

Smallest eigenvalues:
 [1]  0.58800815  0.47419440  0.45919063  0.44037277  0.43657684  0.39258567
 [7]  0.32954546  0.03262054 -0.06081041 -1.76203112

Largest  eigenvalues:
 [1] 76347601 72048439 68477843 66633519 66301830 64619976 62367438 62082282
 [9] 61436158 61023055

Smallest eigenvalues:
 [1]  0.462468722  0.458260595  0.384875201  0.367824485  0.344428880
 [6]  0.218181970  0.191450396  0.093459614  0.007381912 -1.490534726

Largest  eigenvalues:
 [1] 75119060 71992941 68606489 66176769 65742500 64684789 62752958 61602556
 [9] 60868476 60653622

Smallest eigenvalues:
 [1]  0.56185265  0.54210568  0.47569234  0.45346800  0.42957012  0.38267164
 [7]  0.38170993  0.25325944  0.15563271 -0.08828515

Largest  eigenvalues:
 [1] 76114204 72236477 68468808 66977473 66021288 64188532 62534459 62054612
 [9] 61942949 61138690

Smallest eigenvalues:
 [1]  0.4558232  0.4175097  0.3537204  0.3339841  0.2475841  0.2404107
 [7]  0.1705162  0.1629028  0.1259151 -0.7633733

Largest  eigenvalues:
 [1] 76522352 73175556 68715340 67398000 66647724 64854902 62531633 62498188
 [9] 62254823 61309372

Smallest eigenvalues:
 [1]  0.5586266  0.5526287  0.4921719  0.4743769  0.4549045  0.4038731
 [7]  0.3984109  0.3567929  0.3081261 -0.3016955

Largest  eigenvalues:
 [1] 77164127 72405142 68644424 67247483 66323766 64512420 62576539 62342721
 [9] 62162601 61153769

Smallest eigenvalues:
 [1]  0.48716308  0.41673406  0.38688070  0.30490397  0.26953392  0.23240527
 [7]  0.17863313  0.02669953 -0.19969091 -0.25657171

Largest  eigenvalues:
 [1] 78615891 74070376 70083665 68633058 67030476 65372267 63610619 63436103
 [9] 63127338 62295644

Smallest eigenvalues:
 [1]  0.4873156  0.4634307  0.3578956  0.3331954  0.3233987  0.3123022
 [7]  0.3022186  0.2715007  0.2501837 -0.4576190

Largest  eigenvalues:
 [1] 78233313 72792404 68725412 67666840 66373338 64675584 62862872 62745200
 [9] 62559873 61790179

Smallest eigenvalues:
 [1]  0.4564734  0.4240905  0.3443727  0.3325794  0.3324423  0.2588955
 [7]  0.0984446 -0.1178044 -0.3719748 -0.7488622

Largest  eigenvalues:
 [1] 81008761 73593516 69947139 69236475 66765745 64773360 64346571 63198531
 [9] 63100040 62325457

Smallest eigenvalues:
 [1]  0.61259029  0.60732951  0.53437352  0.51495381  0.49212834  0.48904099
 [7]  0.42842757  0.28460105  0.06857686 -2.04336368

Largest  eigenvalues:
 [1] 77174875 73176116 69039870 67324842 66791462 65322684 63019009 62601322
 [9] 62116748 61384826

Smallest eigenvalues:
 [1]  0.54933576  0.51380417  0.47782596  0.45551969  0.34510490  0.27095388
 [7]  0.26813065  0.16104296  0.04072443 -0.75864868

Largest  eigenvalues:
 [1] 77302252 73788277 69019137 67819871 66950020 65033327 62818595 62788717
 [9] 62748066 61632728

Smallest eigenvalues:
 [1]  0.53138711  0.48911246  0.43675105  0.31482460  0.31072777  0.27613402
 [7]  0.21496107  0.20197270  0.04715298 -0.19892965

Largest  eigenvalues:
 [1] 76923241 73568837 70223084 67712402 67443893 65699500 63085515 63008554
 [9] 62587232 61668685

Smallest eigenvalues:
 [1]  0.450209051  0.387324373  0.345866689  0.312662494  0.262500846
 [6]  0.189234073  0.114228042  0.107244635  0.004308756 -0.934283239

Largest  eigenvalues:
 [1] 75335410 72822865 69056538 66751085 66411379 64903946 62926640 62650423
 [9] 61798905 61295707

Smallest eigenvalues:
 [1]  0.46065008  0.38197056  0.37204965  0.24824824  0.19054875  0.16490394
 [7]  0.13560523  0.06256524 -0.17225380 -0.38723394

Largest  eigenvalues:
 [1] 78127038 73373341 69659402 68820583 66779986 64749362 63513055 63201667
 [9] 63020051 61932825

Smallest eigenvalues:
 [1]  0.65055514  0.63948990  0.57695358  0.49846813  0.48689460  0.43348191
 [7]  0.34916637  0.27806090  0.12219865 -0.06065522

Largest  eigenvalues:
 [1] 77695685 73248927 69300254 67073388 67026651 65088235 63092794 62394679
 [9] 62168719 61799383

Smallest eigenvalues:
 [1]  0.38924135  0.35406052  0.33624003  0.32778739  0.27307669  0.24953740
 [7]  0.23083767  0.22453287  0.07673283 -0.16541260

Largest  eigenvalues:
 [1] 77224373 72860050 69358852 67554650 66666579 64991839 62571459 62549027
 [9] 62267392 61051816

Smallest eigenvalues:
 [1]  0.5454172  0.5121232  0.4688329  0.4488098  0.4352464  0.2476439
 [7]  0.2161434  0.1609220  0.1474564 -0.3959362

Largest  eigenvalues:
 [1] 76253037 73535358 68774299 67382563 67093461 65178198 63037789 63018777
 [9] 62401626 61727434

Smallest eigenvalues:
 [1]  0.4822018  0.4638746  0.4171191  0.4152838  0.3777053  0.3422812
 [7]  0.3157871  0.2568775  0.1127558 -1.3095284

Largest  eigenvalues:
 [1] 78660348 73972129 70082224 67926583 67558139 65751680 63261163 63114731
 [9] 63047887 61828539

Smallest eigenvalues:
 [1]  0.5431078  0.5156256  0.4900267  0.4309330  0.4055578  0.3429571
 [7]  0.3182595  0.2991290  0.2025225 -0.4265298

Largest  eigenvalues:
 [1] 76025408 72781770 68831800 67443401 65972578 64210560 62760126 62355615
 [9] 62085119 61523239

Smallest eigenvalues:
 [1]  0.5879611  0.5474388  0.5452024  0.5173931  0.4511520  0.4371621
 [7]  0.4250925  0.2970864  0.2721661 -2.2219751

Largest  eigenvalues:
 [1] 77440981 72354695 68579039 67242930 66414268 64664791 62489303 62339734
 [9] 61902910 60960867

Smallest eigenvalues:
 [1]  0.5374780  0.5261551  0.3962173  0.3884212  0.3457020  0.3373046
 [7]  0.2938120  0.2765028 -1.4034296 -3.9998523

Largest  eigenvalues:
 [1] 77243963 72379382 68674264 67351456 66002575 64129342 62524157 62336532
 [9] 61957453 60907053

Smallest eigenvalues:
 [1]  0.4390944  0.4101958  0.3236849  0.2805306  0.1679936  0.1191453
 [7] -0.1844365 -0.2358975 -0.2858668 -2.4409963

Largest  eigenvalues:
 [1] 77448658 73478825 69033967 67546738 67346516 65247356 63085100 62761462
 [9] 62559450 61619587

Smallest eigenvalues:
 [1]  0.4362494  0.4227834  0.3921364  0.3919615  0.3392415  0.1479311
 [7]  0.1215385  0.1061132 -0.4301498 -5.0122493

Largest  eigenvalues:
 [1] 78144621 72430461 68805071 68331448 65668179 63833683 63402547 61758693
 [9] 61686819 60522687

Smallest eigenvalues:
 [1]  0.47435807  0.43846313  0.39823452  0.26458360  0.18921173  0.15851571
 [7]  0.07700463  0.07628123 -0.14747611 -2.66543543

Largest  eigenvalues:
 [1] 75479584 73126834 68691725 66839234 66805937 64583628 62558375 62239965
 [9] 61889835 61087434

Smallest eigenvalues:
 [1]  0.5690132  0.5624336  0.5174906  0.5023219  0.4833315  0.4825813
 [7]  0.4018707  0.2944678  0.0840317 -1.0725444

Largest  eigenvalues:
 [1] 77949808 72900188 68808576 67696128 65872921 63978078 62735646 62327947
 [9] 62174550 61268892

Smallest eigenvalues:
 [1]  0.49092776  0.39831489  0.30697338  0.26844569  0.26257969  0.25445088
 [7]  0.21259636  0.18645773  0.09680648 -0.71640440

Largest  eigenvalues:
 [1] 77321785 72972348 69500644 67470128 66421233 64928512 62835540 62529297
 [9] 62341889 61261093

Smallest eigenvalues:
 [1]  0.5267426  0.5003280  0.4498634  0.4147667  0.3943344  0.3842105
 [7]  0.3654035  0.2999557  0.2691700 -0.2470747

Largest  eigenvalues:
 [1] 79295243 73286238 70155096 69250248 66176346 64283158 64258978 62788191
 [9] 62710673 61507240

Smallest eigenvalues:
 [1]  0.5714748  0.5659922  0.5297997  0.4990577  0.4879146  0.3859968
 [7]  0.3858936  0.3337741  0.3037146 -4.8679987

Largest  eigenvalues:
 [1] 77808567 72678402 69451539 67947524 66507960 64482159 62953675 62912890
 [9] 62818298 61745998

Smallest eigenvalues:
 [1]  0.5550625  0.5030966  0.4304122  0.3967658  0.3591304  0.3140145
 [7]  0.2905319  0.2775589  0.1135046 -0.1202976

Largest  eigenvalues:
 [1] 78779761 74022729 69580835 69042604 67136333 65101346 63906262 63286988
 [9] 63137985 61966041

Smallest eigenvalues:
 [1]  0.45590828  0.42587567  0.42064033  0.32102977  0.28763047  0.28511791
 [7]  0.18366720  0.08301284 -0.82424471 -1.39875366

Largest  eigenvalues:
 [1] 78076541 72600351 68699186 67927442 66485792 64685170 63015024 62906673
 [9] 62802724 61774215

Smallest eigenvalues:
 [1]  0.57223432  0.56155580  0.51187072  0.48836899  0.42566460  0.41770339
 [7]  0.33753361  0.32969244  0.29033880 -0.04521633

Largest  eigenvalues:
 [1] 77440525 73164670 69008119 67662592 66730965 64652948 62851513 62608601
 [9] 62484465 61137116

Smallest eigenvalues:
 [1]  0.4309983  0.3854496  0.3101752  0.3016417  0.2868240  0.2749075
 [7]  0.2681891  0.2323112  0.2019840 -4.6883570

Largest  eigenvalues:
 [1] 78817525 72809567 69050273 68324764 66434975 64699277 63248340 62352098
 [9] 61906500 61117218

Smallest eigenvalues:
 [1]  0.57014534  0.56999401  0.46839676  0.40722292  0.39586910  0.34939015
 [7]  0.30774642  0.21335055  0.11245027 -0.04889715

Largest  eigenvalues:
 [1] 76793785 72756876 69335326 67556719 67181668 65432748 63075676 62771717
 [9] 62538730 61376045

Smallest eigenvalues:
 [1]  0.56157162  0.55345822  0.39768083  0.30109046  0.28117137  0.21573065
 [7]  0.08772619 -0.08414587 -0.44556665 -3.96076640

Largest  eigenvalues:
 [1] 75835747 72712896 68345040 66641860 66488997 64505396 62372843 62033571
 [9] 61728032 60693284

Smallest eigenvalues:
 [1]  0.51231421  0.43720980  0.41390860  0.32884426  0.32457900  0.24896340
 [7]  0.14033167  0.12409762  0.08540747 -0.01180093

Largest  eigenvalues:
 [1] 77021970 73526232 69489148 67561252 67202321 65203589 63151274 62893230
 [9] 62714357 61717386

Smallest eigenvalues:
 [1]  0.44114998  0.39718736  0.39457352  0.29246040  0.29168453  0.21714202
 [7]  0.20910741  0.18015633  0.05915063 -0.82093623

Largest  eigenvalues:
 [1] 78186596 72843502 69382182 68021337 66719572 65068334 63170432 63159926
 [9] 62847720 61873077

Smallest eigenvalues:
 [1]  0.620839191  0.609358141  0.607164033  0.588918505  0.561933872
 [6]  0.484724508  0.362748018  0.274671470  0.007115184 -0.108696136

Largest  eigenvalues:
 [1] 77792054 72563708 68348978 67599089 66002906 64110999 62583913 62133295
 [9] 62014294 60891324

Smallest eigenvalues:
 [1]  0.48207010  0.43605004  0.42390392  0.34608546  0.34431323  0.32367444
 [7]  0.22749647  0.12896035  0.06031848 -0.06142068

Largest  eigenvalues:
 [1] 77103566 73421072 69908512 67154513 66874728 65139712 63125258 62911216
 [9] 62496111 62135966

Smallest eigenvalues:
 [1]  0.56386231  0.49010969  0.44567713  0.36613244  0.31024201  0.29172466
 [7]  0.28609594  0.14938307  0.06674204 -0.16239646

Largest  eigenvalues:
 [1] 75172499 71938678 67873050 66378199 65807369 63930545 62517447 61344883
 [9] 61195648 60245701

Smallest eigenvalues:
 [1]  0.6140533  0.5663002  0.5339815  0.5015216  0.4524964  0.2906862
 [7]  0.2614498  0.2572475  0.1151126 -2.0149106

Largest  eigenvalues:
 [1] 78809648 72643690 68381502 67823691 66154676 64001727 62972114 62144268
 [9] 62064217 61088426

Smallest eigenvalues:
 [1]  0.61249014  0.51066459  0.44075614  0.43326336  0.40590562  0.30874055
 [7]  0.28790049  0.11973603  0.02216328 -0.22931091

Largest  eigenvalues:
 [1] 77452523 71865557 68878623 66840429 65892875 64237251 62771468 62383656
 [9] 62068803 61294485

Smallest eigenvalues:
 [1]  0.53417849  0.49160453  0.47306168  0.35434021  0.32456402  0.28922058
 [7]  0.26048013  0.17016350  0.03051261 -0.98324248

Largest  eigenvalues:
 [1] 77559002 73639210 69907307 67938769 67396403 65684523 63149606 63083866
 [9] 62812306 61992695

Smallest eigenvalues:
 [1]  0.6061415  0.5926390  0.5775080  0.5340179  0.4602865  0.4169953
 [7]  0.4052033  0.3995662  0.1617461 -0.2125210

Largest  eigenvalues:
 [1] 76293856 73042794 68773258 66743819 66442307 64856334 62206908 61778175
 [9] 61432513 60396119

Smallest eigenvalues:
 [1]  0.4412863  0.4109118  0.3166150  0.3163672  0.2989847  0.2871846
 [7]  0.1941897  0.1632140 -0.1467563 -1.1975323

Largest  eigenvalues:
 [1] 76301322 72263329 68914488 66271035 66204766 64565208 62556004 61860869
 [9] 61533455 60983386

Smallest eigenvalues:
 [1]  0.5691553  0.5157491  0.4919878  0.4840066  0.4179316  0.3777640
 [7]  0.3773019  0.2771862  0.1276372 -1.1243563

Largest  eigenvalues:
 [1] 80597930 73528841 69650624 69636491 66638645 64806593 64697809 63075705
 [9] 62379982 61813164

Smallest eigenvalues:
 [1]  0.3956271  0.3690453  0.3683855  0.3504359  0.3434293  0.3321634
 [7]  0.3289036  0.2912993 -0.0645717 -0.6684154

Largest  eigenvalues:
 [1] 77761812 71864490 68418187 67854988 65558741 63911767 62896895 61859479
 [9] 61831803 60807047

Smallest eigenvalues:
 [1]  0.25561160  0.19199105  0.05578501 -0.08400762 -0.09385599 -0.12955829
 [7] -0.29443055 -0.78802726 -1.91587164 -2.27110083

Largest  eigenvalues:
 [1] 77492520 72721206 68496216 66744056 66548065 64535940 62174270 62124799
 [9] 61546188 60512047

Smallest eigenvalues:
 [1]  0.43005554  0.39099119  0.38472014  0.35721923  0.28251602  0.26128319
 [7]  0.23158714  0.15949365  0.04091214 -1.06838284

Largest  eigenvalues:
 [1] 78993951 73776301 69931542 69342701 66824665 64944804 64072174 63018735
 [9] 62869296 61392187

Smallest eigenvalues:
 [1]  0.5123177  0.4892354  0.4675663  0.4553410  0.4515061  0.3900092
 [7]  0.3750508  0.2300491  0.2153575 -0.1058415

Largest  eigenvalues:
 [1] 79328226 73148351 69121125 67887313 66369976 64589793 63074643 62594801
 [9] 62135293 61435334

Smallest eigenvalues:
 [1]  0.58377311  0.38880435  0.36742986  0.30941403  0.28914541  0.28003175
 [7]  0.25621181  0.24570699 -0.03180994 -0.18301966

Largest  eigenvalues:
 [1] 77918841 72771832 69590585 67556425 66601890 64898021 62636918 62618194
 [9] 62510925 61672163

Smallest eigenvalues:
 [1]  0.42900861  0.41469112  0.36415341  0.32716474  0.32262251  0.25962546
 [7]  0.23365289  0.18822705 -0.02816767 -0.10050295

Largest  eigenvalues:
 [1] 77681408 73233545 69715983 67977900 66451537 64966095 63143309 62705037
 [9] 62645625 61631037

Smallest eigenvalues:
 [1]  0.5353399  0.4847759  0.4563426  0.4389034  0.3921929  0.3666990
 [7]  0.3492315  0.3293210  0.3112218 -0.1497576

Largest  eigenvalues:
 [1] 77656398 74593542 69539397 68245956 67827554 65755209 63671387 63299228
 [9] 62911144 61929572

Smallest eigenvalues:
 [1]  0.46591329  0.43152608  0.39676502  0.35592323  0.19940832  0.19915334
 [7]  0.18260512  0.07678048 -0.07790773 -1.20175538

Largest  eigenvalues:
 [1] 76778804 73631691 69947261 67762294 67189780 65675074 63292927 63210912
 [9] 62622005 62205858

Smallest eigenvalues:
 [1]  0.62480026  0.60513308  0.55196867  0.53033567  0.48448632  0.43275462
 [7]  0.32394105  0.12982561 -0.01749487 -0.10350376

Largest  eigenvalues:
 [1] 76458170 73398599 68889334 67505637 67191310 65104501 63101995 62816218
 [9] 62405583 61609613

Smallest eigenvalues:
 [1]  0.64714521  0.59426285  0.55144251  0.52421489  0.42198160  0.41509051
 [7]  0.35198326  0.32684698  0.24387414 -0.03852206

Largest  eigenvalues:
 [1] 78804107 73246741 69777659 67845249 66649360 64846591 63201730 62847511
 [9] 62768347 62043968

Smallest eigenvalues:
 [1]  0.6139472  0.5714996  0.5651013  0.4774128  0.4559986  0.3474347
 [7]  0.2926480  0.2675503  0.2584136 -1.0274554

Largest  eigenvalues:
 [1] 76168656 73420530 69713342 67851847 66319162 65812841 63075959 62831442
 [9] 61634652 61419471

Smallest eigenvalues:
 [1]  0.6487596  0.5662867  0.5124077  0.4836117  0.4665970  0.4044605
 [7]  0.3796887  0.3588218  0.3033458 -0.5544879

Largest  eigenvalues:
 [1] 77312991 73239310 69420686 67655170 66787426 65175534 62739503 62679570
 [9] 62570031 61223341

Smallest eigenvalues:
 [1]  0.44763154  0.32006305  0.24821560  0.21930577  0.20857028  0.20600399
 [7]  0.19452043  0.17926576  0.02588723 -3.48592062

Largest  eigenvalues:
 [1] 78174492 74274802 69600866 67979355 67953685 65708247 64033944 63255929
 [9] 63017997 62323954

Smallest eigenvalues:
 [1]  0.4522870  0.3420022  0.3294172  0.2924992  0.2899649  0.2431163
 [7]  0.2184490  0.1938031 -0.1118705 -0.1505184

Largest  eigenvalues:
 [1] 75995136 73619866 69245030 67162482 67128298 65416174 62996981 62702071
 [9] 62020699 61417516

Smallest eigenvalues:
 [1]  0.4408793  0.4143093  0.3867732  0.3717432  0.3544544  0.3113710
 [7]  0.2538062  0.2304832  0.2299398 -1.7512971

Largest  eigenvalues:
 [1] 76309447 72625093 69211336 66864117 66168676 64811638 62639840 62124724
 [9] 61916578 60905823

Smallest eigenvalues:
 [1]  0.3871649  0.3866981  0.2845997  0.2751389  0.2691283  0.2541871
 [7]  0.2244560  0.1785875  0.1504328 -0.8205520

Largest  eigenvalues:
 [1] 75933364 72749454 69251078 67307196 66130146 65128035 62726089 62139898
 [9] 61383913 61238680

Smallest eigenvalues:
 [1]  0.66379908  0.56369598  0.55378139  0.48895366  0.44513755  0.39976995
 [7]  0.39401013  0.30423142  0.01102191 -0.16057403

Largest  eigenvalues:
 [1] 77209301 72661909 68743964 66701442 66581966 64746424 62445223 62410813
 [9] 61817813 61367621

Smallest eigenvalues:
 [1]  0.53969104  0.52514344  0.51888726  0.44975055  0.35731474  0.35333462
 [7]  0.31962477  0.05674661  0.05330030 -0.13488868

Largest  eigenvalues:
 [1] 79304943 72511743 69152577 68879948 65864215 64047427 63980852 62444056
 [9] 62083382 61223406

Smallest eigenvalues:
 [1]  0.5625119  0.5618533  0.4480813  0.3491762  0.2960418  0.2802478
 [7]  0.2369759  0.1761882 -0.2342997 -2.7985405

Largest  eigenvalues:
 [1] 77018686 73195081 69356420 67683581 67524846 65419626 63259482 63092624
 [9] 62677446 61770599

Smallest eigenvalues:
 [1]  0.4758027  0.4690746  0.4596764  0.3278722  0.3099201  0.2564229
 [7]  0.2147827  0.2002084  0.1903071 -0.1661220

Largest  eigenvalues:
 [1] 76840837 73043205 68954570 66946938 66933981 64942480 63382208 62375250
 [9] 62208448 62046150

Smallest eigenvalues:
 [1]  0.56857179  0.55762304  0.51816198  0.51441940  0.42126750  0.36025253
 [7]  0.26044192  0.10327385  0.03049733 -0.41771515

Largest  eigenvalues:
 [1] 76763513 72526017 68341178 66483962 66172828 64342221 62516390 61872525
 [9] 61567251 60740125

Smallest eigenvalues:
 [1]  0.60619468  0.56912519  0.44207088  0.43665430  0.35488570  0.34680123
 [7]  0.34395596  0.20934721  0.17916758 -0.06712159

Largest  eigenvalues:
 [1] 79543828 72995115 70252688 67915245 66822344 64938175 63381227 63144347
 [9] 62896144 62026618

Smallest eigenvalues:
 [1]  0.391872059  0.346943438  0.306831079  0.248936693  0.176147351
 [6]  0.161945936  0.085446831 -0.005224048 -1.591494846 -3.523358608

Largest  eigenvalues:
 [1] 77625987 73672519 69140991 67660221 67141197 65272522 62836106 62733643
 [9] 62695319 61134305

Smallest eigenvalues:
 [1]  0.58624856  0.50319283  0.48965830  0.40719522  0.34626416  0.32198924
 [7]  0.32066355  0.21456688  0.02324773 -0.26126780

Largest  eigenvalues:
 [1] 77337773 72985829 68621789 67919231 66891503 64615683 63153088 63016640
 [9] 62968181 62061069

Smallest eigenvalues:
 [1]  0.5447100  0.5074686  0.4980952  0.3507184  0.3380460  0.2235333
 [7]  0.2037923  0.1955483  0.1145680 -3.2715633

Largest  eigenvalues:
 [1] 77884762 73205619 69738142 67788459 66784096 65134140 63353127 63016470
 [9] 62859270 61902937

Smallest eigenvalues:
 [1]  0.38224516  0.36813648  0.32757812  0.31609990  0.18094652  0.16525861
 [7]  0.15823609  0.09153871 -0.16031953 -1.23990224

Largest  eigenvalues:
 [1] 75380603 71409378 67972803 66186916 65819326 64408106 62746070 61316252
 [9] 61010876 60530086

Smallest eigenvalues:
 [1]  0.3963042  0.3815812  0.3780751  0.3532953  0.2955249  0.2723363
 [7]  0.1993975  0.1231163 -0.5349240 -0.9470528

Largest  eigenvalues:
 [1] 77158413 72603113 68939281 67123321 66831222 65085062 62864075 62152174
 [9] 62114098 61352429

Smallest eigenvalues:
 [1]  0.64840843  0.59417961  0.58796697  0.56846007  0.50040726  0.41780735
 [7]  0.40888457  0.33034943  0.26697137 -0.04809979

Largest  eigenvalues:
 [1] 78925455 73510460 69608373 68583636 66873501 64779746 63648296 63520116
 [9] 62519769 61751418

Smallest eigenvalues:
 [1]  0.5885231  0.5196572  0.4871509  0.4705961  0.4378345  0.4221957
 [7]  0.3939678  0.3106384  0.1959882 -0.1588607

Largest  eigenvalues:
 [1] 78174678 73318784 69139051 68464811 66786672 64694341 63423405 62688505
 [9] 62566194 61378212

Smallest eigenvalues:
 [1]  0.54363480  0.48619311  0.39394658  0.37988594  0.36749875  0.29077311
 [7]  0.24297921  0.23166426  0.09832125 -0.10056106

Largest  eigenvalues:
 [1] 76164835 72574722 68869727 66488981 66470566 64856372 62480109 62240834
 [9] 61771553 61025355

Smallest eigenvalues:
 [1]  0.6595562  0.4778347  0.4777201  0.4560887  0.4447419  0.4439584
 [7]  0.2804740  0.2065923  0.1723538 -0.6803653

Largest  eigenvalues:
 [1] 79125120 73674378 69844261 68694087 66991856 65199841 63827488 63224284
 [9] 62768620 62118346

Smallest eigenvalues:
 [1]  0.45792189  0.39662118  0.37191523  0.31746304  0.30048376  0.24817395
 [7]  0.20698871  0.18659572 -0.03312312 -0.40503549

Largest  eigenvalues:
 [1] 75502679 72296464 68629433 66273809 66140496 64531817 62432670 61908921
 [9] 61048234 60777864

Smallest eigenvalues:
 [1]  0.60609753  0.48724689  0.40113697  0.37713882  0.31929558  0.21679750
 [7]  0.17819190  0.17586278  0.04652941 -0.89972217

Largest  eigenvalues:
 [1] 77471304 73210388 69640486 67522013 67144886 65328302 63524970 63316019
 [9] 62551649 62313623

Smallest eigenvalues:
 [1]  0.70633069  0.63494042  0.52931937  0.51913596  0.49005110  0.45592691
 [7]  0.37259819  0.35509308  0.08805054 -0.02293542

Largest  eigenvalues:
 [1] 77107759 72542812 68583888 67506772 66221056 64252207 62571772 62395162
 [9] 61905672 60723747

Smallest eigenvalues:
 [1]  0.5510777  0.4770974  0.4336779  0.3571755  0.3092820  0.2673447
 [7]  0.2257909  0.2223011  0.1467407 -0.4736243

Largest  eigenvalues:
 [1] 77738677 73772435 70099453 67686081 67537435 66248158 63742037 63251858
 [9] 62687434 62193013

Smallest eigenvalues:
 [1]  0.38149718  0.31375098  0.23357183  0.15160711  0.13841068  0.12866970
 [7]  0.09644159  0.04793429 -0.09238711 -0.20647185

Largest  eigenvalues:
 [1] 74847175 72082885 68694949 67467830 65418051 65253126 63481225 61944673
 [9] 61192914 61107086

Smallest eigenvalues:
 [1]  0.6245867  0.5796973  0.5190614  0.4325398  0.4214267  0.3978798
 [7]  0.2926305  0.2460852  0.2409765 -1.5287758

Largest  eigenvalues:
 [1] 77003044 73049864 69670203 67423669 67115769 65230995 63104300 63092017
 [9] 62549201 61780050

Smallest eigenvalues:
 [1]  0.56079886  0.48858244  0.42706765  0.40608031  0.33983060  0.32964365
 [7]  0.15826571  0.09026625 -0.04051922 -3.60849557

Largest  eigenvalues:
 [1] 78911742 74229416 69819436 68577694 67418238 65310360 63962879 63688099
 [9] 62900065 62365426

Smallest eigenvalues:
 [1]  0.60761826  0.52532968  0.46784554  0.46684787  0.40514918  0.33644806
 [7]  0.33215359  0.20057026  0.14943476 -0.08340087

Largest  eigenvalues:
 [1] 77093939 73605575 70064884 67337139 67070127 65444729 63420411 63169131
 [9] 62631460 62158947

Smallest eigenvalues:
 [1]  0.4913825  0.4056712  0.3876215  0.3656003  0.3397728  0.3386400
 [7]  0.3006801  0.2402215  0.2224611 -0.5915374

Largest  eigenvalues:
 [1] 78278016 73185278 69577023 68349020 66386509 65043649 63286249 62704394
 [9] 62380101 61438272

Smallest eigenvalues:
 [1]  0.48108982  0.47874154  0.42974418  0.41663263  0.33642249  0.31500940
 [7]  0.17850291  0.14395950  0.03105633 -0.80111875

Largest  eigenvalues:
 [1] 77657957 73440724 69543981 67937165 67240138 65511561 63648292 63193387
 [9] 62725763 62100080

Smallest eigenvalues:
 [1]  0.6018141  0.5747620  0.5360249  0.4699175  0.4574797  0.4204036
 [7]  0.4152570  0.2483100  0.1915887 -0.2923571

Largest  eigenvalues:
 [1] 78065294 73277054 69399943 68059630 67245411 65088224 63412982 63222595
 [9] 62829993 62127024

Smallest eigenvalues:
 [1]  0.63657869  0.58091123  0.47309795  0.46059524  0.41269535  0.34760522
 [7]  0.34146028  0.19837766  0.06876946 -0.13168017

Largest  eigenvalues:
 [1] 77899343 73614501 69444555 68110459 66799056 64969615 62970056 62770045
 [9] 62610825 61501361

Smallest eigenvalues:
 [1]  0.4357575  0.3732435  0.3645624  0.3592569  0.3552020  0.3080500
 [7]  0.2362022  0.1493750 -0.2002752 -2.0315635

Largest  eigenvalues:
 [1] 78748565 73643944 69582593 68016762 66860298 65045573 63099151 62925793
 [9] 62360766 61736742

Smallest eigenvalues:
 [1]  0.42481389  0.37432981  0.32187572  0.27197142  0.26573855  0.16092107
 [7]  0.15336440  0.09317395 -0.06051743 -0.37033048

Largest  eigenvalues:
 [1] 75711576 73474133 69615062 68381703 66238846 66083098 63634738 62843787
 [9] 61661142 61360370

Smallest eigenvalues:
 [1]  0.5150574  0.4418686  0.4315439  0.4065888  0.3936410  0.3628619
 [7]  0.2642223  0.2554318  0.2273828 -0.3865907

Largest  eigenvalues:
 [1] 77167953 72562780 69275995 67936711 66358637 64458365 62923506 62647748
 [9] 62509635 61541565

Smallest eigenvalues:
 [1]  0.4858002  0.4430913  0.4427014  0.4333576  0.3698012  0.3160379
 [7]  0.2470549  0.2347776 -0.0347408 -0.3396567

Largest  eigenvalues:
 [1] 75647342 72808046 68767115 67600272 66327972 65565166 63383275 61923155
 [9] 61357546 61174884

Smallest eigenvalues:
 [1]  0.5665954  0.5388154  0.5199074  0.4277300  0.3997629  0.3427671
 [7]  0.3306028  0.3027589  0.2764340 -0.7217431

Largest  eigenvalues:
 [1] 76314903 73244073 68898219 66633340 66204347 64881948 62449174 62287504
 [9] 61460890 61023903

Smallest eigenvalues:
 [1]  0.45718424  0.43970941  0.42923825  0.41499432  0.35557182  0.30087818
 [7]  0.24246061  0.16345236  0.15193504 -0.07529902

Largest  eigenvalues:
 [1] 76839816 73110856 69137821 66836645 66808408 64900844 63181676 62580347
 [9] 62121421 61954764

Smallest eigenvalues:
 [1]  0.55903247  0.43355265  0.41496691  0.35873062  0.25666566  0.22644578
 [7]  0.21554201 -0.05872214 -0.14301698 -0.39092403

Largest  eigenvalues:
 [1] 78257825 73878317 70068444 67692061 67422703 65379324 63828005 63364274
 [9] 63001168 62536479

Smallest eigenvalues:
 [1]  0.5408855  0.5147532  0.4866786  0.4243199  0.3457209  0.2782114
 [7]  0.2743892  0.2210687 -0.3567955 -0.4170453

Largest  eigenvalues:
 [1] 74828492 72106498 68418413 66507689 65996805 64265131 62600164 62327676
 [9] 61253172 61178835

Smallest eigenvalues:
 [1]  0.673295193  0.574687077  0.540907735  0.502479163  0.367132647
 [6]  0.223768030  0.201976435  0.159635409 -0.002899571 -0.266462213

Largest  eigenvalues:
 [1] 75424260 73488624 69225364 67815960 66402582 65761639 63391798 63155673
 [9] 61803281 61568243

Smallest eigenvalues:
 [1]  0.62746579  0.47622804  0.46088100  0.45061645  0.41257205  0.35507743
 [7]  0.35081756  0.27222403  0.24943780 -0.04448669

Largest  eigenvalues:
 [1] 76409113 73661609 68976906 67297743 67129175 65208875 62911705 62640918
 [9] 62185613 61584288

Smallest eigenvalues:
 [1]  0.428332447  0.424640594  0.412452830  0.334091949  0.238696832
 [6]  0.169365802  0.057118720 -0.006385144 -1.970289263 -5.042083032

Largest  eigenvalues:
 [1] 76401266 72126884 68019348 66106222 66082281 64278609 62268223 62086039
 [9] 61249800 61123150

Smallest eigenvalues:
 [1]  0.512802957  0.506701441  0.370299085  0.366171296  0.270104741
 [6]  0.264633710  0.224598365  0.133455707 -0.007253256 -0.182442936

Largest  eigenvalues:
 [1] 74425306 72344030 68952509 66328090 66220749 64493755 62491971 62362428
 [9] 61336897 61166965

Smallest eigenvalues:
 [1]  0.6417037  0.6305799  0.6238270  0.5460037  0.5280871  0.4901620
 [7]  0.4179043  0.2256567  0.2035596 -0.1511069

Largest  eigenvalues:
 [1] 75421311 72218935 68140691 66546956 66349631 64256356 62324059 62228651
 [9] 61355438 60817106

Smallest eigenvalues:
 [1]  0.51198871  0.47889834  0.47494702  0.41150978  0.33735183  0.26968989
 [7]  0.24466367  0.14355934  0.04110170 -0.08871892

Largest  eigenvalues:
 [1] 76328620 73072469 68721748 67797823 66733804 64602034 62725627 62635597
 [9] 62572768 61185235

Smallest eigenvalues:
 [1]  0.39879439  0.34658969  0.34227974  0.29372074  0.29067076  0.24536202
 [7]  0.24052590  0.22984693  0.21242451 -0.05608962

Largest  eigenvalues:
 [1] 78351475 72087716 68999413 67775322 66103863 64381376 62813393 62356925
 [9] 62213554 61434482

Smallest eigenvalues:
 [1]  0.46634621  0.44696700  0.44444587  0.38904494  0.30970307  0.27971186
 [7]  0.15933218  0.15497750 -0.02103619 -1.02261753

Largest  eigenvalues:
 [1] 77825658 72707307 68657619 68070980 66507194 64221102 63347452 62681138
 [9] 62603727 61501486

Smallest eigenvalues:
 [1]  0.5808877  0.5248201  0.5037546  0.4978299  0.4760031  0.3534811
 [7]  0.3283899  0.2494806  0.1460201 -1.3094150

Largest  eigenvalues:
 [1] 76850523 72020378 68443319 66873665 65855099 63966071 62201628 61971705
 [9] 61210962 60434400

Smallest eigenvalues:
 [1]  0.56257182  0.51946762  0.50874171  0.39533392  0.34884421  0.33854308
 [7]  0.32399011  0.30889323  0.07327141 -0.27709396

Largest  eigenvalues:
 [1] 76723834 72791755 68701360 67196088 66191959 64499532 62444383 62039791
 [9] 61560440 60507109

Smallest eigenvalues:
 [1]  0.588199818  0.490744505  0.456928410  0.425199350  0.413628178
 [6]  0.369664623  0.314389492  0.256124619  0.228927080 -0.007538688

Largest  eigenvalues:
 [1] 75643366 72063305 68483211 66468486 66354008 64606047 62554869 61887994
 [9] 61546499 60935552

Smallest eigenvalues:
 [1]  0.46849108  0.42356648  0.37590507  0.36593631  0.25564229  0.24939259
 [7]  0.16839968  0.13375163  0.08418436 -0.11394377

Largest  eigenvalues:
 [1] 76837552 72672298 69674492 67392149 66894653 65198267 62927638 62688409
 [9] 62404220 61564771

Smallest eigenvalues:
 [1]  0.56497103  0.53176070  0.47957386  0.45403140  0.43282968  0.38617789
 [7]  0.35841508  0.25000242 -0.03736873 -0.10142668

Largest  eigenvalues:
 [1] 79351341 72323046 69527511 68291631 66037286 63999196 63523577 62733240
 [9] 61993228 61609933

Smallest eigenvalues:
 [1]  0.51974607  0.43813118  0.43121073  0.42081449  0.40181562  0.39122910
 [7]  0.38306838  0.36081799  0.04807745 -2.20500574

Largest  eigenvalues:
 [1] 79087459 72503441 69042285 68596155 65871573 64124110 63635253 62357322
 [9] 61819075 60996272

Smallest eigenvalues:
 [1]  0.4245323  0.3806241  0.3748610  0.3684958  0.3266432  0.3014496
 [7]  0.2646318  0.2438948  0.1678264 -1.0569654

Largest  eigenvalues:
 [1] 79572725 72975042 69620750 69016935 66196187 64353807 64147227 62667807
 [9] 62143927 61363221

Smallest eigenvalues:
 [1]  0.4426613  0.4094225  0.4049305  0.2814929  0.2750891  0.2488869
 [7]  0.2239836  0.2073271  0.1362423 -0.2924667

Largest  eigenvalues:
 [1] 77209847 72740169 69203205 67525192 66938318 64938904 63581358 62826770
 [9] 62612410 62055161

Smallest eigenvalues:
 [1]  0.6562435  0.6373410  0.6362037  0.5686744  0.5194375  0.4414786
 [7]  0.3920645  0.1718008  0.1294767 -0.3612747

Largest  eigenvalues:
 [1] 77070194 72691548 68987407 66853577 66768598 64972372 62721593 62625422
 [9] 62037027 61295413

Smallest eigenvalues:
 [1]  0.46404765  0.44783901  0.38939080  0.37791612  0.37378334  0.30898780
 [7]  0.29122926  0.24283605  0.08790804 -1.09750502

Largest  eigenvalues:
 [1] 78933546 73662319 69730375 68607359 67013221 65389412 63597764 62980343
 [9] 62687451 61658317

Smallest eigenvalues:
 [1]  0.6324682  0.4785468  0.4406933  0.4400356  0.4249065  0.2862495
 [7]  0.2250434  0.2067813 -0.9708542 -1.2065334

Largest  eigenvalues:
 [1] 79736456 74064485 70517850 69253040 67075627 64952314 64270829 64139666
 [9] 62944313 62675861

Smallest eigenvalues:
 [1]  0.51036924  0.46187513  0.38731481  0.34378767  0.31484983  0.23360361
 [7]  0.17180636  0.13030223  0.08488275 -0.32584227

Largest  eigenvalues:
 [1] 78078315 73645533 70133156 67557203 67232525 65775582 63653387 63050005
 [9] 62909694 62098980

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	7.246352	0.8509766	16.16517	0	2.054911	4.448354

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

HR ~ alt + n + steps + PM25

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- HR_fd
covariates <- list(altitude = altitude_fd, 
                   noise = noise_fd,
                   steps = steps_fd,
                   pollution = pollution25_fd)
path_plot <- 'figures/model_HR_alt_noise_steps_PM25_N200'
basis_params <- list(beta_0 = list(nbetabasis = 80, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     noise = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     steps = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     pollution = list(nbetabasis = 80, norder = 4, lambda = 1e3))

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, 
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 19.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Warning message in `^.fd`((outcome - yhatfd), 2):
"The maximum error exceeds the tolerance level."
Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 670 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Smallest eigenvalues:
 [1]  0.582138894  0.534270824  0.513420139  0.471838431  0.454178749
 [6]  0.452357755  0.393288732  0.113200758 -0.006292351 -0.133889058

Largest  eigenvalues:
 [1] 65148070 60331692 57513833 56575966 54963080 53273464 52536849 51999059
 [9] 51763132 50909537

Smallest eigenvalues:
 [1]  0.46398058  0.39857378  0.39331619  0.37421683  0.36338730  0.32369954
 [7]  0.32296612  0.15405775 -0.01615417 -0.18726688

Largest  eigenvalues:
 [1] 65365443 59982211 57005455 56300591 54952863 53026541 52524947 52464909
 [9] 51458872 51418732

Smallest eigenvalues:
 [1]  0.61684261  0.56821037  0.47210371  0.44629476  0.41884613  0.40352989
 [7]  0.35217761  0.25119561 -0.01777933 -0.02260171

Largest  eigenvalues:
 [1] 64122964 60205133 57641181 55742245 55138462 53481183 52205342 51782133
 [9] 51754441 51215694

Smallest eigenvalues:
 [1]  0.51802920  0.44278317  0.41322929  0.39435893  0.27396285  0.24895037
 [7]  0.15988356  0.12814283 -0.02027725 -1.02468671

Largest  eigenvalues:
 [1] 63430096 61116951 57769770 55940737 55403638 54005666 52794869 52490549
 [9] 51932366 51680794

Smallest eigenvalues:
 [1]   0.504300412   0.459567766   0.375101290   0.285114588   0.271590294
 [6]   0.249079905   0.190424226   0.004701724  -4.305062954 -21.397355310

Largest  eigenvalues:
 [1] 63439869 59701325 56726978 55426873 54994492 53721540 52006049 51663306
 [9] 51107182 50744442

Smallest eigenvalues:
 [1]  0.35979152  0.23292737  0.16802264  0.10782127  0.08170898 -0.35660917
 [7] -0.85496108 -0.95355993 -4.62522331 -9.86603748

Largest  eigenvalues:
 [1] 65283344 59961148 57436028 56133285 54867695 53301782 52223246 52091618
 [9] 51563510 51245435

Smallest eigenvalues:
 [1]  0.44183621  0.40462111  0.35524045  0.30993226  0.24503424  0.22476122
 [7]  0.12210689  0.09114042  0.05777706 -1.96546590

Largest  eigenvalues:
 [1] 64463560 60747596 57381735 56142060 55769820 53970691 52847121 52108864
 [9] 51826902 51528514

Smallest eigenvalues:
 [1]  0.49726825  0.40720772  0.35411498  0.33787783  0.32780184  0.32227653
 [7]  0.22797604  0.01210434 -0.40294898 -1.17102763

Largest  eigenvalues:
 [1] 65366604 60578524 58145310 56790936 55198690 53971974 52688634 52494451
 [9] 52266766 51859224

Smallest eigenvalues:
 [1]  0.4920397  0.4383502  0.4284378  0.3534792  0.3144894  0.2845287
 [7]  0.2798502  0.2204291  0.2004139 -1.9568552

Largest  eigenvalues:
 [1] 65244776 60233986 57325326 56361126 55401399 53859713 52441787 52411283
 [9] 52280202 51408821

Smallest eigenvalues:
 [1]  0.40962955  0.37548295  0.30511974  0.29634871  0.25324465  0.19755470
 [7] -0.07159127 -1.07562920 -1.29689904 -2.51595934

Largest  eigenvalues:
 [1] 64955628 59937525 56601139 56562623 54588278 52787426 52548497 52250312
 [9] 51766836 51318097

Smallest eigenvalues:
 [1]  0.5026986  0.4713707  0.3848784  0.3323492  0.2938468  0.2310180
 [7]  0.2201860  0.2159269 -0.2715102 -0.4560355

Largest  eigenvalues:
 [1] 63971864 59877286 57293862 55884049 54757521 53247516 52297372 51843815
 [9] 51716600 51110906

Smallest eigenvalues:
 [1]  0.45536481  0.32896107  0.29719832  0.24224524  0.22137155  0.21727199
 [7]  0.09774093  0.08624682 -0.09241553 -3.87359645

Largest  eigenvalues:
 [1] 64619204 60527206 58122772 55730758 55443362 54197920 52821484 52213299
 [9] 51976204 51801919

Smallest eigenvalues:
 [1]  0.55306088  0.53278941  0.51247437  0.46124527  0.40592721  0.29763718
 [7]  0.29088174  0.21484414 -0.02570754 -0.07793213

Largest  eigenvalues:
 [1] 64785922 60126556 57323918 55879194 55294659 53081383 52272564 52030897
 [9] 51784885 51323664

Smallest eigenvalues:
 [1]   0.45227127   0.36288271   0.34911706   0.34402992   0.31049747
 [6]   0.28662176   0.19562599  -0.03826123  -0.62125560 -11.03690181

Largest  eigenvalues:
 [1] 65111750 60515801 57931089 56540355 55908765 54419429 52607342 52323743
 [9] 52209386 51424588

Smallest eigenvalues:
 [1]  0.47581333  0.43768791  0.37763536  0.31873869  0.31350395  0.30127597
 [7]  0.21202479  0.16111747  0.07821737 -0.35123742

Largest  eigenvalues:
 [1] 64325626 61342753 57571151 56351455 56291213 54409813 53980487 52392028
 [9] 52174093 52034966

Smallest eigenvalues:
 [1]  0.5253661  0.4845086  0.3974313  0.3598291  0.2593125  0.2515001
 [7]  0.2293299  0.1831083  0.1597757 -5.6348275

Largest  eigenvalues:
 [1] 63402595 59957512 57202232 55295724 54905354 53704976 52228116 52111130
 [9] 51426013 51080035

Smallest eigenvalues:
 [1]  0.4059256  0.4057105  0.3507398  0.2603932  0.2410954  0.2277764
 [7]  0.1984418  0.1607915 -1.4570600 -6.1546804

Largest  eigenvalues:
 [1] 64944363 59796905 57230546 56608424 54857074 53384537 52607956 52243509
 [9] 51559732 50844034

Smallest eigenvalues:
 [1]  0.5190173  0.4664545  0.4273429  0.2802843  0.2520270  0.2505320
 [7]  0.2303871  0.1175148 -0.6385760 -2.6030769

Largest  eigenvalues:
 [1] 65109952 59585481 56872588 56043457 54997874 53350166 52230234 52026720
 [9] 51945870 51294711

Smallest eigenvalues:
 [1]   0.2420610   0.2255808   0.1831371   0.1809581  -1.2235746  -1.3653772
 [7]  -3.1410483  -4.1044177  -4.2362828 -28.9074058

Largest  eigenvalues:
 [1] 66371214 59388341 57310200 56728275 54116990 53324108 52626495 51397946
 [9] 51190232 50592708

Smallest eigenvalues:
 [1]  0.5094121  0.4505063  0.4141838  0.3351829  0.1230920  0.0796625
 [7] -0.2902778 -1.4702984 -1.6376954 -9.4512125

Largest  eigenvalues:
 [1] 63433418 60169569 56874462 55324326 55065103 53543681 52073229 51447085
 [9] 50909756 50599958

Smallest eigenvalues:
 [1]  0.303186030  0.292375825  0.004067745 -0.113120212 -0.137378876
 [6] -0.323482728 -0.832901818 -0.988534255 -1.380347465 -2.243194540

Largest  eigenvalues:
 [1] 66600855 60618822 57946490 57342227 55129390 53458960 53273553 53016655
 [9] 51738112 51574550

Smallest eigenvalues:
 [1]  0.43203119  0.31957562  0.23781789  0.19365725  0.18396453  0.05542385
 [7]  0.05058566 -0.01991147 -0.40707677 -3.08390338

Largest  eigenvalues:
 [1] 65853369 60593154 57064085 56842854 55209617 53559969 52804240 52322603
 [9] 52101278 51351213

Smallest eigenvalues:
 [1]  0.457397457  0.320457769  0.242980153  0.207149740  0.149612218
 [6]  0.011288135  0.009577169 -2.026699135 -4.616648523 -6.649590643

Largest  eigenvalues:
 [1] 63511584 59974555 57165485 55456214 54970351 53888720 52509155 51886746
 [9] 51071567 50969646

Smallest eigenvalues:
 [1]  0.5108705  0.4763138  0.4498411  0.3954863  0.2899137  0.2800442
 [7]  0.2375158  0.2154875  0.2004713 -0.6332202

Largest  eigenvalues:
 [1] 64367888 61559209 58169235 56693481 55732368 54101490 52856923 52594194
 [9] 52541862 51853392

Smallest eigenvalues:
 [1]  0.4384280  0.3981057  0.3757465  0.3625340  0.3061225  0.3012047
 [7]  0.2125695  0.1989462  0.1115701 -0.7583390

Largest  eigenvalues:
 [1] 64909383 61174234 58096617 56495606 56491848 54788326 53128603 52664620
 [9] 52385494 51783872

Smallest eigenvalues:
 [1]  0.59479476  0.57035441  0.56250614  0.53616134  0.47446022  0.46023683
 [7]  0.43611164  0.24748370  0.06581347 -0.16892236

Largest  eigenvalues:
 [1] 65278986 60361879 57595282 56808569 55013132 53206151 52712570 51855195
 [9] 51595625 50817231

Smallest eigenvalues:
 [1]  0.4270195  0.3747766  0.3380101  0.3298966  0.2549301  0.2512072
 [7]  0.2473302  0.1969076 -0.6914395 -0.7782192

Largest  eigenvalues:
 [1] 64836123 60299158 57089401 56008101 54977677 53420146 52058688 52002657
 [9] 51640461 50969779

Smallest eigenvalues:
 [1]   0.3707116   0.3389766   0.3311187   0.2886437   0.1036859  -0.3543006
 [7]  -1.7384674  -3.2047003  -4.7830826 -24.1133702

Largest  eigenvalues:
 [1] 63309190 60412405 57228517 55767639 54917999 53192534 51992913 51830170
 [9] 51750055 50838745

Smallest eigenvalues:
 [1]  0.5417332  0.4896123  0.4644829  0.4233054  0.4160776  0.3555748
 [7]  0.2914740  0.2241525  0.2123182 -0.8281746

Largest  eigenvalues:
 [1] 63994471 59863448 57345239 55277102 54535078 53077700 52014300 51441019
 [9] 51209151 51167725

Smallest eigenvalues:
 [1]  0.50725782  0.41934090  0.41383705  0.27729561  0.26473499  0.23669258
 [7]  0.17127266  0.03307805 -0.57878346 -4.67633636

Largest  eigenvalues:
 [1] 65209401 59456049 56827009 55725679 54816956 53240920 51939064 51701773
 [9] 51507516 50728759

Smallest eigenvalues:
 [1]   0.3180695   0.2985033   0.2545072   0.2017825   0.1681180   0.1351658
 [7]  -3.8766700  -6.7190289 -14.7524683 -22.4548769

Largest  eigenvalues:
 [1] 65861406 60532406 57961349 56826820 55219815 53522510 53087901 52841837
 [9] 52092955 51999934

Smallest eigenvalues:
 [1]  0.38039276  0.34481875  0.25907228  0.25181584  0.24961091  0.20629351
 [7]  0.03516675 -0.71212194 -0.98498885 -1.77684346

Largest  eigenvalues:
 [1] 63291128 60576290 57848278 55876190 55127893 54513421 52852185 52534439
 [9] 51507267 51205484

Smallest eigenvalues:
 [1]  0.2935939  0.2815964  0.2526242  0.2324772  0.1792697 -0.2801462
 [7] -0.2824761 -0.6372673 -0.8530628 -1.3696133

Largest  eigenvalues:
 [1] 65085877 59958688 57295578 56122876 55159137 53349778 52187254 52153897
 [9] 51622367 51249778

Smallest eigenvalues:
 [1]  0.4636495  0.4241973  0.3813827  0.3650177  0.3357125  0.2721257
 [7]  0.2604671  0.1814510  0.1254497 -0.6653157

Largest  eigenvalues:
 [1] 63618500 59215353 57076645 55608960 54538361 52994120 51666115 51566125
 [9] 51515881 50645429

Smallest eigenvalues:
 [1]   0.36652231   0.31603571   0.30783626   0.13851873   0.03389022
 [6]  -0.01334603  -0.19900935  -0.67484224 -37.53127421 -53.79307327

Largest  eigenvalues:
 [1] 61202534 59118674 56207698 54922278 54195322 53011050 51880984 50910060
 [9] 50188861 50018904

Smallest eigenvalues:
 [1]  0.37641638  0.28160544  0.27859626  0.23586849  0.13527819  0.01134310
 [7] -0.04573632 -0.45534468 -2.69101621 -3.28285552

Largest  eigenvalues:
 [1] 64969306 61160124 58300373 55738628 55645285 54314350 52544668 52063148
 [9] 51756705 51512001

Smallest eigenvalues:
 [1]  0.45972451  0.44296116  0.39388481  0.30788031  0.29992387  0.24619009
 [7]  0.04157764 -0.34971618 -0.42829049 -7.68965393

Largest  eigenvalues:
 [1] 63054700 60658304 57455065 55580160 55501400 54207960 52569415 52142197
 [9] 51433681 51039231

Smallest eigenvalues:
 [1]  0.39433129  0.36679916  0.31585773  0.21358950  0.21355444  0.20967491
 [7]  0.18896538  0.16737422  0.15641722 -0.07897234

Largest  eigenvalues:
 [1] 63117354 60446388 57348222 55529660 55310689 53699526 52854294 52041619
 [9] 51677137 51450404

Smallest eigenvalues:
 [1]  0.53190929  0.52449781  0.50310948  0.42464075  0.35520278  0.33621567
 [7]  0.31666149  0.25626923  0.22748197 -0.05643541

Largest  eigenvalues:
 [1] 64921528 61126484 57810905 56702431 55673861 54077357 52841896 52665160
 [9] 52439567 51872118

Smallest eigenvalues:
 [1]  0.44402409  0.42693470  0.29321791  0.26607362  0.25239042  0.14994960
 [7]  0.04118788 -0.04611271 -0.39470826 -0.69863187

Largest  eigenvalues:
 [1] 62465018 59542945 56247025 55450127 54488539 52757899 51905864 51575396
 [9] 51059429 50281760

Smallest eigenvalues:
 [1]  0.4905395  0.4679585  0.4323883  0.3402013  0.3265913  0.3046923
 [7]  0.2180993  0.1836426  0.1279358 -0.4123913

Largest  eigenvalues:
 [1] 64685935 60047766 57665155 56052304 55401798 53968115 52258216 52202880
 [9] 52009997 51523502

Smallest eigenvalues:
 [1]  0.5808287  0.5181906  0.4884345  0.3982290  0.3938184  0.3780191
 [7]  0.3550720  0.3309355  0.3187282 -0.7128785

Largest  eigenvalues:
 [1] 64606963 60711096 57811545 56277666 55802660 54242915 52451850 52276209
 [9] 52250244 51371187

Smallest eigenvalues:
 [1]  0.29573646  0.28548900  0.13631423  0.09101294  0.04886930  0.03415961
 [7] -0.02282863 -0.82249094 -1.11838746 -3.33712727

Largest  eigenvalues:
 [1] 64589676 60226187 56738802 56347785 55388184 53393661 52622638 52322757
 [9] 52267541 51292064

Smallest eigenvalues:
 [1]  0.384471971  0.291343405  0.262767255  0.225331121  0.177028896
 [6]  0.155569637  0.111332297 -0.009455158 -1.238470055 -7.872201515

Largest  eigenvalues:
 [1] 64109416 58895242 56559304 55894560 54075817 52357987 51815190 51352236
 [9] 51100554 50050191

Smallest eigenvalues:
 [1]  0.4420265  0.4379181  0.4309511  0.4058506  0.3543849  0.3011116
 [7]  0.2885254  0.2551085  0.2346812 -0.1523098

Largest  eigenvalues:
 [1] 61903871 59891528 56951910 55140813 54734514 53539882 52175722 51527357
 [9] 50791050 50585166

Smallest eigenvalues:
 [1]  0.4183948  0.4079354  0.3893765  0.3639861  0.2685296  0.2215397
 [7]  0.1655500  0.1409848 -0.8635024 -3.6238826

Largest  eigenvalues:
 [1] 66587928 60660483 57483247 56511083 55423761 53772725 52623248 52498535
 [9] 51873341 51740835

Smallest eigenvalues:
 [1]  0.3822995  0.3349637  0.3140252  0.3121702  0.2596931  0.2378911
 [7]  0.2081925  0.1764116 -0.5094574 -0.5130824

Largest  eigenvalues:
 [1] 64674264 60844739 58311335 55890716 55696876 54346296 52850263 52536215
 [9] 51867134 51617760

Smallest eigenvalues:
 [1]  0.63910144  0.61685112  0.58942740  0.55083323  0.49200432  0.42708875
 [7]  0.37312576  0.25492659  0.07855744 -0.29657984

Largest  eigenvalues:
 [1] 65336058 60461009 57568946 56502202 54941750 53162779 52625073 52213058
 [9] 51384393 50977582

Smallest eigenvalues:
 [1]  0.4857895  0.4292037  0.3959083  0.3657526  0.3458585  0.3435992
 [7]  0.3141451  0.1912363  0.1805988 -0.7261910

Largest  eigenvalues:
 [1] 63247401 59893054 57035835 55228200 55061881 53445060 51770939 51733694
 [9] 51211704 50961798

Smallest eigenvalues:
 [1]  0.4487396  0.3845477  0.3725236  0.3365801  0.2878332  0.2565840
 [7]  0.2547981  0.1805501 -3.5341140 -6.1643446

Largest  eigenvalues:
 [1] 65317504 60018953 57252415 57202693 54597809 53165302 52921615 52087658
 [9] 51973519 51145378

Smallest eigenvalues:
 [1]  0.604535685  0.486314249  0.442001847  0.435220009  0.414558723
 [6]  0.297290354  0.248239666  0.142352946 -0.003398047 -1.114340477

Largest  eigenvalues:
 [1] 65167813 61071672 58152822 56867125 55438591 53496575 53089236 52736231
 [9] 51911704 51789930

Smallest eigenvalues:
 [1]  0.545327466  0.519049578  0.504786705  0.451035254  0.393515566
 [6]  0.358569237  0.329280561  0.279436969  0.277642076 -0.006866797

Largest  eigenvalues:
 [1] 64319420 60700234 57722139 56156459 55835862 54557474 52950277 52138403
 [9] 52020571 51475996

Smallest eigenvalues:
 [1]  0.45141749  0.38253218  0.37977975  0.29862668  0.25247099  0.13523288
 [7]  0.06372699 -0.26592498 -0.62203637 -1.16139540

Largest  eigenvalues:
 [1] 64946327 60677566 58167003 56495731 55173087 53604556 52799028 52550215
 [9] 52175469 51877593

Smallest eigenvalues:
 [1]  0.5631793  0.5461064  0.4875077  0.4562461  0.3638974  0.3584800
 [7]  0.3438786  0.2543562  0.1076786 -0.4530413

Largest  eigenvalues:
 [1] 65311917 59906844 56985900 56476882 54854238 52887579 52450675 52138129
 [9] 51639535 51208866

Smallest eigenvalues:
 [1]  0.5939966  0.5270798  0.5032330  0.4229257  0.3969222  0.3754482
 [7]  0.3449907  0.3354566  0.2908666 -0.1194142

Largest  eigenvalues:
 [1] 64259443 60517548 57668439 55916038 55456470 53745249 51805155 51766615
 [9] 51643978 50728624

Smallest eigenvalues:
 [1]  0.4482323  0.4334117  0.3873700  0.3816662  0.3391291  0.2763107
 [7]  0.2725865  0.1455238 -0.7910155 -1.2416415

Largest  eigenvalues:
 [1] 62818285 60170130 57027997 55333910 55008869 53317013 52036779 52008368
 [9] 51125093 51012129

Smallest eigenvalues:
 [1]  0.52338930  0.51916634  0.51802720  0.40898895  0.38106018  0.34818961
 [7]  0.26314532  0.19972866  0.08942279 -0.12396346

Largest  eigenvalues:
 [1] 62221759 59624694 56743772 55346164 54418424 53507238 51779605 51669336
 [9] 50532283 50384938

Smallest eigenvalues:
 [1]  0.4802773  0.4500428  0.3651332  0.3532638  0.3364786  0.2986449
 [7]  0.2825763  0.1524951  0.1286394 -1.6555082

Largest  eigenvalues:
 [1] 63587639 59643610 56854613 55364657 55134545 53461920 52455268 51913882
 [9] 51518403 51288009

Smallest eigenvalues:
 [1]  0.4750561  0.4666026  0.4491465  0.3618929  0.2969885  0.2441727
 [7]  0.2265190 -0.0994749 -0.1879190 -3.8971143

Largest  eigenvalues:
 [1] 65611200 60444404 57773103 56950411 54705607 53304939 53015738 52132293
 [9] 51514878 51169591

Smallest eigenvalues:
 [1]  0.4990037  0.4419385  0.4303572  0.4170202  0.2810512  0.2518895
 [7]  0.2435805  0.2267070  0.2183130 -0.9566458

Largest  eigenvalues:
 [1] 64323691 60147743 57171880 56096714 55165625 53637034 52493195 52032670
 [9] 51999230 51518835

Smallest eigenvalues:
 [1]  0.40554281  0.39307933  0.35224568  0.29881751  0.25156641  0.21184460
 [7]  0.20582112  0.19764824  0.07209213 -5.25581622

Largest  eigenvalues:
 [1] 64909369 61129126 58428614 56188950 55875786 54473679 52532312 52383440
 [9] 52091219 51615600

Smallest eigenvalues:
 [1]  0.3922102  0.3620180  0.3268108  0.2611272  0.2529055  0.2058618
 [7]  0.1975627  0.1959268  0.1217729 -2.1681830

Largest  eigenvalues:
 [1] 65571747 60568455 57776239 56659420 55308631 53780616 52566828 52247656
 [9] 52071813 51337332

Smallest eigenvalues:
 [1]  0.485370356  0.310864100  0.307989957  0.296572828  0.220046394
 [6]  0.151461521  0.002218544 -0.895487191 -1.530775376 -1.939084785

Largest  eigenvalues:
 [1] 62799527 59710533 56958342 55341016 54909034 53705196 52161778 52126877
 [9] 51083987 50906260

Smallest eigenvalues:
 [1]   0.40943220   0.40923920   0.37720660   0.30750753   0.20546174
 [6]   0.15602178   0.08009306  -0.03155124  -1.08163518 -17.64683617

Largest  eigenvalues:
 [1] 65011877 59902886 56763757 56529187 55043132 53415437 52434734 51972918
 [9] 51757720 51043243

Smallest eigenvalues:
 [1]  0.5696885  0.5200058  0.4349116  0.4035829  0.3020217  0.2704845
 [7]  0.2684303  0.2512133  0.2419236 -1.4535085

Largest  eigenvalues:
 [1] 65543313 60966032 58067480 56512064 55696669 54193156 52723471 52612508
 [9] 52109418 51618272

Smallest eigenvalues:
 [1]  0.40096058  0.35083143  0.32859303  0.32601818  0.28127811  0.22925439
 [7]  0.21195304  0.18646779  0.04865597 -2.01116212

Largest  eigenvalues:
 [1] 65900101 59853999 57187752 56603485 54742607 53457136 52650043 52005321
 [9] 51882321 51182385

Smallest eigenvalues:
 [1]  0.4649486  0.4568153  0.4341013  0.4080081  0.3421340  0.2834149
 [7]  0.2537515  0.2349537  0.2327321 -0.3315201

Largest  eigenvalues:
 [1] 65482613 60816554 58048249 56700024 56120910 54524195 52682598 52448386
 [9] 52371316 51439683

Smallest eigenvalues:
 [1]  0.57068226  0.42211693  0.39747428  0.39689597  0.37707957  0.34723472
 [7]  0.30803484  0.24994537 -0.01339311 -1.00383665

Largest  eigenvalues:
 [1] 66420032 60787081 58063763 57216759 55177665 53603304 53344990 52405416
 [9] 51966515 51598951

Smallest eigenvalues:
 [1]   0.35043920   0.31639147   0.29461594   0.26699996   0.23734749
 [6]   0.14742534   0.10872102   0.08751024  -2.59212710 -12.27370009

Largest  eigenvalues:
 [1] 63968624 60587267 57241963 55858968 55822691 54135264 52990040 52280121
 [9] 52026469 51772628

Smallest eigenvalues:
 [1]  0.4420123  0.4357314  0.3516233  0.3426413  0.3073509  0.1924930
 [7]  0.1805966  0.1346656 -0.2101050 -0.8369537

Largest  eigenvalues:
 [1] 64995062 59643408 57089027 56521548 54277184 52755528 52508285 51475254
 [9] 51245996 50417057

Smallest eigenvalues:
 [1]  0.51048804  0.45580278  0.39095756  0.33934288  0.33473126  0.27488713
 [7]  0.27409689 -0.08764137 -0.30070317 -0.40846445

Largest  eigenvalues:
 [1] 64662438 60857915 58215130 56351829 55531551 54074757 53011058 52349669
 [9] 52283685 52163300

Smallest eigenvalues:
 [1]  0.52884928  0.50887246  0.44794902  0.38208101  0.36930356  0.36792831
 [7]  0.33291083  0.25796138  0.01876542 -0.15594624

Largest  eigenvalues:
 [1] 65348685 60272311 57711004 56410396 55565765 53548089 52669521 52176989
 [9] 51818943 51138695

Smallest eigenvalues:
 [1]  0.5127975  0.4966310  0.4265970  0.4125918  0.3396251  0.2625984
 [7]  0.1666105  0.1434122  0.1429262 -0.2603449

Largest  eigenvalues:
 [1] 63718756 61355276 57782812 56375545 55305516 53859789 52852244 52287447
 [9] 52261508 51912831

Smallest eigenvalues:
 [1]  0.4206898  0.3693107  0.3671705  0.3430170  0.3144401  0.3067283
 [7]  0.1995124  0.1496485 -1.0483970 -4.6744849

Largest  eigenvalues:
 [1] 66348277 60918782 57312876 57301833 55696792 53855646 53311968 52484686
 [9] 52284560 51539900

Smallest eigenvalues:
 [1]  0.4335716  0.4292870  0.3543884  0.3436370  0.2887624  0.2803902
 [7] -0.2580284 -1.5438717 -2.0344285 -3.4414541

Largest  eigenvalues:
 [1] 64464386 59772236 56780844 56401755 54635512 52859047 52177665 52142265
 [9] 51642181 51175340

Smallest eigenvalues:
 [1]  0.47922946  0.39915544  0.31475005  0.30556300  0.22686749  0.21518141
 [7]  0.15850637  0.15257790 -0.06018905 -0.54311125

Largest  eigenvalues:
 [1] 66320847 60187470 58003398 55972624 54950478 53151004 52429283 51802356
 [9] 51365090 51037974

Smallest eigenvalues:
 [1]  0.51891681  0.49664889  0.44967162  0.37073948  0.26787808  0.20476697
 [7]  0.18228656  0.17300728  0.04872697 -1.41871962

Largest  eigenvalues:
 [1] 65598631 61340935 58159376 56931134 55986208 54373636 53563457 52922123
 [9] 52463148 52169973

Smallest eigenvalues:
 [1]   0.365058229   0.323195797   0.300704524   0.107977260   0.091708186
 [6]   0.024732365  -0.006456436  -0.066814925  -3.262360890 -24.195205360

Largest  eigenvalues:
 [1] 63588423 59868185 57053870 55623161 54891888 53290107 52035527 51822195
 [9] 51592733 51031827

Smallest eigenvalues:
 [1]  0.6128888  0.6005414  0.5084246  0.4647590  0.3576826  0.3320714
 [7]  0.2924757  0.2352079  0.2192629 -0.0116011

Largest  eigenvalues:
 [1] 63436488 60677069 57270421 55915963 54984756 53995230 52027421 51859383
 [9] 51096587 50804366

Smallest eigenvalues:
 [1]  0.5429188  0.4624436  0.4484672  0.3660855  0.2859350  0.2802123
 [7] -0.2252810 -3.2127511 -4.0366510 -5.3848628

Largest  eigenvalues:
 [1] 65541444 60253537 57759824 56620516 54984595 53379433 52452385 52386620
 [9] 52035835 51615543

Smallest eigenvalues:
 [1]  0.49384678  0.47034096  0.43110013  0.41232906  0.34579495  0.27326848
 [7]  0.20258560 -0.06413743 -0.15323955 -0.42340140

Largest  eigenvalues:
 [1] 65964400 61049404 58365404 56728603 55751973 54084782 53131516 52679136
 [9] 52557385 52283067

Smallest eigenvalues:
 [1]  0.5178194  0.5068474  0.4966723  0.4001511  0.3682761  0.2510546
 [7]  0.1937007  0.1569781 -0.8098995 -6.3224046

Largest  eigenvalues:
 [1] 64696145 59715023 56604277 56306975 54524378 52795171 52360671 51600397
 [9] 51158899 50489429

Smallest eigenvalues:
 [1]  0.4720272  0.4532888  0.4397408  0.3437993  0.2903784  0.2699869
 [7]  0.2437427  0.2251591  0.1048481 -0.3145790

Largest  eigenvalues:
 [1] 62874802 59644683 56751587 54942486 54725488 53265018 51928608 51313040
 [9] 50887639 50504973

Smallest eigenvalues:
 [1]   0.201544408   0.177171397   0.144626455   0.091076722   0.004548103
 [6]  -0.148259185  -0.289884175  -1.575043898 -13.263955105 -79.579311945

Largest  eigenvalues:
 [1] 66433540 60511774 57856772 56895086 55170876 54014777 52720474 52584682
 [9] 52453225 51907112

Smallest eigenvalues:
 [1]  0.46984889  0.40535815  0.38373415  0.31445632  0.30424470  0.20821907
 [7]  0.20479267  0.05942211 -0.19443799 -0.46006852

Largest  eigenvalues:
 [1] 66295014 60055206 57477136 56958999 54760055 53148485 52942568 52550470
 [9] 51745790 51682275

Smallest eigenvalues:
 [1]  0.4332651  0.4308242  0.3583716  0.2661786  0.2522003  0.2274065
 [7]  0.2265533  0.1934069 -0.3544133 -0.7795985

Largest  eigenvalues:
 [1] 64693328 60433656 57576991 56403901 55390048 53911610 52457037 52451694
 [9] 52257789 51384720

Smallest eigenvalues:
 [1]  0.48280950  0.44458607  0.41297101  0.39655617  0.38245266  0.36329757
 [7]  0.32586276  0.27999321  0.06975889 -6.56738212

Largest  eigenvalues:
 [1] 64854384 59736790 57216159 55827698 54986718 53582752 51994993 51922870
 [9] 51396962 50504492

Smallest eigenvalues:
 [1]  0.39820962  0.37804776  0.35628992  0.34829729  0.33528928  0.26461008
 [7]  0.23280099  0.21468200  0.21248646 -0.09839829

Largest  eigenvalues:
 [1] 64267814 60678050 57849347 56272576 55681003 54238859 52495499 52198944
 [9] 52099877 51544577

Smallest eigenvalues:
 [1]  0.41887154  0.31343041  0.30939448  0.27154099  0.25444678  0.17239703
 [7]  0.15336427  0.09724497  0.03846142 -4.62230843

Largest  eigenvalues:
 [1] 64383814 60560185 57378585 55773472 55580811 53903495 52976999 52062940
 [9] 51987916 51724972

Smallest eigenvalues:
 [1]   0.3321982   0.3099001   0.2951779   0.2923714   0.2593001   0.2387524
 [7]   0.1839233  -0.4091854  -2.7724645 -32.5836795

Largest  eigenvalues:
 [1] 62714617 60840721 57265914 55515224 55452445 53767227 52345127 52260058
 [9] 51422482 51241427

Smallest eigenvalues:
 [1]  0.5511623  0.5137978  0.3973151  0.3698572  0.2714385  0.2601094
 [7]  0.2599047  0.2129028 -0.6039468 -3.7364834

Largest  eigenvalues:
 [1] 62892615 60256629 57165253 55863827 54884526 54202055 52521761 52276902
 [9] 51146891 50914739

Smallest eigenvalues:
 [1]  0.4482666  0.4132002  0.4043009  0.3446677  0.3057986  0.2371929
 [7]  0.2231859  0.1849645 -0.3806293 -1.2192000

Largest  eigenvalues:
 [1] 64912913 60365249 57915971 56245247 55245503 53419182 52538053 52231428
 [9] 52175101 51690647

Smallest eigenvalues:
 [1]  0.5429959  0.5029861  0.4617789  0.3660918  0.3307626  0.3030359
 [7]  0.2941898  0.2423092  0.2093103 -1.4799506

Largest  eigenvalues:
 [1] 65310285 61205449 58387605 56788205 56219393 54775783 53121119 52773489
 [9] 52719250 52173340

Smallest eigenvalues:
 [1]  0.5757681  0.5170118  0.3817440  0.3695223  0.3446561  0.2849770
 [7]  0.2656549  0.1959019  0.1725764 -0.2854450

Largest  eigenvalues:
 [1] 65604887 60614573 57557609 56305090 55216214 53469352 52454467 52402152
 [9] 51998177 51419384

Smallest eigenvalues:
 [1]  0.36186136  0.22478492  0.21982184  0.20091140  0.15866189  0.05321775
 [7] -0.02753659 -0.18814786 -0.73649376 -1.83930125

Largest  eigenvalues:
 [1] 63126554 60013297 57218445 55247689 54841283 53218257 52264101 51445755
 [9] 51232175 51009566

Smallest eigenvalues:
 [1]  0.5889792  0.5325782  0.4799873  0.4081175  0.3822931  0.3360016
 [7]  0.3165796  0.2596338  0.1156711 -0.2926909

Largest  eigenvalues:
 [1] 65118790 60088139 57034713 56302051 54940701 53275640 52253927 51582079
 [9] 51517645 50753394

Smallest eigenvalues:
 [1]  0.5462084979  0.4596289757  0.4425864504  0.4092067562  0.3946468524
 [6]  0.3602657817  0.2447315615  0.1547394310  0.0193964287 -0.0004436288

Largest  eigenvalues:
 [1] 61796298 59213323 56855892 54938033 54377620 53172281 51519650 51155755
 [9] 50459207 50163983

Smallest eigenvalues:
 [1]  0.5161071  0.4864884  0.3918835  0.3876054  0.3870837  0.3559756
 [7]  0.3370716  0.2599319  0.1657500 -0.3115592

Largest  eigenvalues:
 [1] 63609026 59775759 57293552 55094734 55002818 53520016 51926489 51647070
 [9] 51198665 51058964

Smallest eigenvalues:
 [1]  0.3844704  0.2869086  0.2678615  0.2414951  0.1662366  0.1649803
 [7] -0.2931335 -1.8512067 -2.2663332 -2.6126528

Largest  eigenvalues:
 [1] 65399203 60358455 58444718 55669337 55604086 54514489 52942546 52772772
 [9] 51926528 51626828

Smallest eigenvalues:
 [1]  0.40034295  0.36388802  0.34484062  0.25063321  0.22174912  0.18652089
 [7]  0.17892611  0.17140740 -0.07209435 -1.44236241

Largest  eigenvalues:
 [1] 63763732 59405332 57413034 55948630 54263154 52938941 51853268 51781222
 [9] 51477112 50766747

Smallest eigenvalues:
 [1]   0.4313798   0.4229571   0.3923769   0.3760412   0.3112095   0.3109464
 [7]   0.2526391  -0.1554225  -0.8900478 -16.5592499

Largest  eigenvalues:
 [1] 63152583 59993602 57085284 55419122 55064076 53533837 51865233 51627201
 [9] 51350229 50770855

Smallest eigenvalues:
 [1]  0.41276988  0.40321953  0.40185311  0.23765414  0.22292144  0.19771954
 [7]  0.16912023  0.08295498 -0.67170684 -1.12303792

Largest  eigenvalues:
 [1] 64139585 59804873 57183976 56051727 54822511 53324425 52168035 51909804
 [9] 51898737 51015452

Smallest eigenvalues:
 [1]  0.53276256  0.46594849  0.43924900  0.39697820  0.31945362  0.29167345
 [7]  0.28980983  0.25929236 -0.01086218 -0.13285833

Largest  eigenvalues:
 [1] 63273773 59720686 57231816 54882059 54713773 53247788 51957631 51438734
 [9] 50977746 50627827

Smallest eigenvalues:
 [1]  0.46748942  0.34423002  0.31387525  0.24507436  0.24340465  0.15076138
 [7]  0.09617273 -0.69562439 -1.18076695 -4.47359899

Largest  eigenvalues:
 [1] 61526702 59905855 57046257 56146055 54189655 54017569 52814392 51694398
 [9] 50826284 50742824

Smallest eigenvalues:
 [1]  0.4923785  0.3984089  0.3937567  0.3549236  0.3122952  0.3109052
 [7]  0.2706105  0.2394305 -0.2794429 -0.9258592

Largest  eigenvalues:
 [1] 62845171 59886485 57063124 55382063 54919764 53291971 51992605 51803111
 [9] 51226728 50848565

Smallest eigenvalues:
 [1]  0.5459344  0.4891997  0.4786678  0.4104942  0.3288842  0.2848951
 [7]  0.2847681  0.1815102  0.1424909 -0.3119798

Largest  eigenvalues:
 [1] 65061303 60674413 57479748 55796434 55694628 53880747 52647245 52183251
 [9] 52014319 51568813

Smallest eigenvalues:
 [1]   0.4503516   0.4380780   0.3798042   0.3404305   0.2878967   0.2793281
 [7]   0.2346284   0.2103938  -0.1151525 -16.0634542

Largest  eigenvalues:
 [1] 63801784 60786631 57408112 56000477 55902736 54203077 52619103 52096529
 [9] 51947571 51564852

Smallest eigenvalues:
 [1]  0.53132581  0.47939255  0.44143427  0.41821041  0.40036708  0.39283256
 [7]  0.26125258  0.25440452  0.04234018 -0.05788324

Largest  eigenvalues:
 [1] 61908991 60921013 57583495 55719933 55087847 53944109 52199272 52187053
 [9] 51311269 51051015

Smallest eigenvalues:
 [1]  0.55633858  0.55459905  0.51682411  0.45409873  0.36279853  0.28371626
 [7]  0.27734235  0.24286158  0.16919659 -0.04879497

Largest  eigenvalues:
 [1] 65870742 60146762 57478444 56195525 55011350 53145199 52490917 51801209
 [9] 51725161 51007665

Smallest eigenvalues:
 [1]  0.29941142  0.28255724  0.26899353  0.26408874  0.24559457  0.18665779
 [7]  0.03204212 -0.16302223 -0.62465421 -0.77217633

Largest  eigenvalues:
 [1] 64692988 61448493 58366388 56660214 55912037 54073882 53831609 52892771
 [9] 52302123 52147463

Smallest eigenvalues:
 [1]  0.4999409  0.4392076  0.3276502  0.3157298  0.2767293  0.2717452
 [7]  0.2070822 -0.2590587 -0.8639667 -1.6282596

Largest  eigenvalues:
 [1] 67366903 60256808 57940051 57564310 55064301 53967328 53436716 52456655
 [9] 51710071 51405849

Smallest eigenvalues:
 [1]  0.5156335  0.4515649  0.3378194  0.3355335  0.3027039  0.2655431
 [7]  0.1546276 -0.2241411 -0.6055852 -2.8591961

Largest  eigenvalues:
 [1] 64976128 59853182 57012931 55533646 54739601 53080864 52033152 51713440
 [9] 51370904 51200155

Smallest eigenvalues:
 [1]  0.45290694  0.44925560  0.40351757  0.30919014  0.25459596  0.17384010
 [7]  0.17026083  0.11022259 -0.02776676 -0.31821990

Largest  eigenvalues:
 [1] 61432810 59985832 57193901 54767519 54531619 53265460 51504147 51440013
 [9] 50665853 50507831

Smallest eigenvalues:
 [1]  0.52622357  0.50680189  0.46369968  0.38817044  0.25210285  0.20384335
 [7]  0.20338961  0.19141173  0.12685740 -0.07178254

Largest  eigenvalues:
 [1] 66202026 60897045 58063314 57194555 55475013 53311879 53307392 52911864
 [9] 52169260 52040648

Smallest eigenvalues:
 [1]  0.52234995  0.45402038  0.43663174  0.41554924  0.40579497  0.28840887
 [7]  0.13245821  0.08557838 -0.75062913 -2.86560419

Largest  eigenvalues:
 [1] 65374252 60863355 57518564 57202689 55322858 53729674 52938897 52731382
 [9] 52403820 51485447

Smallest eigenvalues:
 [1]  0.39084695  0.36914184  0.30025457  0.26474489  0.24560916  0.13375087
 [7] -0.05033575 -0.05521544 -1.65185785 -4.82023978

Largest  eigenvalues:
 [1] 65400558 61101185 57473590 56295735 56083895 54190276 53128989 52606597
 [9] 52276979 51737422

Smallest eigenvalues:
 [1]  0.5780271  0.5484737  0.4845899  0.4175106  0.3248807  0.3082034
 [7]  0.2996564  0.2535816  0.1127043 -1.8725486

Largest  eigenvalues:
 [1] 64195941 60285711 57416563 56098671 55456384 53595903 52126600 52038599
 [9] 51843900 50875133

Smallest eigenvalues:
 [1]  0.4125340  0.3617126  0.3277186  0.3125530  0.2747283  0.2422840
 [7]  0.2351366 -0.0112572 -0.1799453 -3.4878682

Largest  eigenvalues:
 [1] 63717076 59716227 57283402 55579766 55459389 53816847 51984241 51458117
 [9] 51418582 50617527

Smallest eigenvalues:
 [1]   0.158950216   0.138747110   0.095224104  -0.003804913  -0.234584077
 [6]  -0.376242437  -1.934583821  -2.615940916 -11.366270562 -42.885478214

Largest  eigenvalues:
 [1] 62210639 59008470 56523613 54883978 54828048 53128814 52077971 51570901
 [9] 50778089 50548099

Smallest eigenvalues:
 [1]  0.5606641  0.5178252  0.4550787  0.4136515  0.4128867  0.3802478
 [7]  0.2519912  0.1598622  0.1547290 -0.8574677

Largest  eigenvalues:
 [1] 64056664 60121490 56752301 55494222 55381324 53671925 52297441 51526186
 [9] 51485984 50661714

Smallest eigenvalues:
 [1]  0.3618078  0.3443411  0.3132744  0.3096701  0.2477763  0.1948330
 [7]  0.1731113  0.1549858 -0.1465254 -1.7413840

Largest  eigenvalues:
 [1] 65003619 59255885 56773132 56444943 54675165 53113186 52481697 51687999
 [9] 50838184 50270887

Smallest eigenvalues:
 [1]  0.54426953  0.48562884  0.44388094  0.42821535  0.34888349  0.26731143
 [7]  0.23998793  0.12993691 -0.02737212 -0.44424968

Largest  eigenvalues:
 [1] 65550998 60465719 57587850 56121483 55591168 54046566 52740053 52235743
 [9] 52054542 51864556

Smallest eigenvalues:
 [1]  0.42169354  0.39682148  0.39261339  0.33989100  0.32935115  0.22938059
 [7]  0.21809042  0.08154989 -0.51332259 -1.69754904

Largest  eigenvalues:
 [1] 62982266 60428341 57530010 55442263 55109750 53755454 52044607 51863246
 [9] 51237195 50876446

Smallest eigenvalues:
 [1]  0.52459098  0.51053602  0.35515245  0.33980637  0.30118029  0.21321678
 [7]  0.18689065  0.12651958 -0.08038237 -0.27084950

Largest  eigenvalues:
 [1] 62531812 59705008 56872443 55459454 54529444 53538600 52154088 51877923
 [9] 51114746 50752980

Smallest eigenvalues:
 [1]  0.52171155  0.49562694  0.49447592  0.44617475  0.38149637  0.31870354
 [7]  0.29634753  0.25018251  0.24601879 -0.05523009

Largest  eigenvalues:
 [1] 64247196 60702959 57811455 56511277 55326045 53743379 52828963 52591858
 [9] 51993151 51674647

Smallest eigenvalues:
 [1]  0.4856958  0.4851811  0.4698809  0.4536448  0.3643883  0.2650687
 [7] -0.6305192 -2.6167447 -6.9863113 -8.5079493

Largest  eigenvalues:
 [1] 65767631 60192997 57414536 56986437 55017791 53821130 52858098 52238089
 [9] 52077024 51222271

Smallest eigenvalues:
 [1]  0.62210840  0.51544880  0.51387347  0.48528008  0.32260528  0.24645020
 [7]  0.12895498 -0.07462728 -0.42245680 -1.01614870

Largest  eigenvalues:
 [1] 65192444 60626017 57792212 56461719 55435968 53943961 52519697 52470748
 [9] 52090557 51424514

Smallest eigenvalues:
 [1]  0.6123584  0.5180206  0.4697137  0.4490226  0.3160412  0.2512016
 [7]  0.2429981  0.2276873 -0.3757075 -2.4693377

Largest  eigenvalues:
 [1] 64512255 60939379 57510406 55856670 55830455 54158421 52430522 52328012
 [9] 51957775 51395342

Smallest eigenvalues:
 [1]  0.50285305  0.42119011  0.33842476  0.32740418  0.32042739  0.23890470
 [7]  0.19142499  0.08581807 -1.07829160 -1.57508291

Largest  eigenvalues:
 [1] 63212056 60557886 56946985 55900077 55025855 53336499 52238259 51773561
 [9] 51602547 50807734

Smallest eigenvalues:
 [1]  0.45464091  0.43894610  0.40747460  0.35503655  0.31265786  0.29094006
 [7]  0.23802606 -0.01934277 -0.28903710 -4.57884983

Largest  eigenvalues:
 [1] 65020984 59922993 57531605 56134514 54805829 53182111 52268454 51935433
 [9] 51843598 51096607

Smallest eigenvalues:
 [1]  0.56759586  0.56189578  0.41514216  0.38441990  0.37557169  0.33648270
 [7]  0.31638758  0.30483067  0.09840617 -0.14551585

Largest  eigenvalues:
 [1] 63645797 60322326 57525748 55656889 55258278 53726751 52232143 51994825
 [9] 51743852 51118727

Smallest eigenvalues:
 [1]  0.3709913079  0.3575170694  0.3507039142  0.1969533121  0.1864759946
 [6]  0.1562555900  0.0005067288 -0.1428596895 -1.4036005271 -4.8821616389

Largest  eigenvalues:
 [1] 64609448 59304612 56830482 54940485 54928090 53223922 52235880 51373447
 [9] 51291503 50684140

Smallest eigenvalues:
 [1]  0.5378951  0.4152804  0.4125642  0.3603796  0.3574761  0.3439116
 [7]  0.2817114  0.2490014 -1.1908588 -2.1304555

Largest  eigenvalues:
 [1] 63262192 60140606 57396805 55933981 54780326 53424578 52233240 51771048
 [9] 51709538 51262078

Smallest eigenvalues:
 [1]  0.4139446  0.4003821  0.3210964  0.2948652  0.2792177  0.2462764
 [7]  0.1485048 -0.1665783 -0.2396231 -1.1166169

Largest  eigenvalues:
 [1] 65025560 59874668 57719944 55994411 54705952 53532693 52281068 51764539
 [9] 51555256 50870097

Smallest eigenvalues:
 [1]  0.27577537  0.27200639  0.22353516  0.19749033  0.18221636  0.17288771
 [7]  0.14576046  0.06904516  0.04295397 -7.41265447

Largest  eigenvalues:
 [1] 62544032 60326473 57361667 55714935 55141761 53576873 52373218 52255801
 [9] 51519940 50889022

Smallest eigenvalues:
 [1]  0.34824419  0.32624775  0.32412938  0.30055734  0.28486927  0.24196818
 [7]  0.18425453  0.12732401  0.06721902 -1.14091795

Largest  eigenvalues:
 [1] 63695684 59558522 57054951 54907965 54775839 53308952 51675649 51204229
 [9] 51060347 50525826

Smallest eigenvalues:
 [1]  0.4461087  0.4100242  0.3564076  0.3077360  0.2705415  0.2075168
 [7]  0.1856098 -0.2798966 -1.4998011 -1.7307294

Largest  eigenvalues:
 [1] 65060073 59788240 57010817 56374372 54962676 53241951 52533464 52326643
 [9] 51834648 51339657

Smallest eigenvalues:
 [1]  0.4345425  0.3460610  0.3452705  0.3419106  0.2650077  0.1179957
 [7] -0.0407012 -0.0478749 -0.6777024 -2.7087721

Largest  eigenvalues:
 [1] 65968492 59864148 57144255 56690856 54655176 53140523 52731877 52259841
 [9] 51488220 51465275

Smallest eigenvalues:
 [1]  0.5542803  0.5512591  0.5228604  0.4515252  0.4155063  0.3076948
 [7]  0.2845276  0.2396812  0.1807905 -0.3428144

Largest  eigenvalues:
 [1] 63905137 59502253 56433069 55165699 54726656 53026970 51790581 51360145
 [9] 51208848 50453061

Smallest eigenvalues:
 [1]  0.464282566  0.429567178  0.415205333  0.378129428  0.336070306
 [6]  0.259183622  0.216600995  0.033002374  0.006506839 -0.042244432

Largest  eigenvalues:
 [1] 63444504 59522734 56847150 54871722 54615621 53105096 51765857 51333580
 [9] 51148670 50729429

Smallest eigenvalues:
 [1]  0.2372722011  0.2225235054  0.2015075882  0.0929144775 -0.0006222235
 [6] -0.2148215623 -0.2224678712 -0.4906172915 -3.0041167833 -3.3593404025

Largest  eigenvalues:
 [1] 65984700 59620554 56934014 56331887 54491746 53085033 52386737 51831911
 [9] 51436998 51028028

Smallest eigenvalues:
 [1]   0.42762804   0.41302478   0.40983814   0.40478580   0.35859747
 [6]   0.29442122   0.24534593  -0.08207897  -0.22919430 -10.25323178

Largest  eigenvalues:
 [1] 66549384 60508087 58540776 57026439 55228675 53282403 52964350 52299347
 [9] 51874854 51561945

Smallest eigenvalues:
 [1]  0.43601688  0.43273579  0.35929767  0.23928188  0.20507564  0.17869410
 [7]  0.16006524  0.15735591  0.06578892 -0.00884030

Largest  eigenvalues:
 [1] 64630586 60822955 58244976 55906329 55794335 54472403 52524935 52152055
 [9] 52006919 51281686

Smallest eigenvalues:
 [1]  0.40359710  0.29078424  0.28913387  0.24170298  0.13901900  0.09786114
 [7]  0.05907958 -0.07789732 -0.62712754 -1.53270335

Largest  eigenvalues:
 [1] 66245908 60488538 58068049 57335231 54946414 53464666 53188835 52880647
 [9] 51973737 51603106

Smallest eigenvalues:
 [1]  0.5617142  0.5599401  0.5083362  0.4206503  0.4119482  0.3668112
 [7]  0.3366286  0.2675939  0.0604494 -0.3029912

Largest  eigenvalues:
 [1] 63735402 60132302 56906030 55650046 55220216 53401815 51648460 51633654
 [9] 51566797 50685450

Smallest eigenvalues:
 [1]   0.40801604   0.40389371   0.33990475   0.31620434   0.31242965
 [6]   0.29992452   0.19358977   0.05662348  -2.66980776 -16.78142650

Largest  eigenvalues:
 [1] 63715977 60355191 57482558 56348171 55093563 53422203 52593371 52129938
 [9] 51897846 51409226

Smallest eigenvalues:
 [1]  0.4359027  0.3340343  0.3214657  0.3154707  0.2913169  0.2623459
 [7]  0.1672228  0.1357154 -0.1990377 -0.6847689

Largest  eigenvalues:
 [1] 66348176 60141875 57861809 57171768 54956008 53665745 53265811 52015686
 [9] 51831777 51070947

Smallest eigenvalues:
 [1]  0.35136998  0.30718827  0.30041682  0.27201388  0.15773403  0.15405150
 [7]  0.09808916 -0.05159188 -0.41221943 -2.22285813

Largest  eigenvalues:
 [1] 65043567 60219670 57130463 56659700 55000249 53405129 52629781 52582847
 [9] 52067161 51633049

Smallest eigenvalues:
 [1]  0.51304442  0.50070467  0.46793052  0.27801358  0.24674705  0.23081110
 [7] -0.02424976 -0.04756692 -0.45654980 -5.69860578

Largest  eigenvalues:
 [1] 65920403 59915422 57226585 56292137 54626891 53049380 52511637 51598153
 [9] 51550425 50591028

Smallest eigenvalues:
 [1]  0.42857068  0.42233951  0.33428665  0.28511286  0.27304769  0.06738081
 [7]  0.06159214 -0.02269885 -0.04753362 -2.62666136

Largest  eigenvalues:
 [1] 65373132 60371013 57772896 56582558 54839576 53505278 52709407 52231512
 [9] 51683667 51424207

Smallest eigenvalues:
 [1]   0.5527861   0.5191890   0.5109496   0.4552053   0.3569596   0.3308421
 [7]   0.1655400  -0.2481752  -0.2485755 -14.8087171

Largest  eigenvalues:
 [1] 64298426 59365986 56712783 55646048 54461595 52413836 51695841 51218018
 [9] 51195453 50362335

Smallest eigenvalues:
 [1]  0.5879522  0.5586164  0.4919110  0.4150249  0.3334988  0.3268393
 [7]  0.1071417 -0.1503952 -0.3219681 -1.5340869

Largest  eigenvalues:
 [1] 65576323 59905413 56922328 56518290 54638236 52638453 52332864 51549585
 [9] 51496916 50719685

Smallest eigenvalues:
 [1]  0.4452586  0.4253285  0.3897178  0.2382964  0.2189670  0.1750966
 [7]  0.1718941 -0.2858584 -0.8273859 -1.8439859

Largest  eigenvalues:
 [1] 66414068 60487398 57456568 57264512 55076190 53346019 53204558 52899585
 [9] 51922869 51881458

Smallest eigenvalues:
 [1]  0.579322470  0.495724326  0.475819493  0.457585349  0.357925325
 [6]  0.281455716  0.260275895 -0.001111107 -0.025555299 -0.430857479

Largest  eigenvalues:
 [1] 64228370 59963578 56998759 55226178 54795231 53208368 51859128 51758102
 [9] 51371890 51137177

Smallest eigenvalues:
 [1]  0.5053258  0.4497076  0.3842383  0.2980560  0.2917675  0.1977349
 [7]  0.1435539 -0.1076327 -0.1294795 -0.2666228

Largest  eigenvalues:
 [1] 64171263 59863976 57283743 55783843 54713585 53345568 52096852 51865869
 [9] 51747188 50845488

Smallest eigenvalues:
 [1]  0.4874405  0.4831283  0.4762235  0.4539044  0.4132227  0.2655075
 [7]  0.2654035  0.1649278 -0.7497195 -3.6836471

Largest  eigenvalues:
 [1] 64703810 60404872 56947943 56118265 55487160 53720828 51980623 51859404
 [9] 51791012 50951196

Smallest eigenvalues:
 [1]  0.53090711  0.52857996  0.40532111  0.31788968  0.29253928  0.28888361
 [7]  0.19107938  0.15011937  0.09222173 -0.41676164

Largest  eigenvalues:
 [1] 66256197 60857400 58269889 56445434 55358595 53862156 52668530 52366326
 [9] 51998104 51534903

Smallest eigenvalues:
 [1]  0.5632778  0.5368090  0.4897684  0.4513131  0.3952916  0.3864297
 [7]  0.3376703  0.1976449 -0.6951041 -1.5668546

Largest  eigenvalues:
 [1] 65400796 60174958 57188597 56547107 55292785 53800498 52453111 52216088
 [9] 52037523 51347479

Smallest eigenvalues:
 [1]  0.4661901  0.4080849  0.3753071  0.3083683  0.2636065  0.2484938
 [7]  0.2471375  0.2301789  0.1823539 -0.7611671

Largest  eigenvalues:
 [1] 64533648 59908454 56634158 55939317 54790492 53195839 51984942 51947753
 [9] 51519753 50875168

Smallest eigenvalues:
 [1]  0.55301142  0.53508523  0.48531364  0.46827562  0.28645905  0.26865378
 [7]  0.02387740  0.00851412 -0.04974736 -2.88107699

Largest  eigenvalues:
 [1] 65593782 60854360 57499461 55971282 55457354 53540754 52087735 51980213
 [9] 51712925 51238089

Smallest eigenvalues:
 [1]   0.4606986   0.4150882   0.3895332   0.3698456   0.3016220   0.1967325
 [7]  -0.2412423  -0.4353416  -4.2177200 -12.4418833

Largest  eigenvalues:
 [1] 66642222 60497163 58211313 57644600 54848392 53687334 53568098 52186766
 [9] 51817447 51307454

Smallest eigenvalues:
 [1]   0.4444366   0.4443511   0.4334750   0.4235253   0.3942360   0.3622654
 [7]   0.3180757   0.2967322   0.2288908 -26.3081421

Largest  eigenvalues:
 [1] 64396580 59472323 56986246 56387089 54520198 52437651 52340066 52099638
 [9] 51148609 50775198

Smallest eigenvalues:
 [1]  0.4832095  0.4816598  0.4099703  0.4003063  0.3778948  0.3354794
 [7]  0.3217115  0.2173993  0.1108074 -1.8167742

Largest  eigenvalues:
 [1] 64261862 60209997 57363944 55525902 55499370 53860182 51978820 51639716
 [9] 51407576 50509109

Smallest eigenvalues:
 [1]  0.4159491  0.3887005  0.3636342  0.3339376  0.2719207  0.2071950
 [7] -0.1554395 -0.1753642 -1.6493714 -3.1613924

Largest  eigenvalues:
 [1] 65831936 60436230 57527128 56524973 55460560 54029766 52557061 52076846
 [9] 51920156 50700276

Smallest eigenvalues:
 [1]  0.4991566  0.4450847  0.3848060  0.3752293  0.2972533  0.2585703
 [7]  0.2508491  0.1809243  0.1793704 -0.4216766

Largest  eigenvalues:
 [1] 64369103 60376898 57361903 56147636 55339820 53647877 52442006 52110402
 [9] 51926524 51411287

Smallest eigenvalues:
 [1]   0.3919340   0.3685712   0.2556420   0.2305837   0.2224366   0.1234887
 [7]  -0.2761569  -0.3616016 -11.4560427 -16.1561883

Largest  eigenvalues:
 [1] 65412366 59923422 57748249 56026030 55116757 53840008 52628318 52101955
 [9] 52094337 51747853

Smallest eigenvalues:
 [1]  0.5405937  0.4704579  0.4415416  0.3790221  0.3078424  0.2719302
 [7]  0.2296209  0.0186659 -0.0744638 -0.7226621

Largest  eigenvalues:
 [1] 65520519 60275203 57988226 56788103 54892970 53276053 52799941 52066448
 [9] 51868418 51291721

Smallest eigenvalues:
 [1]  0.57591289  0.53984830  0.44469187  0.40822789  0.35845191  0.26293753
 [7]  0.16328850  0.07937359 -0.04800096 -6.00683329

Largest  eigenvalues:
 [1] 64289485 59455696 56834512 55315299 54648085 53056009 51574283 51470745
 [9] 51377222 50566365

Smallest eigenvalues:
 [1]  0.58586685  0.51402486  0.42743002  0.40341103  0.34743473  0.22118159
 [7]  0.16053106  0.08174534  0.06713376 -0.40198544

Largest  eigenvalues:
 [1] 63682699 60558805 57862601 55217118 55062996 53841954 52020460 51958573
 [9] 51242398 51026267

Smallest eigenvalues:
 [1]  0.50906806  0.43992522  0.38269723  0.37411904  0.34578560  0.31168999
 [7]  0.22278832  0.09681184 -0.08672713 -1.92598298

Largest  eigenvalues:
 [1] 65216969 60390600 58111830 55821549 55480546 53756032 52516394 52155805
 [9] 52037381 51570033

Smallest eigenvalues:
 [1]  0.37125346  0.33622651  0.29554754  0.28392163  0.25954336  0.18204743
 [7]  0.10794663  0.07439459 -1.71415284 -1.76398125

Largest  eigenvalues:
 [1] 66281357 60659706 58058772 56696467 55097852 53702741 52758194 52705716
 [9] 52016429 51860011

Smallest eigenvalues:
 [1]  0.4915993  0.4851726  0.4418545  0.4320093  0.4096783  0.3744207
 [7]  0.3444420  0.1834299  0.1197684 -0.1764419

Largest  eigenvalues:
 [1] 61917877 59848034 56853819 54935056 54622197 53424167 51985452 51214462
 [9] 50675931 50435386

Smallest eigenvalues:
 [1]  0.44518733  0.41460183  0.32436259  0.31668699  0.29987897  0.19623957
 [7]  0.19542040  0.07259145 -2.80552716 -2.92745036

Largest  eigenvalues:
 [1] 66640375 61095951 57961718 57353193 56134267 54440333 53381865 53295039
 [9] 52478193 52079181

Smallest eigenvalues:
 [1]  0.4634656  0.3698625  0.3634382  0.3519396  0.3517787  0.3205757
 [7]  0.3197558  0.2100936  0.1818245 -0.3952971

Largest  eigenvalues:
 [1] 64753557 60999215 57910651 56065071 55968898 54252348 52532757 52183472
 [9] 52080847 51572769

Smallest eigenvalues:
 [1]  0.3858889  0.3639822  0.3448909  0.3411816  0.2677283  0.2321544
 [7]  0.1140600 -0.1581726 -0.7332295 -1.4332558

Largest  eigenvalues:
 [1] 65565004 59630014 57366436 56865100 54699649 53420088 52803464 51950272
 [9] 51565967 51071268

Smallest eigenvalues:
 [1]  0.4878207  0.4736053  0.4604077  0.4501137  0.4259043  0.2673243
 [7]  0.2605347  0.2207386  0.1528024 -0.8640331

Largest  eigenvalues:
 [1] 63872043 60705633 57978116 56097159 55768979 54475466 52770612 52723140
 [9] 51950648 51649096

Smallest eigenvalues:
 [1]   0.4226829   0.4049011   0.3693947   0.3473756   0.2799854   0.2396624
 [7]   0.1791423   0.1474199  -4.0729856 -19.3983485

Largest  eigenvalues:
 [1] 64321911 60430367 57812735 55732140 55625407 54268799 52640600 52389440
 [9] 51708865 51207869

Smallest eigenvalues:
 [1]   0.5553300   0.4967537   0.4364663   0.4144603   0.3296271   0.3032553
 [7]   0.2884542   0.2636767   0.1265461 -18.7405014

Largest  eigenvalues:
 [1] 63101342 60157442 57042025 55467023 54738047 53721113 51871042 51779396
 [9] 51009249 50904160

Smallest eigenvalues:
 [1]  0.4966046  0.4709479  0.3776067  0.3097582  0.2638198  0.2393345
 [7]  0.1111486 -0.1408088 -0.8568489 -1.4758753

Largest  eigenvalues:
 [1] 65270513 61372036 57764697 56673041 56384759 54655131 53518208 52651284
 [9] 52366803 51905607

Smallest eigenvalues:
 [1]  0.44346563  0.42564798  0.34981173  0.31166490  0.29445893  0.25320201
 [7]  0.22600226  0.21321413  0.07203382 -1.65710364

Largest  eigenvalues:
 [1] 63898644 59870162 57230832 55478703 54860298 53458313 51864385 51618377
 [9] 51568458 50839329

Smallest eigenvalues:
 [1]  0.46244840  0.38948767  0.37215329  0.26736355  0.19798737  0.16938847
 [7]  0.12489110 -0.01901132 -0.76193337 -3.55169477

Largest  eigenvalues:
 [1] 65952490 59884255 57836859 56179865 55038290 53870873 52556097 52365838
 [9] 52069754 51507352

Smallest eigenvalues:
 [1]  0.42999778  0.38555428  0.37323619  0.36471501  0.32681658  0.32183526
 [7]  0.15807602  0.05987858 -6.59816174 -7.33697480

Largest  eigenvalues:
 [1] 64034822 60439047 57778130 55756713 55345882 54104653 51944458 51895153
 [9] 51443279 50903441

Smallest eigenvalues:
 [1]  0.6424924  0.6164485  0.5648250  0.4252163  0.3786334  0.3785901
 [7]  0.3333032  0.2573348 -0.2328014 -0.3363637

Largest  eigenvalues:
 [1] 65843703 60504600 57741779 56989262 54939473 52987954 52922512 52512440
 [9] 51803876 51612969

Smallest eigenvalues:
 [1]  0.56231586  0.39004207  0.36305529  0.32163075  0.27072760  0.24938666
 [7]  0.22502081  0.08064115 -0.35063075 -0.43664614

Largest  eigenvalues:
 [1] 65587673 60830487 57764657 56726586 55570430 53833902 52855569 52680560
 [9] 52038380 51483534

Smallest eigenvalues:
 [1]  0.4295399  0.3392148  0.3266543  0.3067237  0.2652543  0.2038584
 [7]  0.1140841 -0.1150886 -0.2993984 -1.2668640

Largest  eigenvalues:
 [1] 65242863 60345619 57795897 56458293 55203857 53578015 53318279 52652814
 [9] 51949893 51697251

Smallest eigenvalues:
 [1]   0.430067710   0.422533650   0.298756962   0.277670314   0.149106526
 [6]   0.004114766  -0.151584554  -1.716368655 -14.456496183 -15.246523300

Largest  eigenvalues:
 [1] 64570556 60491679 57362371 55997647 55204651 53481933 51974861 51894203
 [9] 51866692 50972864

Smallest eigenvalues:
 [1]  0.4367080  0.3518828  0.3323773  0.3312061  0.3238202  0.3020763
 [7]  0.2846286  0.2665455 -0.1121726 -1.1884098

Largest  eigenvalues:
 [1] 65735735 60835951 58215531 56787345 55486000 54009957 52739215 52403891
 [9] 52355074 51511373

Smallest eigenvalues:
 [1]  0.34953304  0.34263765  0.33106232  0.28835138  0.28621615  0.27790996
 [7]  0.24896089  0.20303937  0.08655229 -2.27140333

Largest  eigenvalues:
 [1] 65095325 60085501 57590523 56051404 54770889 53440447 52167452 51943210
 [9] 51656173 51275428

Smallest eigenvalues:
 [1]  0.6592048  0.6404003  0.5166595  0.4033482  0.4028323  0.3708722
 [7]  0.3462916  0.2698337  0.2648815 -0.7286708

Largest  eigenvalues:
 [1] 64613077 59920510 57132441 55773065 55111497 53670501 52220693 51902478
 [9] 51703973 50873263

Smallest eigenvalues:
 [1]  0.37891647  0.31123961  0.30510601  0.19230167  0.17716224  0.03259586
 [7] -0.17742905 -0.64515518 -2.02278639 -2.28797808

Largest  eigenvalues:
 [1] 65900707 60756964 58434230 56451026 55575079 54007667 52663257 52506551
 [9] 52413928 51885792

Smallest eigenvalues:
 [1]  0.45556575  0.36751171  0.35966646  0.26996310  0.26295304  0.19468767
 [7]  0.18823328 -0.03956099 -0.15294538 -0.34344492

Largest  eigenvalues:
 [1] 63440266 61070682 56983675 55922306 55303250 54043908 52022979 51873568
 [9] 51411685 50654573

Smallest eigenvalues:
 [1]  0.4905209  0.4643631  0.4284030  0.4142746  0.2207196  0.1673253
 [7] -0.5509606 -1.6271276 -7.1104395 -9.8297614

Largest  eigenvalues:
 [1] 65516259 59914351 57209289 56836790 54941499 52939629 52716622 52506521
 [9] 51921697 51562362

Smallest eigenvalues:
 [1]  0.4106379  0.3301665  0.2167164  0.2040239  0.1352433  0.1261937
 [7] -0.1479056 -1.4012180 -1.9481681 -4.5814904

Largest  eigenvalues:
 [1] 62053635 59553829 56229488 54892512 54870917 53141701 52027549 52017605
 [9] 50939490 50742460

Smallest eigenvalues:
 [1]  0.23339206  0.19264821  0.14566220  0.09516121  0.01871251 -0.10373377
 [7] -0.28396276 -0.87932007 -1.53954870 -2.86300275

Largest  eigenvalues:
 [1] 65363760 61528790 58337241 57320176 55442653 53749587 53451881 52751825
 [9] 52355324 51516724

Smallest eigenvalues:
 [1]  0.46900975  0.45756721  0.45639449  0.42779764  0.38861220  0.27796359
 [7]  0.24700575  0.20415410  0.16402602 -0.02413903

Largest  eigenvalues:
 [1] 62994291 59486543 56982678 54894778 54810845 53335460 52007252 51275553
 [9] 50918118 50544221

Smallest eigenvalues:
 [1]  0.56332150  0.56235172  0.53824983  0.53555934  0.46745360  0.45266697
 [7]  0.38544392  0.23974666  0.09397433 -0.07977456

Largest  eigenvalues:
 [1] 63506834 60585083 57685873 55448152 55411504 53919463 52154542 51873020
 [9] 51453738 50900873

Smallest eigenvalues:
 [1]  0.45586335  0.44886781  0.38949076  0.37173644  0.36319228  0.27477958
 [7]  0.04376298  0.04111338 -0.18370843 -9.00470598

Largest  eigenvalues:
 [1] 65263619 60764933 57655387 57042414 55057333 53274063 53081235 52058941
 [9] 51956356 51192634

Smallest eigenvalues:
 [1]  0.42942178  0.42424857  0.39652557  0.38896025  0.33227749  0.31281139
 [7]  0.26494138 -0.09445423 -0.51650472 -1.42408393

Largest  eigenvalues:
 [1] 64162879 60036713 57612890 55807625 54920771 53641231 51860806 51835422
 [9] 51778135 50900906

Smallest eigenvalues:
 [1]  0.5132643  0.5029630  0.4351605  0.4099295  0.3557336  0.2691699
 [7]  0.2262361  0.1695444  0.1412563 -1.3564060

Largest  eigenvalues:
 [1] 63726205 60267131 57125561 55734594 55459744 53931121 52284879 51836487
 [9] 51321733 50949508

Smallest eigenvalues:
 [1]  0.6947738  0.5524289  0.5163589  0.3769426  0.3621315  0.3343969
 [7]  0.3005910  0.2647608  0.1340909 -0.1257241

Largest  eigenvalues:
 [1] 63915112 60359994 57515484 55705835 55580355 53864952 52717574 51906035
 [9] 51811247 51374724

Smallest eigenvalues:
 [1]   0.17399293   0.14668297   0.13014329   0.10154982   0.05478427
 [6]  -0.07858091  -0.08885453  -0.38554795  -2.55661303 -10.46824644

Largest  eigenvalues:
 [1] 63671141 59391123 56451760 55603415 54857795 53157005 51835080 51557921
 [9] 50900544 50269519

Smallest eigenvalues:
 [1]  0.5565602876  0.4412926206  0.3703934677  0.3242838418  0.2929735410
 [6]  0.2866446591  0.2326488857  0.0004668943 -0.4870154074 -0.5942967261

Largest  eigenvalues:
 [1] 64621816 60829664 57869410 56017177 55439920 53843014 52863578 52242244
 [9] 52173231 51954614

Smallest eigenvalues:
 [1]   0.4294170   0.2906370   0.2838302   0.2368419   0.2036671   0.1859544
 [7]   0.1632616   0.1387046  -1.4531621 -15.6338062

Largest  eigenvalues:
 [1] 64679069 59651279 56971323 56061394 54739390 53132849 52317677 52062137
 [9] 51683223 51105237

Smallest eigenvalues:
 [1]   0.4768358   0.4633440   0.4134908   0.3899816   0.3311158   0.3232596
 [7]   0.2825004  -0.6337067  -6.9747085 -26.9398822

Largest  eigenvalues:
 [1] 64526309 60636211 57295159 56336653 55681572 54043629 52302861 52158735
 [9] 52010805 51129006

Smallest eigenvalues:
 [1]  0.44937738  0.41200232  0.38136894  0.26573141  0.22418340  0.18096288
 [7]  0.15753976  0.12372860  0.01736977 -0.90399644

Largest  eigenvalues:
 [1] 65485371 61207567 58668150 56571645 55672649 54252856 52769983 52643571
 [9] 52480537 51858158

Smallest eigenvalues:
 [1]  0.4927097  0.3541109  0.3403424  0.3067935  0.3039201  0.2957033
 [7]  0.2955304  0.2553524  0.1724951 -0.6452331

Largest  eigenvalues:
 [1] 64363823 59914191 56930183 55718190 54838230 53186891 51957963 51857211
 [9] 51396822 51066086

Smallest eigenvalues:
 [1]  0.4445254  0.4325453  0.4180866  0.3392527  0.3293453  0.2918831
 [7]  0.2819983  0.2135124  0.1794837 -0.9750292

Largest  eigenvalues:
 [1] 65079999 60507571 57459036 56624897 54934481 53631010 52558210 52483901
 [9] 51857988 51722368

Smallest eigenvalues:
 [1]  0.35238406  0.30235391  0.28126035  0.23503907  0.23020427  0.01862637
 [7] -0.54217517 -0.62257215 -1.66134727 -6.06466464

Largest  eigenvalues:
 [1] 64206520 59327298 57117161 55543154 54364857 53267864 51922715 51723964
 [9] 51532529 51021170

Smallest eigenvalues:
 [1]  0.3727948  0.3474193  0.3254185  0.3116484  0.2841517  0.2740666
 [7]  0.2120624  0.1155873 -0.4931777 -3.9524265

Largest  eigenvalues:
 [1] 62045232 59317993 56434316 54636107 54404068 53041601 51763938 51297251
 [9] 50613816 50489818

Smallest eigenvalues:
 [1]  0.3933471  0.3471600  0.3320841  0.3306430  0.2960491  0.2025489
 [7]  0.1797307  0.1717850  0.1313368 -3.8661918

Largest  eigenvalues:
 [1] 64896235 60908382 57840302 56154951 55754018 54406921 52751216 52680298
 [9] 52092783 51906524

Smallest eigenvalues:
 [1]  0.58382175  0.46840075  0.43570285  0.39391324  0.38179398  0.33526374
 [7]  0.33285675  0.15951703 -0.05347295 -9.23003284

Largest  eigenvalues:
 [1] 64021201 60112179 57377663 55482512 55476044 54003150 52367237 52205834
 [9] 51580870 51232105

Smallest eigenvalues:
 [1]  0.5679771  0.5136341  0.4454096  0.4098713  0.3246302  0.2852869
 [7]  0.2810462  0.2742600  0.1594525 -0.9096981

Largest  eigenvalues:
 [1] 62402250 59945731 56876040 55088529 54775174 53395944 51771857 51663222
 [9] 50733360 50563583

Smallest eigenvalues:
 [1]  0.5208800  0.5131013  0.4176284  0.3495412  0.3087863  0.2598037
 [7]  0.2594486  0.1430163  0.1112036 -0.1455603

Largest  eigenvalues:
 [1] 64730411 60918235 58019251 56041332 55812023 54316581 52664103 52328449
 [9] 52179450 51424259

Smallest eigenvalues:
 [1]  0.51429120  0.49676158  0.44222096  0.39439018  0.34219113  0.31474323
 [7]  0.11792681  0.05927812 -0.03319816 -7.07977194

Largest  eigenvalues:
 [1] 63952055 59936772 57256508 55541418 55167004 53683301 52276794 51994404
 [9] 51563416 51075028

Smallest eigenvalues:
 [1]  0.31044308  0.25629393  0.16914060  0.13848943  0.12932323  0.04998798
 [7] -0.53621952 -0.99503219 -1.38720389 -3.18335418

Largest  eigenvalues:
 [1] 62771592 60134043 57204467 55531513 55205386 53424257 52509237 52349368
 [9] 51375022 51158186

Smallest eigenvalues:
 [1]   0.3435085   0.3334230   0.2694998   0.2170939   0.1734174   0.1204316
 [7]   0.1135274  -0.7253679  -5.1454549 -29.7942473

Largest  eigenvalues:
 [1] 65575891 60206493 57181444 56748017 55287651 53731993 52651717 52450969
 [9] 52098622 51678461

Smallest eigenvalues:
 [1]  0.54896002  0.53930877  0.52887691  0.32190308  0.27647123  0.23428633
 [7]  0.22939166  0.06935047 -0.02291231 -0.05160940

Largest  eigenvalues:
 [1] 63033814 60881869 57725918 56353474 54964041 54488758 52888474 52591832
 [9] 51648111 51144277

Smallest eigenvalues:
 [1]  0.53688674  0.50979492  0.35955751  0.34266514  0.33681509  0.22482783
 [7]  0.18510949  0.10494858  0.04029477 -1.21583142

Largest  eigenvalues:
 [1] 63082588 61122435 57922257 56548851 55201858 54717729 52950649 52864058
 [9] 51948054 51283083

Smallest eigenvalues:
 [1]  0.37055333  0.24397796  0.22535539  0.22064736  0.20276503  0.20001838
 [7]  0.16633918  0.05716543 -1.93005306 -6.40058671

Largest  eigenvalues:
 [1] 65278890 59918567 57430993 56262550 54734647 53438270 52354384 52071414
 [9] 51797266 51290060

Smallest eigenvalues:
 [1]  0.457640508  0.434488032  0.415186189  0.378885804  0.370192720
 [6]  0.294331408  0.156670212  0.151513969  0.002483472 -0.068920470

Largest  eigenvalues:
 [1] 64260653 60839144 58165575 56247786 55338077 53814764 52079468 52014303
 [9] 51922844 51010359

Smallest eigenvalues:
 [1]   0.34855723   0.32653035   0.21678353   0.20444853   0.03070099
 [6]  -1.47484974  -2.61706685  -9.63598610 -10.65152405 -11.81698325

Largest  eigenvalues:
 [1] 65085852 59936137 57667199 56556491 55233158 54006823 53023309 52398653
 [9] 52347806 51973266

Smallest eigenvalues:
 [1]   0.3381866   0.3227711   0.3098073   0.2812932   0.2717524   0.2368776
 [7]   0.1772994  -1.2831674  -2.5541371 -15.3659377

Largest  eigenvalues:
 [1] 64668112 60361693 57195391 56379975 54830152 53255052 52520586 52363800
 [9] 51869621 51710322

Smallest eigenvalues:
 [1]  0.6008290  0.5774503  0.5152635  0.4450602  0.4363860  0.4048657
 [7]  0.2738052  0.2437140  0.1016007 -0.2659326

Largest  eigenvalues:
 [1] 65662001 59818585 56814940 56366223 54458983 52704285 52380267 51463555
 [9] 51209721 50711322

Smallest eigenvalues:
 [1]  0.36773786  0.34527390  0.31587361  0.28753809  0.24899620  0.07115531
 [7]  0.07013047  0.02301751 -0.29917983 -0.55715220

Largest  eigenvalues:
 [1] 64833014 59910569 57528814 55484897 55387991 53913139 51807501 51686018
 [9] 51570911 50822061

Smallest eigenvalues:
 [1]  0.42114651  0.41012319  0.27469020  0.21575691  0.20137663  0.09823638
 [7]  0.03508838 -0.45886452 -0.91304983 -2.30407978

Largest  eigenvalues:
 [1] 64361593 60247304 57389767 55946292 55801165 54225426 52448197 52389107
 [9] 51873376 51778606

Smallest eigenvalues:
 [1]   0.5239711   0.4660117   0.4390764   0.4384642   0.2931430   0.2334313
 [7]   0.2302813   0.1873801   0.1763725 -11.2653385

Largest  eigenvalues:
 [1] 63453016 60212635 57687679 55459311 55121073 53799618 52661547 51824672
 [9] 51279725 51028949

Smallest eigenvalues:
 [1]  0.4941352  0.3978747  0.3490921  0.2902397  0.2815614  0.2734541
 [7]  0.2595843  0.2544340 -1.5936816 -4.4238888

Largest  eigenvalues:
 [1] 65845680 59805365 57340790 56821329 54719602 53206672 52712707 52219037
 [9] 51702344 51220631

Smallest eigenvalues:
 [1]   0.51356322   0.49695658   0.49159728   0.43954030   0.34125666
 [6]   0.23246579   0.20326497   0.14610412   0.02726586 -15.33415248

Largest  eigenvalues:
 [1] 64413183 60109496 56859240 56060069 55029419 53201102 52047343 52006692
 [9] 51767086 50956372

Smallest eigenvalues:
 [1]  0.5355418  0.4460271  0.4436493  0.3404052  0.2988852  0.2740152
 [7]  0.2665325  0.2030855 -0.1478093 -0.3066490

Largest  eigenvalues:
 [1] 64688108 60314315 57637293 55560905 55330792 53920476 52587938 52238865
 [9] 51664518 51446987

Smallest eigenvalues:
 [1]  0.50025753  0.44788931  0.37637313  0.34216412  0.28581862  0.27678297
 [7]  0.09094782 -0.01622387 -1.34507222 -6.79008198

Largest  eigenvalues:
 [1] 64534920 59809700 56904018 56148298 55038247 53457244 52232116 52175519
 [9] 51688107 51115216

Smallest eigenvalues:
 [1]  0.48890093  0.38292492  0.36992951  0.35624224  0.23811757  0.23788674
 [7]  0.18817711 -0.05535112 -0.38692746 -1.37068085

Largest  eigenvalues:
 [1] 63534652 59675338 57395507 55357123 54840424 53632265 52284759 51921644
 [9] 51519247 51114186

Smallest eigenvalues:
 [1]  0.50408815  0.43963425  0.41289794  0.38187241  0.35225835  0.34647649
 [7]  0.34299125  0.32091325  0.31336602 -0.02669146

Largest  eigenvalues:
 [1] 62895176 59742572 57136264 55640866 54940740 53281578 51674828 51576426
 [9] 51509171 50484428

Smallest eigenvalues:
 [1]  0.5317972  0.4111299  0.3156682  0.2807998  0.2799069  0.2146495
 [7]  0.1659147  0.1238339 -0.6588994 -0.7753490

Largest  eigenvalues:
 [1] 64118211 60527814 57381779 55982082 55740875 54021148 52745121 52385741
 [9] 52140453 51552308

Smallest eigenvalues:
 [1]   0.50709128   0.49099777   0.40388220   0.37044460   0.35276207
 [6]   0.05156476   0.03688797  -2.64826461  -3.19911244 -10.65902213

Largest  eigenvalues:
 [1] 63856036 60138867 56921212 55829284 55189170 53515160 51835841 51665493
 [9] 51643967 50642379

Smallest eigenvalues:
 [1]  0.513142749  0.395678723  0.356456868  0.339783740  0.223403441
 [6]  0.200601311  0.005595955 -0.353177970 -0.424262348 -1.266350097

Largest  eigenvalues:
 [1] 63734011 59548656 56744384 55444984 54823432 53028764 52564218 51473893
 [9] 51308682 50890905

Smallest eigenvalues:
 [1]   0.41250445   0.36135583   0.23407873   0.12024406   0.02703175
 [6]  -0.59760540  -1.05935942  -1.15977714 -14.21677087 -25.84205488

Largest  eigenvalues:
 [1] 65953425 59815186 57442187 56142899 54845114 53314603 52321618 52044911
 [9] 51935666 50849781

Smallest eigenvalues:
 [1]  0.36615439  0.31326129  0.28495931  0.21551577  0.19159089  0.13238991
 [7]  0.02555591 -1.91107869 -6.16149963 -8.45163422

Largest  eigenvalues:
 [1] 64811459 59869089 57150571 55992868 55291305 53664492 52036887 51766814
 [9] 51265665 50214149

Smallest eigenvalues:
 [1]  0.45007466  0.43451046  0.41871822  0.34876442  0.27131051  0.25260930
 [7]  0.17996303  0.13108908 -0.04422398 -3.82919130

Largest  eigenvalues:
 [1] 62928653 59214590 56752903 54675098 54613992 53038678 51411295 51156372
 [9] 50814684 50462889

Smallest eigenvalues:
 [1]  0.49268166  0.48263594  0.41107868  0.40034653  0.37068409  0.26057429
 [7]  0.14597205  0.07235150  0.03807847 -2.53513236

Largest  eigenvalues:
 [1] 62292103 59532020 56365181 54874367 54688050 53050250 52035823 51398565
 [9] 50818688 50648019

Smallest eigenvalues:
 [1]  0.5278855  0.4758727  0.4338333  0.4282913  0.4171706  0.3689617
 [7]  0.2936994  0.2033135 -0.1243822 -1.4423889

Largest  eigenvalues:
 [1] 65577663 59767918 56997841 56864343 54757559 52901387 52889416 51675037
 [9] 51295138 50629651

Smallest eigenvalues:
 [1]  0.5204820  0.4225804  0.4155447  0.3779917  0.3631986  0.2949551
 [7]  0.2277822 -0.1807936 -1.1845013 -1.5216757

Largest  eigenvalues:
 [1] 65648655 60112696 57563338 56832083 54708105 52908926 52670447 52074726
 [9] 51670763 51203976

Smallest eigenvalues:
 [1]  0.39859094  0.34904025  0.31045039  0.26102341  0.12235162  0.09026301
 [7]  0.02238457  0.02061492 -4.92707840 -5.92397543

Largest  eigenvalues:
 [1] 65156532 61344783 57639545 57079460 56097183 54121380 53700622 52650893
 [9] 52612872 52099386

Smallest eigenvalues:
 [1]  0.37820033  0.35014782  0.33763113  0.33480218  0.28982951  0.26945971
 [7]  0.20797659  0.19721865  0.08415929 -0.95241435

Largest  eigenvalues:
 [1] 66168494 59692238 57024740 56703378 54335689 52848992 52839439 52011249
 [9] 51248214 51202882

Smallest eigenvalues:
 [1]  0.4334646  0.3884285  0.3570164  0.3296284  0.2183761  0.2167296
 [7]  0.1806627  0.1454605 -0.8857873 -2.3714396

Largest  eigenvalues:
 [1] 64370625 59268930 56707960 55440157 54615398 53011247 51796337 51390240
 [9] 51073100 50413122

Smallest eigenvalues:
 [1]  0.58426383  0.58321723  0.53197649  0.44854330  0.40623896  0.39575861
 [7]  0.36774993  0.17371816 -0.04097231 -0.25655805

Largest  eigenvalues:
 [1] 63924784 59492838 56665637 55629089 54358797 52804916 51649014 51467250
 [9] 50915770 50044818

Smallest eigenvalues:
 [1]   0.3318537   0.2901188   0.2727990   0.2651640   0.2297298   0.1693474
 [7]  -0.1287857  -0.1425885  -3.0594349 -21.9744984

Largest  eigenvalues:
 [1] 65592052 60782668 58385805 56880154 55344360 54145498 52816661 52488715
 [9] 52267393 51392132

Smallest eigenvalues:
 [1]  0.45676739  0.44932882  0.36923430  0.34882823  0.30920800  0.27799927
 [7]  0.12146820  0.07497249 -0.27544281 -1.73156160

Largest  eigenvalues:
 [1] 62977568 60268357 57461357 55734827 55323960 54132613 52305680 52225240
 [9] 51333933 51131169

Smallest eigenvalues:
 [1]   0.37591592   0.34939391   0.28394355   0.22288594   0.02183537
 [6]  -0.13688291  -0.89638787  -1.87339689  -4.26093626 -33.15763459

Largest  eigenvalues:
 [1] 65204940 59795188 56925205 55414986 54673291 53127366 51908386 51523503
 [9] 51404041 51047409

Smallest eigenvalues:
 [1]  0.4117747  0.4005399  0.3992011  0.3304966  0.3046413  0.2551265
 [7]  0.1850499  0.1543968  0.1345448 -0.5482180

Largest  eigenvalues:
 [1] 63981840 59956176 57294991 55683757 55268825 53483755 52624990 51617780
 [9] 51583966 51339124

Smallest eigenvalues:
 [1]  0.54588648  0.54438498  0.46984053  0.43218464  0.41920238  0.28237188
 [7]  0.27370193  0.26754378 -0.04608023 -0.24557334

Largest  eigenvalues:
 [1] 64539581 59781570 56704900 55390191 54696216 53173699 51644082 51473733
 [9] 51166525 50415484

Smallest eigenvalues:
 [1]  0.3113205  0.2909393  0.2809136  0.2588262  0.1333198 -1.0004547
 [7] -1.4927454 -2.0314479 -2.2647917 -2.7687152

Largest  eigenvalues:
 [1] 65283855 60509423 57883477 55654332 55307358 53762030 52333977 51810699
 [9] 51671180 51616296

Smallest eigenvalues:
 [1]  0.4837935  0.4553574  0.4505911  0.4154184  0.4053612  0.4034359
 [7]  0.3928558  0.2583591  0.2003834 -0.3563524

Largest  eigenvalues:
 [1] 64274093 60120534 57524312 55883456 55363625 53796518 52096232 51948413
 [9] 51746521 50995978

Smallest eigenvalues:
 [1]  0.48284963  0.37793857  0.36901334  0.33060318  0.26928105  0.26230950
 [7]  0.22734393  0.18096328  0.03577805 -0.62467375

Largest  eigenvalues:
 [1] 63420055 60508344 57049049 55589578 55244582 53565600 52629417 51657562
 [9] 51581482 51412647

Smallest eigenvalues:
 [1]  0.4399150  0.4208253  0.2980640  0.2855796  0.2076432  0.1894704
 [7]  0.1833774  0.1710420 -1.2419875 -2.0152343

Largest  eigenvalues:
 [1] 63836011 60169673 57052417 55458551 55344531 53806757 52367084 52214421
 [9] 51573106 51281117

Smallest eigenvalues:
 [1]  0.53875488  0.47593114  0.38327921  0.38137554  0.36900828  0.35832974
 [7]  0.31410037  0.28686666  0.01598865 -0.63067804

Largest  eigenvalues:
 [1] 65686353 60443186 57702067 56451625 55058677 53640595 52604128 51954061
 [9] 51756421 51141710

Smallest eigenvalues:
 [1]  0.6032834  0.4546018  0.4216246  0.3932967  0.3325949  0.2875735
 [7]  0.2786494  0.2449993  0.2355360 -1.2404562

Largest  eigenvalues:
 [1] 66173796 60524674 57939570 56573687 55321825 53972627 52685442 52488056
 [9] 51963098 51526695

Smallest eigenvalues:
 [1]  0.47471732  0.41001096  0.37543119  0.35652599  0.18515664  0.15704361
 [7]  0.06375342 -0.08862345 -1.52155284 -1.85649957

Largest  eigenvalues:
 [1] 65208262 60859311 58154447 56587520 55354355 54065181 52496298 52355682
 [9] 52128816 51219621

Smallest eigenvalues:
 [1]   0.39010591   0.38772164   0.34102365   0.29848154   0.08962970
 [6]   0.06336244  -0.79794362  -1.84033589  -2.13556826 -15.01566994

Largest  eigenvalues:
 [1] 64984035 59649025 56652940 56467108 54477533 53017444 52281300 51805761
 [9] 51518878 50541685

Smallest eigenvalues:
 [1]  0.565502102  0.481928124  0.450176821  0.444762778  0.254680255
 [6]  0.185377803  0.168778671  0.006248232 -0.791545041 -1.916082975

Largest  eigenvalues:
 [1] 63903269 60301926 57102455 55441762 55389464 53852520 52380464 52100368
 [9] 51532276 51361169

Smallest eigenvalues:
 [1]  0.34335350  0.32955884  0.31210499  0.28523221  0.20733693  0.17953085
 [7]  0.15290637  0.09511059 -0.35694884 -8.53844157

Largest  eigenvalues:
 [1] 62109519 60423723 57509442 56030908 55091527 54258754 52722879 52428320
 [9] 51586847 51080760

Smallest eigenvalues:
 [1]  0.54457663  0.50456799  0.42099679  0.39756795  0.25794836  0.21988428
 [7]  0.09436892  0.03252724 -1.21052870 -2.42474555

Largest  eigenvalues:
 [1] 64225085 60746350 57121270 55768021 55680021 54068193 52412244 52254165
 [9] 51603579 51149800

Smallest eigenvalues:
 [1]  0.4249970  0.4218964  0.3080185  0.2841112  0.2789110  0.2096348
 [7]  0.2081632  0.1909149 -0.8827535 -1.0276920

Largest  eigenvalues:
 [1] 65997044 60156927 57604506 57299503 54940742 53533320 53270265 52143358
 [9] 52073714 51213849

Smallest eigenvalues:
 [1]  0.56352954  0.54750293  0.50053218  0.44036317  0.39531692  0.37396949
 [7]  0.28074698  0.20713717 -0.05200555 -0.50019092

Largest  eigenvalues:
 [1] 63554401 60391406 57058316 55398723 55028791 53332468 52090579 51626648
 [9] 51437210 51198436

Smallest eigenvalues:
 [1]  0.5216278  0.4307288  0.4200359  0.4128112  0.3793602  0.3494066
 [7]  0.3266821  0.2936509  0.2189408 -0.5980169

Largest  eigenvalues:
 [1] 65356849 60605480 58034169 56449423 55321652 53935545 52534872 52302176
 [9] 52238990 51552313

Smallest eigenvalues:
 [1]  0.5670216  0.4868008  0.4643145  0.3776589  0.3357970  0.1967524
 [7] -0.2041937 -0.2798641 -0.3427553 -1.2985528

Largest  eigenvalues:
 [1] 64857935 60050708 57421086 56157476 54776540 53297154 52221990 52155247
 [9] 51937533 51432883

Smallest eigenvalues:
 [1]  0.5204519  0.4595059  0.3175062  0.3045108  0.2837890  0.2703324
 [7]  0.2699931  0.2489191  0.1548238 -0.3876310

Largest  eigenvalues:
 [1] 63658788 59593115 57205743 55884840 54326103 52897787 51868289 51569947
 [9] 51179189 50504370

Smallest eigenvalues:
 [1]  0.60215041  0.52312027  0.43963147  0.40742445  0.36040984  0.32678984
 [7]  0.23726243  0.15771312  0.08797395 -1.64710534

Largest  eigenvalues:
 [1] 63729224 59870168 57103599 55552808 54842836 53335001 51700393 51589148
 [9] 51532808 50732599

Smallest eigenvalues:
 [1]  0.51699535  0.50554701  0.46953293  0.36119902  0.33526766  0.24925559
 [7]  0.20661811  0.01767268 -0.20654133 -2.27933558

Largest  eigenvalues:
 [1] 65474350 59576281 57216172 56437852 54575757 52772914 52502288 51935481
 [9] 51389338 51061769

Smallest eigenvalues:
 [1]  0.5694480  0.5523880  0.5045152  0.5028494  0.4763201  0.4132950
 [7]  0.2830584  0.2491897  0.2015181 -1.2580334

Largest  eigenvalues:
 [1] 64449168 60170429 57194726 56224052 54591774 53132886 52092576 51819879
 [9] 51444546 50890557

Smallest eigenvalues:
 [1]  0.56190068  0.46452296  0.44329888  0.34392623  0.29880342  0.29704275
 [7]  0.23897772  0.22827357  0.10759848 -0.02860955

Largest  eigenvalues:
 [1] 63464266 60584499 57340173 55646098 55046927 53508497 52082130 52056645
 [9] 51779392 51375070

Smallest eigenvalues:
 [1]   0.26208087   0.24585301   0.21944902   0.16933434   0.04943113
 [6]  -0.13696131  -0.21953305  -0.49880907  -7.20362046 -30.09318837

Largest  eigenvalues:
 [1] 64549792 59673595 57439029 57057742 54531930 53038942 52667570 52626709
 [9] 51898041 51161085

Smallest eigenvalues:
 [1]  0.4085359  0.3940913  0.3764065  0.2795715  0.2534743  0.2310830
 [7]  0.2050530 -0.1491286 -0.6555420 -0.7526958

Largest  eigenvalues:
 [1] 66595143 61672174 58871135 57767475 55776318 54171919 53697429 53028618
 [9] 52612064 52299067

Smallest eigenvalues:
 [1]  0.41985536  0.34744602  0.33963154  0.31382586  0.30230572  0.26991030
 [7]  0.07564455 -0.06564710 -0.21107038 -1.26331436

Largest  eigenvalues:
 [1] 64905909 60196206 57572316 56064966 54472796 53404938 52155079 51985153
 [9] 51755697 51473477

Smallest eigenvalues:
 [1]  0.56665657  0.53420415  0.45797345  0.40978592  0.40664044  0.32174511
 [7]  0.31384912  0.25903760  0.21983098 -0.03078901

Largest  eigenvalues:
 [1] 62874763 59657330 56979933 55310913 55017296 53414808 51892802 51589644
 [9] 51130094 50719204

Smallest eigenvalues:
 [1]  0.4523856  0.4283625  0.3907697  0.3051477  0.3035231  0.2303833
 [7]  0.2218429 -0.2850989 -1.8029084 -3.7914718

Largest  eigenvalues:
 [1] 65377809 60305610 57946480 56234647 55036341 53466446 52154180 52099074
 [9] 51646246 51298890

Smallest eigenvalues:
 [1]  0.5122451  0.4252697  0.3474607  0.2704993  0.2536186  0.2107707
 [7] -0.1067480 -0.7252001 -1.4469827 -2.4991351

Largest  eigenvalues:
 [1] 66019221 60793026 58029059 56541345 55605992 54053986 52853602 52756445
 [9] 52535871 51894446

Smallest eigenvalues:
 [1]  0.5480063  0.5343391  0.4154038  0.3745385  0.3115282  0.3097118
 [7]  0.2899511  0.2644871  0.2550387 -1.1419339

Largest  eigenvalues:
 [1] 65957063 60428386 57695892 56899556 55281366 53945526 52960656 52205228
 [9] 52171616 51310725

Smallest eigenvalues:
 [1]  0.42313923  0.40991807  0.35546893  0.26965487  0.25743431  0.21984232
 [7]  0.17762344  0.03473504 -0.20072486 -0.35606531

Largest  eigenvalues:
 [1] 62806641 59341796 57064658 54891543 54129130 53333256 51664474 51193060
 [9] 50610187 50399707

Smallest eigenvalues:
 [1]  0.40742609  0.38145632  0.33882274  0.29279607  0.24472277  0.24151625
 [7] -0.03001365 -0.16345436 -0.65571891 -1.35975963

Largest  eigenvalues:
 [1] 65031702 60393149 57758210 55406343 54893085 53524044 52187803 51585040
 [9] 51402406 51309189

Smallest eigenvalues:
 [1]  0.5486390  0.5156129  0.4195664  0.3918329  0.3564056  0.3364130
 [7]  0.3078334  0.2899076  0.1423248 -0.4230701

Largest  eigenvalues:
 [1] 65568706 59932364 57300922 56389533 54783745 53382263 52496445 51913007
 [9] 51894024 51087781

Smallest eigenvalues:
 [1]  0.5202029  0.5140320  0.5114391  0.4569729  0.3193646  0.2008783
 [7]  0.1655013 -0.1041523 -0.1415162 -1.9817074

Largest  eigenvalues:
 [1] 62284853 59429629 56001815 54760569 54235189 52787325 51521834 50790275
 [9] 50296574 49994857

Smallest eigenvalues:
 [1]  0.458718532  0.438775672  0.346712783  0.292639995 -0.002781101
 [6] -0.488893223 -0.595328606 -0.631138311 -0.997272931 -8.262999017

Largest  eigenvalues:
 [1] 64068459 59915218 57262574 55742748 55510255 53935162 52591694 52047434
 [9] 51691952 51551054

Smallest eigenvalues:
 [1]  0.48634602  0.47936263  0.46160011  0.40297858  0.29135504  0.25391103
 [7]  0.15862343 -0.07041424 -0.27646361 -2.43797582

Largest  eigenvalues:
 [1] 64332644 59897209 56470920 55183410 54838770 52954550 51578078 51243264
 [9] 51196083 50683648

Smallest eigenvalues:
 [1]   0.082846267  -0.005581226  -0.030466258  -0.197740171  -0.296137775
 [6]  -1.473451796  -3.707591644 -15.051128134 -16.126222283 -22.053085868

Largest  eigenvalues:
 [1] 63027655 59188696 56172161 54910120 54447753 52918552 52066746 51512786
 [9] 50886452 50576636

Smallest eigenvalues:
 [1]  0.61443220  0.58391278  0.52931697  0.46519635  0.38714309  0.31769963
 [7]  0.31209848  0.28466427 -0.02873817 -0.26177468

Largest  eigenvalues:
 [1] 64458968 60497059 57228017 56402655 55114734 53271518 52691697 52401047
 [9] 51809570 51546118

Smallest eigenvalues:
 [1]  0.47498698  0.43907139  0.38818481  0.36293211  0.33091355  0.29491259
 [7]  0.09201517 -0.10576516 -0.35183403 -1.04367754

Largest  eigenvalues:
 [1] 63381666 60251291 57431491 55902782 55061044 53274016 52041578 51976478
 [9] 51865078 50966852

Smallest eigenvalues:
 [1]   0.48231828   0.47064359   0.45700345   0.40907645   0.40052300
 [6]   0.22379677   0.20123232   0.12988660   0.04069322 -10.46087346

Largest  eigenvalues:
 [1] 62951268 60869894 57175218 55863040 55280518 53985731 52289225 51903576
 [9] 51316391 51023437

Smallest eigenvalues:
 [1]  0.4530239  0.4006749  0.3989586  0.3836229  0.3066514  0.2944299
 [7]  0.2567527  0.2222983 -0.8898274 -1.8020845

Largest  eigenvalues:
 [1] 65057921 60038553 57735901 56732147 54912000 53663192 52542060 52343902
 [9] 51908462 51562676

Smallest eigenvalues:
 [1]   0.36550792   0.35813549   0.35230397   0.34406144   0.26305876
 [6]   0.24066573   0.23861919  -0.09986753  -1.20440284 -38.91301801

Largest  eigenvalues:
 [1] 64280823 60552879 57440472 56068947 55365706 53849815 52481967 52422169
 [9] 52004825 51428756

Smallest eigenvalues:
 [1]  0.30389990  0.18237623  0.13047252  0.06924863  0.04933696 -0.46901345
 [7] -0.90598384 -2.05739524 -3.17678867 -4.88804782

Largest  eigenvalues:
 [1] 65814289 59346236 56544729 56045852 54180737 52715817 52117799 51668468
 [9] 51386058 50818227

Smallest eigenvalues:
 [1]  0.4704790  0.4511027  0.4456544  0.3703976  0.3397021  0.3101340
 [7]  0.2253259  0.1486695 -0.6726460 -7.8476789

Largest  eigenvalues:
 [1] 64782270 60821047 57882959 55958174 55825667 54258539 53097850 52174524
 [9] 52009772 51779557

Smallest eigenvalues:
 [1]  0.45904995  0.42647196  0.37888662  0.34251901  0.29816932  0.25406977
 [7]  0.18202582  0.14217355 -0.02940969 -0.37898229

Largest  eigenvalues:
 [1] 65024544 60817490 58143012 56262786 55649739 53885789 52846642 52231988
 [9] 52155433 51763212

Smallest eigenvalues:
 [1]  0.5455218  0.5303258  0.5080793  0.3732920  0.3393157  0.2854801
 [7]  0.2603636  0.2111399  0.1835342 -0.2537073

Largest  eigenvalues:
 [1] 61683626 59828641 57000643 55188322 54322432 53347141 52305285 51362369
 [9] 50994008 50451246

Smallest eigenvalues:
 [1]   0.23649434   0.19348165   0.19312155   0.15397270   0.13096985
 [6]   0.10018482  -0.03443138  -1.16534576  -3.06160539 -16.53599980

Largest  eigenvalues:
 [1] 66341359 60227728 57649906 57445546 55089442 53828172 53084267 52272703
 [9] 52117761 51550276

Smallest eigenvalues:
 [1]  0.5319380  0.4680688  0.4220319  0.3854596  0.3137564  0.2823258
 [7]  0.2642564  0.1643395  0.1085846 -0.7460929

Largest  eigenvalues:
 [1] 64284462 61047810 57952905 56361682 56287940 54565769 52995151 52526545
 [9] 52332539 51733625

Smallest eigenvalues:
 [1]   0.3872983   0.3718288   0.2864391   0.2854666   0.2345735   0.1857269
 [7]   0.1423190   0.1057419  -1.5526508 -20.2690897

Largest  eigenvalues:
 [1] 64179396 59689006 56898099 55128441 54901988 53398530 51759432 51524378
 [9] 51175761 50990164

Smallest eigenvalues:
 [1]  0.56961296  0.50211579  0.44720842  0.42223273  0.28130779  0.27534215
 [7]  0.25147123  0.21537915  0.13279976 -0.02095331

Largest  eigenvalues:
 [1] 64184582 60436894 57899031 55767740 54944131 54249461 52922033 51960906
 [9] 51704696 51225030

Smallest eigenvalues:
 [1]  0.53460627  0.48513699  0.45841813  0.41870000  0.35149039  0.26360364
 [7]  0.18542450  0.18530241  0.06283988 -0.02437856

Largest  eigenvalues:
 [1] 65182962 60004574 57855558 55896936 54950303 53383366 52172631 52169501
 [9] 51908222 51320099

Smallest eigenvalues:
 [1]  0.51792872  0.47212651  0.39845731  0.36518041  0.30676181  0.17766244
 [7]  0.16946911  0.02711115 -0.19072387 -1.27581554

Largest  eigenvalues:
 [1] 63289504 60655951 57091378 55756244 55607503 53517099 52384267 51853917
 [9] 51375768 50877973

Smallest eigenvalues:
 [1]   0.35428402   0.31058178   0.24239380   0.22800816   0.14366385
 [6]   0.12448140   0.03062687  -0.47869851  -5.06478606 -23.70376459

Largest  eigenvalues:
 [1] 64145724 59963504 57210943 55354251 55349428 53391942 52545954 51901404
 [9] 51661341 51559959

Smallest eigenvalues:
 [1]  0.51276329  0.49977214  0.45915053  0.43379300  0.30729224  0.21820161
 [7]  0.21343604  0.07972120  0.07041202 -0.47744528

Largest  eigenvalues:
 [1] 64650803 60190840 56983154 55833077 55120328 53489655 52413247 51909332
 [9] 51714069 51121776

Smallest eigenvalues:
 [1]  0.5025642  0.4721828  0.3668636  0.3230614  0.3146502  0.2637488
 [7]  0.2031941 -0.1467369 -1.4206695 -2.1226795

Largest  eigenvalues:
 [1] 63715589 60111156 57618041 56047231 55312315 54392889 52805750 52044473
 [9] 51444691 51115785

Smallest eigenvalues:
 [1]  0.57618936  0.50437109  0.44253556  0.40162290  0.38143383  0.37137165
 [7]  0.34330487  0.30554625  0.29375354 -0.01864911

Largest  eigenvalues:
 [1] 64837960 60267482 57162178 56120568 55417987 53476621 52603059 52252707
 [9] 51659271 51478283

Smallest eigenvalues:
 [1]  0.58747222  0.46247493  0.40615564  0.37252154  0.30938274  0.28769590
 [7]  0.27621797  0.21745839 -0.09714347 -0.32569202

Largest  eigenvalues:
 [1] 62227312 59514272 57100534 55172135 54543366 53429789 51792465 51402797
 [9] 50634725 50505127

Smallest eigenvalues:
 [1]  0.46147735  0.38056247  0.29618611  0.29002196  0.25084440  0.23936072
 [7]  0.16339231  0.08561973 -0.22944040 -0.86014343

Largest  eigenvalues:
 [1] 64639040 60353994 57656192 55508975 55380277 53875566 52403306 52172145
 [9] 51728105 51354625

Smallest eigenvalues:
 [1]  0.57988811  0.51784458  0.51381191  0.45793024  0.37170030  0.25735942
 [7] -0.06295068 -0.13836125 -0.52675154 -1.11966227

Largest  eigenvalues:
 [1] 63573915 59632503 56521656 55296162 54347553 52699011 51471821 51310638
 [9] 51268506 50448895

Smallest eigenvalues:
 [1]  0.5214007  0.4768875  0.4298152  0.4212942  0.3716958  0.3493964
 [7]  0.3239597  0.2362379  0.0699308 -0.1126082

Largest  eigenvalues:
 [1] 62602423 59104969 56230342 54975342 54357951 52666610 51535995 51278994
 [9] 50949311 50449507

Smallest eigenvalues:
 [1]   0.4619851   0.4373467   0.2804770   0.2619680   0.2446529   0.1830913
 [7]   0.1278125  -1.0903324 -10.9656909 -15.0244509

Largest  eigenvalues:
 [1] 62694405 60767248 56922074 55840588 55311746 54200471 52499931 52427577
 [9] 51266031 51192816

Smallest eigenvalues:
 [1]  0.4691136  0.4675890  0.4521460  0.4215578  0.3961748  0.3735821
 [7]  0.3233972  0.3086474  0.2560002 -2.5796506

Largest  eigenvalues:
 [1] 64598599 59810243 57125325 56740307 54552084 53168614 52570067 51720052
 [9] 51627871 50864959

Smallest eigenvalues:
 [1]  0.4950739  0.4182841  0.3632045  0.3131121  0.2895653  0.2741059
 [7]  0.2276522  0.1932157 -2.8474786 -4.3829595

Largest  eigenvalues:
 [1] 65116606 60196932 57591854 55723036 55332585 53907481 52410544 51780837
 [9] 51767593 51596822

Smallest eigenvalues:
 [1]  0.42881371  0.42843055  0.41330292  0.34826939  0.27471201  0.25118000
 [7]  0.22749707  0.05175862 -0.14980698 -0.62629763

Largest  eigenvalues:
 [1] 65562037 60096164 57572794 56167306 55241240 53826638 52312279 52252265
 [9] 52149083 51267152

Smallest eigenvalues:
 [1]  0.4398722  0.3542322  0.3352858  0.3278937  0.2830944  0.2761435
 [7]  0.2545866  0.2401905  0.2218608 -2.2757988

Largest  eigenvalues:
 [1] 64910548 60538846 57331118 56481801 55065655 53573763 52537394 52188850
 [9] 51958811 51082411

Smallest eigenvalues:
 [1]  0.5825820  0.5214181  0.4655219  0.3664353  0.2955329  0.2874229
 [7]  0.2437339  0.1509109  0.0836512 -0.2135389

Largest  eigenvalues:
 [1] 63600227 60522491 58172235 55890903 55116795 54617482 52792353 52355593
 [9] 51564019 51377719

Smallest eigenvalues:
 [1]  0.5395627  0.4969850  0.4725656  0.4008540  0.3506297  0.3187900
 [7]  0.2486233  0.1379814 -0.1586557 -3.6408846

Largest  eigenvalues:
 [1] 65308883 60894089 57845627 55820089 55800405 54306633 52204139 52164038
 [9] 52004589 51414024

Smallest eigenvalues:
 [1]  0.48776266  0.42660923  0.41964758  0.27900997  0.15372980  0.06051094
 [7]  0.04615386  0.03363386 -0.44282030 -0.98324188

Largest  eigenvalues:
 [1] 64127109 59514626 56570703 55316417 54641692 53116269 51745080 51484933
 [9] 51407195 50627684

Smallest eigenvalues:
 [1]  0.4480195  0.4290202  0.3620698  0.3434233  0.2289225  0.2185495
 [7]  0.2069439  0.1831452 -0.3371043 -0.7102083

Largest  eigenvalues:
 [1] 64740647 60270422 57081019 55734153 55635788 53974028 52272544 52230024
 [9] 51709908 51293591

Smallest eigenvalues:
 [1]  0.42985231  0.41042422  0.34230539  0.23361449  0.22150275  0.14118708
 [7] -0.06674456 -0.10785911 -0.23598135 -1.44185056

Largest  eigenvalues:
 [1] 63494786 60188033 57139279 55480965 54894605 53421251 52359781 51744015
 [9] 51676020 51441694

Smallest eigenvalues:
 [1]  0.4120311  0.3530477  0.3252676  0.3194421  0.2684833  0.2350737
 [7]  0.2124143 -0.2327599 -1.7259560 -2.9801417

Largest  eigenvalues:
 [1] 65316751 60665054 57846664 56859640 55050516 53122244 52641226 52524708
 [9] 51873115 51425983

Smallest eigenvalues:
 [1]  0.52949050  0.51977566  0.46030365  0.40256656  0.35034502  0.33285267
 [7]  0.24269094  0.20226650  0.16547097 -0.01262839

Largest  eigenvalues:
 [1] 65187895 60407227 57679795 56043085 55501186 53840607 52319963 52289786
 [9] 52257984 51238223

Smallest eigenvalues:
 [1]  0.5355013  0.4866217  0.4790100  0.4635764  0.3058997  0.2970957
 [7]  0.2919438  0.2288407  0.1453966 -3.0520384

Largest  eigenvalues:
 [1] 65569100 60320504 57311932 57140365 55450412 53761219 53027667 52832023
 [9] 52099835 51575430

Smallest eigenvalues:
 [1]  0.48432657  0.41722013  0.37305041  0.37101165  0.33759755  0.31536109
 [7]  0.23168491  0.10351043  0.01477636 -1.72761011

Largest  eigenvalues:
 [1] 63970672 59407406 56841595 55606637 54763370 53214451 51755641 51679362
 [9] 51332227 50420492

Smallest eigenvalues:
 [1]  0.44908713  0.33672758  0.29858326  0.27079519  0.24723851  0.24280154
 [7]  0.10900399  0.05530902 -0.18665752 -3.96915671

Largest  eigenvalues:
 [1] 62826251 59780839 56951517 55170505 54967555 53287056 51909405 51533791
 [9] 51047624 50584780

Smallest eigenvalues:
 [1]  0.4030885  0.3232050  0.3224300  0.3159119  0.1967794  0.1060946
 [7] -0.2897242 -0.3686685 -1.4298307 -7.2426381

Largest  eigenvalues:
 [1] 65759220 60303184 57770024 56244253 55241131 53816392 52653183 52439571
 [9] 52234521 51364901

Smallest eigenvalues:
 [1]  0.5345002  0.4299528  0.4105145  0.4070320  0.4041669  0.3091196
 [7]  0.2758072  0.2374550  0.0174245 -0.6222161

Largest  eigenvalues:
 [1] 63727698 59807558 56994452 55703662 54611526 53082872 51973343 51831475
 [9] 51644300 50924872

Smallest eigenvalues:
 [1]  0.5726498  0.5451262  0.3782607  0.3726637  0.3318796  0.3125551
 [7]  0.2861111  0.2766571  0.2449393 -1.8759456

Largest  eigenvalues:
 [1] 65742674 60936223 57944267 56924360 55434213 53981498 52850324 52456395
 [9] 52027138 51468123

Smallest eigenvalues:
 [1]  0.38466282  0.34412500  0.31278743  0.30168756  0.23161936 -0.02942748
 [7] -0.25532381 -0.45614524 -4.35004079 -5.87324734

Largest  eigenvalues:
 [1] 65762066 60747064 57700127 56797864 55418049 54033630 52750361 52219799
 [9] 51915712 51537272

Smallest eigenvalues:
 [1]  0.52767391  0.49658116  0.47108715  0.39378270  0.34990204  0.34411725
 [7]  0.33183697  0.31351879  0.26861629 -0.05393078

Largest  eigenvalues:
 [1] 63450183 60049111 57222506 55744530 54958459 53491121 51822211 51784969
 [9] 51723151 50800995

Smallest eigenvalues:
 [1]  0.3995092  0.3728310  0.3359519  0.3328351  0.2261396  0.2118650
 [7]  0.1919549  0.1627495 -0.6917800 -0.8362633

Largest  eigenvalues:
 [1] 65287175 59755730 57164905 56180634 54982685 53480718 52292760 52168119
 [9] 51420429 50551183

Smallest eigenvalues:
 [1]   0.18401539   0.14786746   0.06978497   0.04196946  -0.84799536
 [6]  -2.82244893  -2.91878869  -7.83955027 -10.48930386 -10.72465611

Largest  eigenvalues:
 [1] 63015292 59343386 56806285 54941365 54676381 53133107 51948958 51370627
 [9] 50939976 50505795

Smallest eigenvalues:
 [1]   0.4162112   0.3950567   0.3814943   0.3436694   0.3189936   0.2129440
 [7]   0.1635790  -0.3169176  -0.3860692 -19.4047729

Largest  eigenvalues:
 [1] 65649748 60371426 56967309 56704262 55039215 53297497 52701752 52199412
 [9] 52005626 51578201

Smallest eigenvalues:
 [1]  0.5782234  0.4555175  0.3931808  0.3645335  0.3009528  0.2992097
 [7]  0.2659478  0.2355635  0.1816481 -1.1072331

Largest  eigenvalues:
 [1] 64933711 60068767 57613945 55830360 54769876 53494796 51992486 51883485
 [9] 51870576 51180093

Smallest eigenvalues:
 [1]  0.3864456  0.3462517  0.3379102  0.3135665  0.1996375  0.1664430
 [7]  0.1406302 -0.1032846 -0.7843584 -8.0654301

Largest  eigenvalues:
 [1] 64984888 59654481 57039415 55800905 54704032 53336990 51936026 51840380
 [9] 51777594 51076770

Smallest eigenvalues:
 [1]  0.4050711  0.3740097  0.3333073  0.2391651  0.1913153  0.1636822
 [7]  0.1235815 -0.2511083 -1.3444760 -2.0810993

Largest  eigenvalues:
 [1] 62823361 60091349 56781597 55657152 55344127 53850259 52184449 52093415
 [9] 51217848 50950622

Smallest eigenvalues:
 [1]  0.4314467  0.4165944  0.4120417  0.4038097  0.4012641  0.3845278
 [7]  0.3272880  0.2725798  0.2274015 -1.4135281

Largest  eigenvalues:
 [1] 65653811 60055155 57417268 56343302 55034186 53681498 52401672 52220181
 [9] 52020759 51258859

Smallest eigenvalues:
 [1]  0.4758727  0.4608726  0.4556556  0.4323938  0.3701018  0.2365879
 [7]  0.2144270  0.1550570  0.1502910 -0.5561089

Largest  eigenvalues:
 [1] 63738614 60369039 56690112 55442243 55213960 53556840 52328046 51690484
 [9] 51385012 51218123

Smallest eigenvalues:
 [1]  0.56306153  0.52658127  0.47173434  0.45383100  0.42391527  0.42125430
 [7]  0.20202586  0.19171824  0.11256320 -0.03131913

Largest  eigenvalues:
 [1] 63656171 60871318 58012191 55488091 55388539 53966137 52083580 51992877
 [9] 51481041 51059512

Smallest eigenvalues:
 [1]  0.5011419  0.4319145  0.4033364  0.4013300  0.3480772  0.2668091
 [7]  0.2404480  0.1824264  0.1629935 -1.3841629

Largest  eigenvalues:
 [1] 64912517 60749296 58085408 56624964 55472811 53995104 52562384 52418681
 [9] 51998494 51274172

Smallest eigenvalues:
 [1]   0.020042392  -0.004704113  -0.073676077  -0.306308087  -0.827563103
 [6]  -1.333066779  -1.896066519  -4.566893032 -31.788612443 -95.315975672

Largest  eigenvalues:
 [1] 64822268 60796234 57662204 57111115 55806840 53922927 53290073 52906370
 [9] 52168635 52147320

Smallest eigenvalues:
 [1]   0.41169973   0.37842981   0.29016466   0.23843720   0.22037619
 [6]   0.10446320   0.03065762  -3.20189543  -6.47881696 -20.93161279

Largest  eigenvalues:
 [1] 64472378 60524225 56835352 55875543 55252204 53432428 52377265 51855424
 [9] 51297033 51274609

Smallest eigenvalues:
 [1]  0.44767431  0.43901405  0.41997561  0.37608988  0.35429693  0.29154808
 [7]  0.27659556  0.09143168 -0.21071695 -0.41305720

Largest  eigenvalues:
 [1] 64216696 60158780 57132664 55841669 55023064 53131348 51899238 51828994
 [9] 51677814 50817483

Smallest eigenvalues:
 [1]  0.5741196  0.5505421  0.4556008  0.4103342  0.4017258  0.3393958
 [7]  0.3138406  0.2927986  0.2920543 -0.9103729

Largest  eigenvalues:
 [1] 64753797 60531812 57880718 55843819 55816233 54306976 52496266 52454427
 [9] 51908585 51597589

Smallest eigenvalues:
 [1]  0.3954106  0.3613995  0.3325060  0.3275516  0.2974220  0.2710702
 [7]  0.2502615  0.2367582 -0.6378864 -1.1384685

Largest  eigenvalues:
 [1] 63327263 60199961 57124033 55791567 55489946 53626769 51780834 51686690
 [9] 51605775 50720783

Smallest eigenvalues:
 [1]   0.43212595   0.32741429   0.32567039   0.26011858   0.25440367
 [6]   0.24957935   0.15788884   0.05547981  -1.68471039 -19.49401894

Largest  eigenvalues:
 [1] 66625704 60475109 57803166 57116582 54846214 53455785 53159817 52109215
 [9] 51885727 51418221

Smallest eigenvalues:
 [1]  0.5788304  0.4919517  0.4915447  0.4019376  0.3892566  0.3432942
 [7]  0.2706531  0.2270635  0.2212239 -2.2417639

Largest  eigenvalues:
 [1] 63714784 60193815 57566657 55528026 54809956 53380310 51738601 51726574
 [9] 51665693 50873681

Smallest eigenvalues:
 [1]  0.4161256  0.3370086  0.2706851  0.2617583  0.2553429  0.2475482
 [7]  0.1902336  0.1843731  0.1410241 -2.9327487

Largest  eigenvalues:
 [1] 64423892 60500851 57670418 55968544 55437163 53889326 52529896 52031286
 [9] 51790159 51348478

Smallest eigenvalues:
 [1]  0.48957690  0.47015299  0.46006675  0.37604773  0.30726435  0.29129516
 [7]  0.27364006  0.04752531 -0.39124815 -2.31135055

Largest  eigenvalues:
 [1] 62651510 59904429 56950294 55563333 54590043 53724832 51829871 51815446
 [9] 50687549 50427098

Smallest eigenvalues:
 [1]  0.6039265  0.6017610  0.4566132  0.4070116  0.4021365  0.3577973
 [7]  0.3567614  0.2973197  0.2168300 -0.2109041

Largest  eigenvalues:
 [1] 62583035 60103371 57022040 55489174 54749865 53764644 52200558 51838826
 [9] 50925905 50699356

Smallest eigenvalues:
 [1]  0.3847111  0.3608571  0.2838315  0.2586309  0.1807085  0.1160849
 [7] -0.2037558 -0.9309813 -2.4501460 -7.1487017

Largest  eigenvalues:
 [1] 63856990 59529917 57103437 55498374 54886353 52969433 52444737 51763721
 [9] 51519941 51227290

Smallest eigenvalues:
 [1]  0.4643036  0.4563959  0.3411069  0.3097260  0.3085544  0.2178306
 [7]  0.1817973  0.1560109 -0.1715189 -1.5199293

Largest  eigenvalues:
 [1] 64265624 60475686 57731537 55879962 55602103 54342353 52472337 52274148
 [9] 51857597 51075721

Smallest eigenvalues:
 [1]  0.53319784  0.48387200  0.43300546  0.41839598  0.39414981  0.28614480
 [7]  0.26960483  0.16740033  0.01359703 -0.01666494

Largest  eigenvalues:
 [1] 64780318 59968615 57461963 56077034 55154664 53411297 52749414 52175812
 [9] 51776000 51697869

Smallest eigenvalues:
 [1]  0.5328656  0.5176262  0.4643269  0.4480038  0.4409601  0.4248786
 [7]  0.3531666  0.1299633 -0.3455052 -6.7485879

Largest  eigenvalues:
 [1] 65200333 60587153 57865091 57121154 55281982 53291432 53269892 53163590
 [9] 51778087 51717128

Smallest eigenvalues:
 [1]   0.31608215   0.24069674   0.11354433   0.04292511   0.01785595
 [6]  -0.09365783  -0.28427092  -0.43040014  -0.58442752 -17.43913944

Largest  eigenvalues:
 [1] 65373349 60285595 57009054 56624893 54527763 53111888 52493104 51968697
 [9] 51378361 51278289

Smallest eigenvalues:
 [1]  0.58440307  0.56496377  0.42533665  0.38660801  0.32656081  0.30282690
 [7]  0.26696556  0.26276361  0.22767641 -0.01716992

Largest  eigenvalues:
 [1] 65697616 60555321 58192546 56877296 54969200 53739581 53002544 52134666
 [9] 52075852 51494691

Smallest eigenvalues:
 [1]  0.44304822  0.37265766  0.29829633  0.23858726  0.22991867  0.21105634
 [7]  0.19873996  0.11486178  0.03595543 -1.24070248

Largest  eigenvalues:
 [1] 65342020 61300072 58005750 56454558 56428480 54779343 53309136 52659273
 [9] 52450986 52106185

Smallest eigenvalues:
 [1]  0.38217472  0.36485588  0.35094592  0.26728381  0.23247778  0.16547567
 [7]  0.09538476  0.02860731 -0.21735869 -7.72457098

Largest  eigenvalues:
 [1] 63334095 59538581 56408176 54624483 54402005 52758295 51463953 50776258
 [9] 50634070 50495323

Smallest eigenvalues:
 [1]   0.30397583   0.25558232   0.14471632   0.07601755  -0.60589255
 [6]  -0.61994491  -1.51095916  -2.95515444  -3.28992655 -10.47873558

Largest  eigenvalues:
 [1] 65763203 60741780 58185593 55956732 55824054 54485045 52861625 52690921
 [9] 52135509 51680100

Smallest eigenvalues:
 [1]  0.4991781  0.4334595  0.4152560  0.4009806  0.3702056  0.3682359
 [7]  0.3159687  0.3019355  0.1282064 -0.4315340

Largest  eigenvalues:
 [1] 62955938 60050256 57713871 55067021 54941557 53317947 52294149 51478923
 [9] 51347523 51157836

Smallest eigenvalues:
 [1]  0.5323462  0.4857399  0.4214185  0.3833629  0.3711478  0.3337403
 [7]  0.3203418  0.2487450  0.2050167 -0.7882811

Largest  eigenvalues:
 [1] 62996951 59727261 56551448 55281072 54686373 53071931 51755436 51471138
 [9] 51214747 50837088

Smallest eigenvalues:
 [1]  0.5946170  0.5183249  0.4916747  0.4180030  0.3871741  0.3863442
 [7]  0.3564048  0.3301643  0.2541634 -0.3942726

Largest  eigenvalues:
 [1] 63730409 60186546 57120299 55601606 55461010 53529881 52272292 52027080
 [9] 51440718 51050315

Smallest eigenvalues:
 [1]  0.36330113  0.35735802  0.35020490  0.19922920  0.18943896  0.01681169
 [7] -0.05716524 -0.47010158 -1.07214941 -6.99305943

Largest  eigenvalues:
 [1] 63722148 60829231 58148699 55463999 55318700 53917759 52690089 52480727
 [9] 51897707 51633096

Smallest eigenvalues:
 [1]  0.55222586  0.45823215  0.45177975  0.42486961  0.37224121  0.31678248
 [7]  0.29644523  0.15944283  0.02937954 -3.19650320

Largest  eigenvalues:
 [1] 63376026 59945953 56749059 55369233 55319556 53519502 52251627 51778446
 [9] 51407958 51070679

Smallest eigenvalues:
 [1]  0.58592843  0.52194145  0.47764782  0.44381887  0.44376518  0.40030160
 [7]  0.37257114  0.26480777  0.22298196 -0.07080257

Largest  eigenvalues:
 [1] 63485082 60569211 57530077 55770973 55523739 54042364 52642565 52029172
 [9] 51497996 51340575

Smallest eigenvalues:
 [1]  0.43136605  0.38550549  0.32649466  0.26778635  0.25121159  0.21327358
 [7]  0.13904030  0.09686388 -0.27884036 -4.44577419

Largest  eigenvalues:
 [1] 64448487 59833774 56855923 55369714 54605800 52882258 51626295 51474303
 [9] 51108687 50964307

Smallest eigenvalues:
 [1]  0.54795927  0.53691621  0.52213423  0.46169288  0.39491044  0.36204463
 [7]  0.34326572  0.31803810  0.23958644 -0.05511732

Largest  eigenvalues:
 [1] 65491196 60107113 57099988 55892860 54944890 53350633 52059768 51820849
 [9] 51759235 51251340

Smallest eigenvalues:
 [1]  0.39344414  0.37724984  0.34940665  0.27996271  0.12144554  0.00261382
 [7] -0.02613744 -1.41686733 -1.68098458 -3.46434352

Largest  eigenvalues:
 [1] 65277080 60941411 58112631 56686881 55668835 54300135 52824995 52493835
 [9] 52304768 51892882

Smallest eigenvalues:
 [1]  0.6063189  0.5308484  0.3461956  0.3320219  0.2734973  0.2677669
 [7]  0.2644860  0.2240272 -0.2719019 -1.2216412

Largest  eigenvalues:
 [1] 64558238 60087415 57245728 56167307 55028116 53528956 52308840 52233006
 [9] 51927752 51181048

Smallest eigenvalues:
 [1]  0.56291728  0.45060296  0.43171305  0.37414273  0.30983884  0.25363964
 [7]  0.13281164 -0.03918815 -0.14024569 -1.60148114

Largest  eigenvalues:
 [1] 65287755 60389075 56786491 56654701 54984713 53309914 52584893 51906870
 [9] 51833710 50930864

Smallest eigenvalues:
 [1]  0.51487497  0.48276612  0.43027291  0.36304155  0.30814851  0.27853417
 [7]  0.23836498  0.09051503 -0.05880217 -0.28942108

Largest  eigenvalues:
 [1] 65860429 60418873 58047819 57069157 55026846 53186002 53070411 52928777
 [9] 52127774 51922596

Smallest eigenvalues:
 [1]   0.38513789   0.35329402   0.30083898   0.23472265   0.17805962
 [6]   0.13328944   0.09622418   0.03881459  -1.38401051 -48.34514255

Largest  eigenvalues:
 [1] 65344881 60958579 57688499 56599388 56063322 54457052 52876054 52660175
 [9] 52656877 52090257

Smallest eigenvalues:
 [1]  0.4312859  0.4173851  0.3891183  0.3484750  0.3449000  0.3259633
 [7]  0.2577873  0.2073475  0.1676589 -5.2918387

Largest  eigenvalues:
 [1] 63255498 59533713 56828169 55259564 54862849 53599530 51904267 51385857
 [9] 50949594 50448282

Smallest eigenvalues:
 [1]  0.63734119  0.57445111  0.52384105  0.42092156  0.38533863  0.37679104
 [7]  0.33042094  0.29810122  0.23653938 -0.02378385

Largest  eigenvalues:
 [1] 63600365 60051132 57470063 55396019 55391954 53784579 52302689 51889047
 [9] 51544347 51095898

Smallest eigenvalues:
 [1]  0.51994774  0.51639376  0.47663901  0.46760953  0.32900118  0.31842745
 [7]  0.30924047  0.26801878 -0.03818643 -1.16756900

Largest  eigenvalues:
 [1] 63662271 60485632 57527631 56326118 55614006 54584158 52731053 52344902
 [9] 51634205 51146867

Smallest eigenvalues:
 [1]  0.48328920  0.42787750  0.36987557  0.30745724  0.30352216  0.27737620
 [7]  0.26770761  0.04073542 -1.48947386 -2.50340650

Largest  eigenvalues:
 [1] 64167773 59543924 56578038 56000180 54821535 53184462 52002393 51735733
 [9] 51597789 50581031

Smallest eigenvalues:
 [1]  0.3837986  0.3189130  0.2606605  0.2598902  0.2277843  0.2170432
 [7]  0.1256639 -0.1040040 -0.8911664 -1.0151174

Largest  eigenvalues:
 [1] 64005904 61156880 58089652 56573854 55502220 54837168 52846203 52639711
 [9] 51865067 51440816

Smallest eigenvalues:
 [1]  0.35742058  0.34568332  0.33108576  0.29742645  0.21909574  0.17427533
 [7]  0.12305939  0.06227753 -0.13489715 -0.76433901

Largest  eigenvalues:
 [1] 63232132 60131839 57142035 55517821 55100759 53803981 52586383 52193985
 [9] 51617067 51315934

Smallest eigenvalues:
 [1]  0.5466208  0.4967246  0.3807028  0.3712237  0.2574054  0.2535420
 [7]  0.2340367  0.2301929  0.1325831 -0.1254779

Largest  eigenvalues:
 [1] 64052832 60691122 57469384 56026900 55660761 53956005 52736235 52131179
 [9] 52114103 51282560

Smallest eigenvalues:
 [1]  0.4037012  0.3521072  0.3280791  0.2550376  0.2417018  0.2400799
 [7]  0.2278215  0.1771234 -0.7800077 -6.1343407

Largest  eigenvalues:
 [1] 62133088 59409572 56274144 54916464 54198771 53182483 51833913 50767242
 [9] 50291487 50061494

Smallest eigenvalues:
 [1]  0.53718516  0.48817502  0.40652090  0.40084619  0.37524395  0.34283589
 [7]  0.32066116  0.25596458  0.16594763 -0.03977973

Largest  eigenvalues:
 [1] 64666573 59813277 56967995 55927469 54979719 53237422 52018191 51599059
 [9] 51411081 50654344

Smallest eigenvalues:
 [1]  0.5863206  0.5540619  0.3660004  0.3357883  0.3308424  0.3035866
 [7]  0.2564905  0.1926957  0.1348714 -0.6011687

Largest  eigenvalues:
 [1] 64549217 60455773 57580895 55754282 55281208 53622331 52292144 51778729
 [9] 51761486 51282293

Smallest eigenvalues:
 [1]  0.4233936  0.3923690  0.3565185  0.3522399  0.2706483  0.1992710
 [7]  0.1937219  0.1574523 -0.4014794 -0.7171172

Largest  eigenvalues:
 [1] 64772814 60561956 57355931 56220468 55725827 53578165 53198393 52350586
 [9] 52340102 51879462

Smallest eigenvalues:
 [1]   0.06490486  -1.80228086  -2.69572036  -3.52033941  -3.55069947
 [6]  -3.84548309  -5.71278350 -31.46560668 -35.47167959 -63.46264795

Largest  eigenvalues:
 [1] 64997748 59963960 57058946 56641242 54610984 53009910 52891822 52115119
 [9] 51965522 51151556

Smallest eigenvalues:
 [1]  0.4831236  0.4593811  0.4016475  0.3778138  0.3434826  0.3240533
 [7]  0.2739518 -0.2593484 -0.3011723 -1.0297635

Largest  eigenvalues:
 [1] 65545649 60161552 57590318 56614626 55251940 53558575 52815210 52746128
 [9] 51984869 51710529

Smallest eigenvalues:
 [1]  0.5499005  0.4761912  0.4751196  0.3409258  0.2214093  0.1936841
 [7]  0.1374441 -0.2217093 -0.2720919 -0.4819296

Largest  eigenvalues:
 [1] 64653491 59996375 57353618 56287928 54929199 53304119 52242095 52139553
 [9] 51892960 51162272

Smallest eigenvalues:
 [1]  0.482074080  0.460566062  0.385325015  0.228719676  0.204170119
 [6]  0.203174929  0.196435913  0.055128857 -0.005558804 -0.326605294

Largest  eigenvalues:
 [1] 62768595 60424613 57366627 56084040 54315705 54177786 52396494 51857246
 [9] 50831455 50780357

Smallest eigenvalues:
 [1]  0.33616348  0.30931887  0.24539654  0.21218479  0.19538602  0.16675887
 [7] -0.04329842 -0.69152847 -3.69108248 -3.70084264

Largest  eigenvalues:
 [1] 66730562 60734822 58651687 56911715 55320015 53843097 52873511 52833433
 [9] 52210005 52131775

Smallest eigenvalues:
 [1]  0.3611995  0.3274914  0.3050859  0.3032461  0.2313873  0.1929277
 [7] -0.6057555 -1.7203846 -6.0100409 -6.2851009

Largest  eigenvalues:
 [1] 65276626 60435392 57738273 56471316 55756719 54336068 52382170 52308816
 [9] 52272510 51459525

Smallest eigenvalues:
 [1]  0.4335927  0.3927939  0.3713157  0.3186559  0.2776129  0.2157777
 [7]  0.1130594 -0.1613570 -0.4355709 -0.7732010

Largest  eigenvalues:
 [1] 63031142 60317934 57502074 55434523 54969485 53726933 52281038 52160996
 [9] 51554053 51441035

Smallest eigenvalues:
 [1]  0.5193983  0.4570162  0.3336109  0.2595471  0.2309372  0.1836258
 [7]  0.1728076  0.1150490 -0.1525138 -0.9321288

Largest  eigenvalues:
 [1] 65418361 61047491 58192914 56319833 56028300 54807647 53364910 52520563
 [9] 52260960 52038206

Smallest eigenvalues:
 [1]  0.4268365  0.3927026  0.3802362  0.2556951  0.2540186  0.1327133
 [7] -0.1691681 -0.1740369 -0.7788713 -7.8781130

Largest  eigenvalues:
 [1] 62830070 60802078 56983708 55954913 55551738 53578210 52451131 51827853
 [9] 51608119 50635326

Smallest eigenvalues:
 [1]  0.53814031  0.43750791  0.42313005  0.34093855  0.32466209  0.23680186
 [7]  0.17705006  0.11334663  0.01340931 -0.08469750

Largest  eigenvalues:
 [1] 63555464 60490871 57430637 55738280 54921299 53881775 52456179 52068906
 [9] 51293499 51061757

Smallest eigenvalues:
 [1]  0.4333640  0.4317225  0.3928476  0.3572899  0.2367908  0.1986234
 [7]  0.1922412  0.1784152  0.1477908 -1.9821548

Largest  eigenvalues:
 [1] 65152205 59676858 57135198 56774622 54493271 53259100 52539180 51869170
 [9] 51610097 51147730

Smallest eigenvalues:
 [1]  0.48435633  0.40264210  0.36446977  0.36301620  0.32316294  0.24950164
 [7]  0.19704065  0.09462268 -0.96091428 -1.29952398

Largest  eigenvalues:
 [1] 64065666 59934080 56998028 55770122 55225703 53370099 52637581 51871130
 [9] 51796019 51531562

Smallest eigenvalues:
 [1]  0.4106107  0.3917283  0.3747283  0.2766745  0.2655919  0.2452429
 [7]  0.1711048 -0.1104001 -0.5303969 -0.6167583

Largest  eigenvalues:
 [1] 66347962 59627369 57501559 56844415 54610971 53257406 52851364 51812852
 [9] 51751618 51205624

Smallest eigenvalues:
 [1]  0.3818560  0.3622534  0.3585395  0.3434945  0.3060358  0.2726398
 [7]  0.1727128  0.1078282 -1.1614511 -6.9716373

Largest  eigenvalues:
 [1] 65220544 60027510 57054620 55816913 55283493 53766530 51961272 51960431
 [9] 51725012 50968240

Smallest eigenvalues:
 [1]  0.4059022  0.3530834  0.3361140  0.3195295  0.2869012  0.2324727
 [7]  0.1811697  0.1787874  0.1682798 -1.3636802

Largest  eigenvalues:
 [1] 62953397 60254564 57754141 55633894 55078550 53966077 51886474 51805769
 [9] 51118635 50921819

Smallest eigenvalues:
 [1]  0.619214797  0.616442213  0.584535630  0.460510220  0.435279445
 [6]  0.345675152  0.303333379  0.246263739  0.167528658 -0.002613377

Largest  eigenvalues:
 [1] 63338416 60494701 57078485 55733066 54895248 53254074 52016268 51831658
 [9] 51710907 51100720

Smallest eigenvalues:
 [1]  0.4716803  0.3844930  0.3749503  0.3587162  0.3251543  0.3150077
 [7]  0.2847899  0.2483912  0.1770407 -2.3884923

Largest  eigenvalues:
 [1] 65042623 60892258 57715940 56646422 56036754 54388616 52892757 52558994
 [9] 52485842 51851005

Smallest eigenvalues:
 [1]  0.4895471  0.4573535  0.4067461  0.4025775  0.3292774  0.3281108
 [7]  0.3122810  0.1748698  0.1436429 -2.3075010

Largest  eigenvalues:
 [1] 64436462 60550646 57432767 56493112 55535528 53834227 52602911 52405994
 [9] 52347225 51596706

Smallest eigenvalues:
 [1]  0.4855649  0.4806738  0.4493792  0.4257337  0.4082319  0.3735515
 [7]  0.3304049  0.2607255  0.1915591 -0.9385318

Largest  eigenvalues:
 [1] 64387570 59921530 57110558 55931866 55157099 53491320 51791941 51746275
 [9] 51692209 50844819

Smallest eigenvalues:
 [1]  0.40843473  0.32427276  0.31404083  0.28269195  0.25819740  0.20088638
 [7]  0.15872948 -0.05990638 -0.40760688 -1.56795718

Largest  eigenvalues:
 [1] 61387319 59136736 56580228 54256121 54200180 52605164 51293670 51223159
 [9] 50441478 50253623

Smallest eigenvalues:
 [1]   0.28950387   0.21357170   0.19234762   0.17185247   0.03154836
 [6]  -2.17331564  -4.86923620 -13.51039474 -20.12396804 -21.59833755

Largest  eigenvalues:
 [1] 65245542 60127559 57761262 56001396 55146296 53612514 52432609 52082065
 [9] 51579811 51486569

Smallest eigenvalues:
 [1]  0.39205837  0.31352983  0.30824127  0.18453919  0.13212866  0.12475500
 [7] -0.03321208 -0.43045756 -1.82916584 -6.20041403

Largest  eigenvalues:
 [1] 63583849 59890614 56364157 55975814 54306776 52795132 51825314 51663233
 [9] 51222232 50367169

Smallest eigenvalues:
 [1]   0.4417341   0.4038176   0.2764126   0.2090916   0.1918436   0.1719696
 [7]   0.1196186  -1.2944904  -3.1554940 -10.6048038

Largest  eigenvalues:
 [1] 64910314 59780734 56499646 55538812 54685551 53039032 51768858 51550473
 [9] 51236687 51055376

Smallest eigenvalues:
 [1]  0.49598739  0.47153020  0.38643072  0.32012031  0.29891131  0.28403887
 [7]  0.19823060  0.10982614 -0.07062857 -1.37500070

Largest  eigenvalues:
 [1] 64122822 60164936 57021753 56138603 54995170 53078490 52399287 52108555
 [9] 51936459 51337943

Smallest eigenvalues:
 [1]  0.43790307  0.42965487  0.42093261  0.39689484  0.32490137  0.29326572
 [7]  0.18560769  0.14404229  0.08376391 -5.96082852

Largest  eigenvalues:
 [1] 62395166 59918541 56974262 55364335 54878954 53654648 52038522 52011692
 [9] 51105441 50938925

Smallest eigenvalues:
 [1]  0.58033472  0.55348785  0.55319654  0.46123111  0.39062386  0.33984309
 [7]  0.33279145  0.26923419  0.26738863 -0.02851748

Largest  eigenvalues:
 [1] 63921647 60853449 57697019 56174340 55496605 53631706 52174747 52131082
 [9] 52016515 50972321

Smallest eigenvalues:
 [1]  0.44672618  0.42344827  0.28009525  0.21728263  0.04270283 -0.24956196
 [7] -0.38973148 -0.65082647 -1.04833091 -1.20644654

Largest  eigenvalues:
 [1] 64033331 60440040 57434177 55940394 55471909 53570874 52698263 52079971
 [9] 51945936 51654200

Smallest eigenvalues:
 [1]  5.229017e-01  4.872134e-01  4.091669e-01  3.871437e-01  3.374349e-01
 [6]  2.724708e-01  2.646559e-02  4.953285e-05 -2.159932e-01 -1.022007e+01

Largest  eigenvalues:
 [1] 64585766 60772815 57768232 55733029 55649730 54203728 52804990 52194973
 [9] 51786908 51641055

Smallest eigenvalues:
 [1]   0.39485902   0.35743264   0.29258255   0.26565283   0.21072465
 [6]   0.05240952  -0.52427941  -1.78479060  -3.69658365 -13.50641203

Largest  eigenvalues:
 [1] 65252481 60701004 58545524 56854701 55362679 54052209 52863939 52717160
 [9] 52422373 51850961

Smallest eigenvalues:
 [1]   0.4260388   0.3843881   0.3199751   0.2957491   0.2919985   0.2727853
 [7]   0.2296530   0.1868074  -0.2691620 -33.6905296

Largest  eigenvalues:
 [1] 64659464 60283454 57135113 56598090 54910010 53312651 52638118 51763427
 [9] 51735213 50828911

Smallest eigenvalues:
 [1]  0.45245959  0.43137403  0.42789055  0.41377461  0.27000240  0.15589950
 [7]  0.06469077  0.02853310 -0.55176870 -4.58658188

Largest  eigenvalues:
 [1] 65043370 60333388 57283807 56284134 55269108 53172234 52410858 52087600
 [9] 51866501 51260698

Smallest eigenvalues:
 [1]  0.39484097  0.32028836  0.28356366  0.26924378  0.16560932  0.02345127
 [7] -0.29873418 -0.54655779 -1.30287880 -3.55914105

Largest  eigenvalues:
 [1] 63300354 59384292 56769794 55386602 54802349 53057496 51936379 51613263
 [9] 51292005 50570245

Smallest eigenvalues:
 [1]  0.5090463  0.4855877  0.4854849  0.4402381  0.3986666  0.3634851
 [7]  0.3071932  0.2615275  0.1640894 -0.4264008

Largest  eigenvalues:
 [1] 63605236 59899879 56995324 55933483 54689395 53049682 51927081 51768912
 [9] 51065334 50474857

Smallest eigenvalues:
 [1]  0.4426110  0.3924150  0.3596015  0.3576191  0.2842544  0.2478722
 [7]  0.2419023  0.2189636 -0.6422768 -1.0990688

Largest  eigenvalues:
 [1] 65854651 60392332 58206567 57219409 54917368 53739538 53203900 51959474
 [9] 51769853 51272527

Smallest eigenvalues:
 [1]  0.4949781  0.4140768  0.3787345  0.3448595  0.3333660  0.3259888
 [7]  0.2844763  0.2524878  0.1310555 -1.6280998

Largest  eigenvalues:
 [1] 64238811 60040281 57171062 56542604 54825437 53367394 52436649 52229641
 [9] 51998420 51034604

Smallest eigenvalues:
 [1]  0.35386660  0.31129898  0.27713572  0.26879827  0.25843558  0.23912535
 [7]  0.17438173  0.06320406 -0.12203291 -1.33315029

Largest  eigenvalues:
 [1] 66317305 60312688 58051522 56936628 55235273 53884129 52940023 52699727
 [9] 51739837 51548984

Smallest eigenvalues:
 [1]  0.5510319  0.5161116  0.5037409  0.4154655  0.4120026  0.3990238
 [7]  0.3271287  0.2679941  0.2270957 -0.1703969

Largest  eigenvalues:
 [1] 64154331 60503779 57492130 55541542 55345073 53710495 51905311 51791781
 [9] 51718372 51017918

Smallest eigenvalues:
 [1]   0.4462222   0.4413162   0.3764029   0.3592977   0.2907381   0.2880201
 [7]   0.2393497   0.1297328  -4.4514676 -15.6981149

Largest  eigenvalues:
 [1] 63816159 60564082 57121921 55900641 55222074 54073102 51895720 51650771
 [9] 51268021 50550616

Smallest eigenvalues:
 [1]  0.581633838  0.494953119  0.465368073  0.406638838  0.325886603
 [6]  0.313158887  0.306838249  0.268819250  0.207593516 -0.009696508

Largest  eigenvalues:
 [1] 65146062 60099226 56879229 56228445 54718501 52981955 52338662 51812001
 [9] 51147366 51014058

Smallest eigenvalues:
 [1]   0.398131529   0.381355802   0.364193841   0.321923968   0.318962823
 [6]   0.287641207   0.199177536   0.175516353   0.008682012 -13.697321706

Largest  eigenvalues:
 [1] 62586258 59671900 56939990 55172669 54620691 53391229 51834535 51496248
 [9] 50957699 50791267

Smallest eigenvalues:
 [1]  0.5373549  0.3872080  0.3834492  0.3232014  0.3185726  0.3099545
 [7]  0.2930033 -0.3948456 -0.6872954 -0.7143613

Largest  eigenvalues:
 [1] 65016429 60373698 57780454 56620777 55399207 53834880 52838026 52743138
 [9] 52149093 51270082

Smallest eigenvalues:
 [1]   0.4628780   0.3568853   0.3260001   0.2822877   0.2800484   0.2474752
 [7]   0.2427732   0.2266537   0.2103802 -46.3683064

Largest  eigenvalues:
 [1] 63598151 59883891 57031902 55800920 54973653 53321992 51884066 51850233
 [9] 51779028 51005041

Smallest eigenvalues:
 [1]  0.5545398  0.5217730  0.5112008  0.4545997  0.4518587  0.3429025
 [7]  0.2798084  0.2561103  0.1991687 -0.1232933

Largest  eigenvalues:
 [1] 64484433 60315178 57468264 55982883 54868379 53522754 52060384 52016813
 [9] 51755214 51244827

Smallest eigenvalues:
 [1]  0.58673801  0.56720582  0.50854628  0.40485383  0.39769796  0.35089211
 [7]  0.25830660  0.22392965  0.01674273 -0.93324220

Largest  eigenvalues:
 [1] 63886977 60729946 57621728 55869068 55771665 54311748 52564797 52165203
 [9] 51889929 51282359

Smallest eigenvalues:
 [1]   0.34698327   0.24479120   0.21234660   0.19986008   0.17859472
 [6]   0.09196713   0.06446403  -0.22413795 -14.59909836 -21.32771476

Largest  eigenvalues:
 [1] 64865361 60133172 56897101 56342744 55436304 53807472 52311100 52247735
 [9] 51796752 51360835

Smallest eigenvalues:
 [1]  0.37312771  0.37184272  0.36667553  0.32592863  0.02734883  0.02222577
 [7] -0.06980914 -0.16022570 -0.81788154 -1.96318679

Largest  eigenvalues:
 [1] 64687280 59339129 56755609 55437233 53972644 52396293 51836459 51311588
 [9] 50960750 50905212

Smallest eigenvalues:
 [1]  0.5897315  0.5828536  0.5721948  0.5049707  0.4852852  0.3320432
 [7]  0.3168799  0.2096651  0.1794736 -0.9524993

Largest  eigenvalues:
 [1] 64715781 60298513 56894736 56242623 55206968 53365362 52215443 52039307
 [9] 51799506 50854229

Smallest eigenvalues:
 [1]  0.4642808  0.4515403  0.4476178  0.3966770  0.3521420  0.2985550
 [7]  0.2366061  0.1849280  0.1127254 -0.6650059

Largest  eigenvalues:
 [1] 65738517 60204478 57370096 56469144 55383243 53559289 52556160 52479965
 [9] 51578968 51266802

Smallest eigenvalues:
 [1]  0.5572239  0.4581508  0.4485191  0.3912046  0.3837334  0.2791748
 [7]  0.2131950  0.1473619  0.1430001 -0.2701492

Largest  eigenvalues:
 [1] 65247883 60923462 57981055 56172890 56056063 54551032 52922420 52639435
 [9] 52234702 51988180

Smallest eigenvalues:
 [1]  0.4278794  0.3476179  0.3183024  0.2369793  0.2132186  0.1871104
 [7] -0.1011245 -0.2236885 -5.7885355 -5.9580871

Largest  eigenvalues:
 [1] 64286370 60488102 57529748 55757762 55600341 54161487 52751630 52529613
 [9] 51838513 51656311

Smallest eigenvalues:
 [1]  0.46965636  0.38818181  0.23838787  0.21927810  0.12616960  0.02622104
 [7] -0.49254969 -0.58047406 -0.61184724 -0.66725288

Largest  eigenvalues:
 [1] 62967702 59133922 56397725 55423130 54243728 52665853 51389320 51213887
 [9] 51164835 50103864

Smallest eigenvalues:
 [1]   0.42825641   0.39942765   0.36942551   0.33032954   0.26166593
 [6]   0.23420744   0.23011344   0.11908614  -0.09278426 -26.28260262

Largest  eigenvalues:
 [1] 62750030 59768004 56684393 55236055 55054427 53387009 52023520 51215090
 [9] 51066586 50587866

Smallest eigenvalues:
 [1]  0.4816451  0.4668635  0.2941645  0.2504987  0.2145759  0.1991994
 [7]  0.1981649  0.1351890  0.1006855 -0.8509431

Largest  eigenvalues:
 [1] 63257582 60351017 57108991 55608188 55059808 53621656 51913832 51618678
 [9] 50875572 50648289

Smallest eigenvalues:
 [1]  0.54546501  0.51450324  0.48724536  0.45671083  0.39243157  0.36990241
 [7]  0.34163215  0.05913585 -0.11125103 -0.11468128

Largest  eigenvalues:
 [1] 64991354 59947584 57046232 56478948 54597889 53066801 52412655 51765989
 [9] 51355717 50773118

Smallest eigenvalues:
 [1]  0.44728753  0.35795645  0.33933782  0.32804442  0.21225882  0.21049584
 [7]  0.15980083  0.14846945 -0.06079634 -0.18078756

Largest  eigenvalues:
 [1] 67266219 60669648 57623456 56922178 55185723 53488630 53024284 52573740
 [9] 52055097 51973084

Smallest eigenvalues:
 [1]  0.4866668  0.4786676  0.4489369  0.3615731  0.3022249  0.2778196
 [7]  0.2182407 -0.1331183 -0.2604480 -0.8549073

Largest  eigenvalues:
 [1] 64523437 59928819 57432788 55326168 55255790 53452493 52103472 51758429
 [9] 51592691 50858343

Smallest eigenvalues:
 [1]   0.43850409   0.38427917   0.25357374   0.24798042  -0.05440934
 [6]  -0.24140800  -0.71673711  -4.93092252  -8.02792029 -20.90923070

Largest  eigenvalues:
 [1] 65249773 60106396 57294159 56064667 54739048 53252048 52352397 51677287
 [9] 51463083 50458460

Smallest eigenvalues:
 [1]  0.5991883  0.5281029  0.5178836  0.4622291  0.4454491  0.4059809
 [7]  0.2962903  0.1331650 -0.1296811 -1.1521993

Largest  eigenvalues:
 [1] 64526084 60285005 57265766 56190777 55278706 53471709 52690261 52267597
 [9] 51623127 51275306

Smallest eigenvalues:
 [1]  0.4188800  0.3487356  0.3279679  0.3269908  0.3075070  0.2495696
 [7]  0.2208671  0.2091194 -1.3076344 -4.1788323

Largest  eigenvalues:
 [1] 64366927 60693923 57820655 55579550 55544610 54149107 52438327 51997257
 [9] 51667113 51598606

Smallest eigenvalues:
 [1]   0.4661149   0.4407696   0.3560121   0.3428487   0.3228056   0.2507656
 [7]   0.1896730   0.1462090  -2.6825332 -28.2155618

Largest  eigenvalues:
 [1] 61986590 59683254 56485676 55499970 54402611 53489888 51767450 51112500
 [9] 50399418 50229598

Smallest eigenvalues:
 [1]  0.5329010  0.4513208  0.4414890  0.3713458  0.3555911  0.3053348
 [7]  0.2269964 -0.2588324 -0.3180586 -0.4310804

Largest  eigenvalues:
 [1] 65358608 60603954 58086456 56869578 55079701 53290685 52894107 52768550
 [9] 51954210 51784438

Smallest eigenvalues:
 [1]  0.5617092  0.5354533  0.4306728  0.4148428  0.3158316  0.3071711
 [7]  0.2266957  0.2207708  0.2206010 -0.5619875

Largest  eigenvalues:
 [1] 64734970 60953231 57507971 56017674 55625522 54040222 52357535 52323881
 [9] 52120162 51547714

Smallest eigenvalues:
 [1]   0.4700373   0.4265857   0.4048073   0.3963303   0.3359164   0.3233833
 [7]   0.2706780   0.2436359  -0.2125806 -10.2950976

Largest  eigenvalues:
 [1] 64422931 60170357 57548662 56342241 55244688 53709279 52339785 51944408
 [9] 51928136 50815782

Smallest eigenvalues:
 [1]  0.596600063  0.580191868  0.541670645  0.530609083  0.497916460
 [6]  0.436080669  0.306870086  0.241490864  0.169635234 -0.001726538

Largest  eigenvalues:
 [1] 64294945 60516733 57663696 55909461 55163800 53264149 52199414 52112162
 [9] 51571047 51089777

Smallest eigenvalues:
 [1]  0.4961910  0.4902026  0.4806140  0.4553746  0.4390719  0.2595080
 [7]  0.1791196 -0.2440164 -0.6227254 -3.0845770

Largest  eigenvalues:
 [1] 64387207 60315566 57771970 55909323 55112907 53611629 52287926 52091550
 [9] 51807467 51117083

Smallest eigenvalues:
 [1]   0.3165348   0.2868056   0.2435300   0.2355389   0.1478802   0.1392101
 [7]   0.1313882  -1.8590454  -7.4206405 -12.6158730

Largest  eigenvalues:
 [1] 64169161 60745713 57632644 55876968 55282915 54205999 52662057 52153117
 [9] 51798160 51468295

Smallest eigenvalues:
 [1]   0.4425852   0.4177886   0.3940021   0.2782246   0.1765252  -0.2251043
 [7]  -1.3219801  -2.1602911  -7.2638773 -16.2835269

Largest  eigenvalues:
 [1] 65463398 59849089 57004151 56818991 54575699 52753964 52405633 51836765
 [9] 51404133 50852713

Smallest eigenvalues:
 [1]  0.595002753  0.499714627  0.496328368  0.429235879  0.405218161
 [6]  0.382180088  0.262937485  0.200909666  0.002652293 -0.499905603

Largest  eigenvalues:
 [1] 64468475 60624678 57449008 55784301 55496268 53769662 52911557 51938199
 [9] 51561082 51431505

Smallest eigenvalues:
 [1]   0.402866174   0.391950759   0.326876034   0.280944028   0.274173956
 [6]   0.182973124  -0.005183514  -0.534444484  -1.481506686 -21.430849617

Largest  eigenvalues:
 [1] 64859279 60681333 57672223 55802533 55648619 54313291 52602615 52348499
 [9] 51829606 51524747

Smallest eigenvalues:
 [1]  0.4119543  0.4046272  0.3730116  0.3507124  0.3311649  0.2710863
 [7]  0.1903433  0.1051565 -0.1564091 -0.1932710

Largest  eigenvalues:
 [1] 65973088 60914917 57724318 56058834 55645614 53826329 52704344 52195036
 [9] 51983071 51843962

Smallest eigenvalues:
 [1]  0.47219064  0.38574298  0.37339287  0.34166300  0.33395930  0.27276534
 [7]  0.24513438  0.22089711  0.03058645 -1.93180410

Largest  eigenvalues:
 [1] 65625374 60427104 57648340 56737618 55186455 53755204 52605260 52450966
 [9] 51990118 51601657

Smallest eigenvalues:
 [1]  0.5020374  0.4191968  0.3869501  0.2561177  0.2272818  0.2118193
 [7] -0.2205335 -0.3867581 -1.6421047 -2.6228899

Largest  eigenvalues:
 [1] 66398218 61009272 58434454 56750705 55942717 54161086 53024288 52873617
 [9] 52418817 52080028

Smallest eigenvalues:
 [1]  0.38320997  0.36041026  0.32108723  0.31321878  0.24711360  0.23687529
 [7]  0.18993739  0.09900609 -0.11287443 -7.11540963

Largest  eigenvalues:
 [1] 65209274 59383444 56863153 56030463 54684419 53108447 51999627 51305003
 [9] 51194510 50584511

Smallest eigenvalues:
 [1]  0.44748223  0.41966422  0.40973741  0.29212575  0.24848101  0.24345831
 [7]  0.20466526  0.09570455 -0.10115300 -0.28204296

Largest  eigenvalues:
 [1] 66835808 61391501 58492227 56927542 55580044 53831180 53109222 52908205
 [9] 52086839 52022214

Smallest eigenvalues:
 [1]  0.55870135  0.52577165  0.47899852  0.46535595  0.46441455  0.44421676
 [7]  0.23913658  0.23565963  0.04982777 -0.05214577

Largest  eigenvalues:
 [1] 62705148 60130743 56777315 55465905 55262063 53405581 52249528 51664529
 [9] 51217419 50464234

Smallest eigenvalues:
 [1]  0.6335170  0.6058209  0.5532983  0.5524656  0.4573758  0.4543889
 [7]  0.3424434  0.2313038  0.2235777 -0.8873691

Largest  eigenvalues:
 [1] 64776839 60419149 57624121 56267497 55176198 53743129 52237618 52009423
 [9] 51825588 50989582

Smallest eigenvalues:
 [1]  0.4809460  0.4000531  0.3643749  0.3633007  0.3445975  0.3377922
 [7]  0.2070527  0.1865913 -0.5667321 -2.3734881

Largest  eigenvalues:
 [1] 64019446 59980557 57263975 56189248 54889406 53251221 52132000 52064996
 [9] 51700317 50635496

Smallest eigenvalues:
 [1]  0.6369606  0.5302138  0.5200224  0.4815634  0.4375574  0.3863850
 [7]  0.3701213  0.3085190  0.2146247 -0.1748042

Largest  eigenvalues:
 [1] 65155071 61211659 58338330 56544796 56325039 54708452 53472067 52642735
 [9] 52528081 51940575

Smallest eigenvalues:
 [1]  0.4785571  0.4746846  0.4410983  0.4118512  0.3841887  0.3668965
 [7]  0.3277161  0.1811739  0.1408216 -0.6609918

Largest  eigenvalues:
 [1] 64909126 61115423 58179149 56212328 56057032 54498844 52544017 52510847
 [9] 52190004 51690883

Smallest eigenvalues:
 [1]  0.47117178  0.46469081  0.41250110  0.34659523  0.34399625  0.32194163
 [7]  0.31081005  0.12085568  0.06078797 -2.71815573

Largest  eigenvalues:
 [1] 64350075 59518803 56663317 55984812 54508994 52817657 51998067 51519314
 [9] 51497351 50560359

Smallest eigenvalues:
 [1]  0.4346896  0.3733635  0.3646124  0.3505277  0.2973378  0.2606022
 [7]  0.2281173  0.1832396 -1.3018144 -6.9913078

Largest  eigenvalues:
 [1] 64948744 60146340 57352168 56005045 55060614 53669277 52084438 51805155
 [9] 51760344 50830627

Smallest eigenvalues:
 [1]   0.40427683   0.34842963   0.30804670   0.24481902   0.15717935
 [6]   0.05892585  -0.00211258  -0.78667016  -1.56359745 -12.26724365

Largest  eigenvalues:
 [1] 65621086 60871049 58196565 56339127 55622847 54115936 52829808 52349538
 [9] 52103273 51605139

Smallest eigenvalues:
 [1]  0.51651388  0.48494782  0.46418786  0.46389734  0.44118384  0.41089926
 [7]  0.40272391  0.30869897  0.09280225 -0.11407244

Largest  eigenvalues:
 [1] 63662340 59634720 57365275 55432102 54967724 53265366 51598050 51544271
 [9] 51452041 50482966

Smallest eigenvalues:
 [1]  0.32354642  0.32169932  0.26056856  0.25879940  0.21499204  0.11053373
 [7] -0.08515092 -0.54543152 -1.41498525 -2.72793053

Largest  eigenvalues:
 [1] 65450136 59518139 57091560 56065267 54313443 52782946 52178448 51804085
 [9] 51517405 51122820

Smallest eigenvalues:
 [1]  0.4367802  0.3624695  0.3374817  0.3349788  0.2379174  0.2035338
 [7] -1.1352942 -1.7838715 -3.0375818 -8.8461238

Largest  eigenvalues:
 [1] 65747952 60107712 57451055 57318072 54778518 53192069 53168751 52449707
 [9] 52265871 51682659

Smallest eigenvalues:
 [1]   0.37074622   0.32964236   0.25232790   0.23409043   0.14494076
 [6]   0.13759617   0.11152770   0.07757987  -0.57253582 -13.93100786

Largest  eigenvalues:
 [1] 65781897 59924479 57497598 56680141 54718461 53090438 52722620 51923643
 [9] 51659170 51122536

Smallest eigenvalues:
 [1]  0.5831168  0.5639826  0.3837977  0.3826191  0.3035591  0.2863617
 [7]  0.2745112  0.2731092  0.2431454 -1.4086800

Largest  eigenvalues:
 [1] 65137463 60643966 57849733 56184126 55552678 54203133 52339115 52319215
 [9] 52256902 51332130

Smallest eigenvalues:
 [1]  0.3683887  0.3512420  0.3408925  0.3232900  0.2787079  0.2724606
 [7]  0.2245215  0.1846142 -0.2622792 -1.5402836

Largest  eigenvalues:
 [1] 64623202 60783323 57881613 56446604 55995575 54235915 52386160 52236666
 [9] 52109384 51197995

Smallest eigenvalues:
 [1]  0.46198582  0.45573780  0.43610679  0.36581319  0.35699677  0.34375384
 [7]  0.25456610  0.14674583  0.08096377 -0.26255144

Largest  eigenvalues:
 [1] 64448147 61161415 57735874 56329391 55854340 54270310 52482906 52143619
 [9] 52012443 51288637

Smallest eigenvalues:
 [1]  0.4454687  0.4390658  0.4226786  0.3351076  0.3039356  0.2955374
 [7]  0.2863432  0.2531215  0.1173429 -0.3254932

Largest  eigenvalues:
 [1] 63319878 59730634 56756909 55304533 54739660 53105694 51500323 51455907
 [9] 51228466 50587355

Smallest eigenvalues:
 [1]  0.50226669  0.45125814  0.41137682  0.33723767  0.33328902  0.21965764
 [7]  0.12710130  0.04384981 -0.12613060 -1.86189819

Largest  eigenvalues:
 [1] 61730491 59517124 56837496 54670470 54418834 52959528 51681618 51557314
 [9] 50819779 50630242

Smallest eigenvalues:
 [1]  0.4082084  0.3809722  0.3175078  0.3117375  0.3034126  0.2684511
 [7]  0.2369499  0.2207037 -0.3627658 -0.9675033

Largest  eigenvalues:
 [1] 64127099 60297681 57598985 55669821 55220419 53732401 51926088 51745300
 [9] 51737051 51057534

Smallest eigenvalues:
 [1]  0.472090059  0.457929953  0.372775765  0.320080079  0.255523639
 [6]  0.234289583  0.228135878  0.005882272 -0.007653789 -0.180203494

Largest  eigenvalues:
 [1] 65302765 60951090 58156776 55806616 55607269 54387828 52698923 52422608
 [9] 51864350 51707824

Smallest eigenvalues:
 [1]  0.5217158  0.4826237  0.3938609  0.3764443  0.3246314  0.2812599
 [7]  0.2804431  0.2751018 -0.8850331 -1.4925676

Largest  eigenvalues:
 [1] 64889062 59795307 57211664 55956867 54999276 53616969 52016384 51972910
 [9] 51716295 51143142

Smallest eigenvalues:
 [1]  0.42296270  0.41268900  0.40888269  0.37646961  0.31108342  0.27795950
 [7]  0.19224440  0.16648144  0.15671339 -0.09273714

Largest  eigenvalues:
 [1] 64267331 60084489 57393624 55524141 55430005 53850331 52270825 52006573
 [9] 51570610 51225934

Smallest eigenvalues:
 [1]  3.193495e-01  2.013858e-01  9.200554e-02  8.926988e-02  9.936771e-04
 [6] -2.215423e-02 -1.101043e-01 -8.727731e-01 -1.565285e+01 -1.840693e+01

Largest  eigenvalues:
 [1] 62460189 60161864 56292925 55248765 55189474 53442812 51989511 51885954
 [9] 50976871 50455187

Smallest eigenvalues:
 [1]  0.5385928  0.4965616  0.4868131  0.4751368  0.4265040  0.4066629
 [7]  0.3680893  0.3539590  0.2986524 -0.9663422

Largest  eigenvalues:
 [1] 65287550 60627157 57758124 56718238 55491871 53974496 52592540 52320014
 [9] 51865157 51279229

Smallest eigenvalues:
 [1]  0.56935255  0.56354283  0.54377823  0.53103914  0.47037046  0.37939205
 [7]  0.36660544  0.33274338  0.31475206 -0.05407509

Largest  eigenvalues:
 [1] 65572468 61072960 58293329 57137740 55616490 53992113 53098514 52812922
 [9] 52335700 51810663

Smallest eigenvalues:
 [1]  0.39771853  0.36605174  0.35853521  0.28550846  0.22965467 -0.06847966
 [7] -0.30470030 -1.54637995 -2.25399036 -9.44133852

Largest  eigenvalues:
 [1] 63105488 60083343 57030489 55284656 55239587 53482165 52226953 51869946
 [9] 51269099 51061421

Smallest eigenvalues:
 [1]  0.5171361  0.4865891  0.4518466  0.4104234  0.3556949  0.2574824
 [7]  0.2164616  0.1135890 -0.4051819 -0.4166858

Largest  eigenvalues:
 [1] 64173327 60655314 58378402 55888399 55454987 54630121 52780321 52214480
 [9] 51606673 51422334

Smallest eigenvalues:
 [1]  0.4029243  0.4018202  0.3899124  0.3105355  0.2693868  0.2628813
 [7]  0.2519655  0.2371773  0.2353172 -0.7939161

Largest  eigenvalues:
 [1] 64607546 60727005 57790348 55740800 55681926 54315022 52456711 52037329
 [9] 51845447 51196923

Smallest eigenvalues:
 [1]  0.366884917  0.275665985  0.218540002  0.007691799 -0.006153075
 [6] -0.191619157 -0.672055184 -0.864089060 -0.901121715 -1.334254853

Largest  eigenvalues:
 [1] 62099733 60216656 56901223 55598598 55188973 53763432 52376058 51891639
 [9] 50930336 50819007

Smallest eigenvalues:
 [1]  0.42610577  0.33129939  0.32683798  0.26952448  0.25144868  0.24254517
 [7]  0.11172515  0.07045316 -2.62996106 -6.92126661

Largest  eigenvalues:
 [1] 63799434 60628491 57881872 55808186 55791607 54155629 52676672 52200287
 [9] 51794047 51657184

Smallest eigenvalues:
 [1]  0.5487412  0.4565224  0.4462112  0.4244772  0.4183680  0.3785733
 [7]  0.3549216  0.3367931  0.3349219 -0.4078569

Largest  eigenvalues:
 [1] 63489102 59887664 56903379 55705661 54786918 53210919 51700762 51474477
 [9] 51185618 50363963

Smallest eigenvalues:
 [1]  0.5405838  0.4536518  0.4077796  0.3958012  0.3701455  0.3227531
 [7]  0.2808164  0.2673987  0.1986518 -1.3182308

Largest  eigenvalues:
 [1] 64164268 60062226 56977050 56058612 55020514 53400863 52003669 51861822
 [9] 51733894 51039032

Smallest eigenvalues:
 [1]  0.4270398  0.2864364  0.2571402  0.2373492  0.2039900  0.1876548
 [7]  0.1817205 -2.1896355 -3.1294113 -6.5270451

Largest  eigenvalues:
 [1] 64892434 59937071 56962640 56583702 54665060 53176919 52351480 52247487
 [9] 51744908 51006328

Smallest eigenvalues:
 [1]   0.5341144   0.4107927   0.4005878   0.3090971   0.2481083   0.2461680
 [7]  -0.1281613  -0.2992312  -0.6081750 -19.7901473

Largest  eigenvalues:
 [1] 65382267 60099102 57087956 55870202 54976591 53418825 52080401 52032896
 [9] 51658714 51250411

Smallest eigenvalues:
 [1]  0.51259405  0.50985427  0.46812844  0.38045732  0.36816855  0.36809214
 [7]  0.27374988  0.23827465 -0.02485813 -0.38040892

Largest  eigenvalues:
 [1] 62650980 59780044 56743963 55194066 54722693 53315350 51948454 51735596
 [9] 50874021 50628503

Smallest eigenvalues:
 [1]  0.50521696  0.46510991  0.43458252  0.39244545  0.38267005  0.35211441
 [7]  0.34020312  0.09802594  0.04738960 -0.02482130

Largest  eigenvalues:
 [1] 63739581 60305508 57361615 55468862 54863352 53439318 51993580 51522328
 [9] 51517327 51152138

Smallest eigenvalues:
 [1]  0.46761774  0.42545473  0.42043402  0.38920906  0.30095922  0.27767208
 [7]  0.25500262  0.17357523  0.17339234 -0.07817236

Largest  eigenvalues:
 [1] 64608709 61206609 58213748 56061023 55700191 54158954 52831963 52208762
 [9] 52180561 51948289

Smallest eigenvalues:
 [1]  0.4989402  0.4619286  0.3987685  0.3691881  0.3585004  0.2764301
 [7]  0.2401817 -0.1596020 -0.2613991 -0.5504757

Largest  eigenvalues:
 [1] 63736179 59813801 57434454 55337619 54933574 53661507 51936093 51500664
 [9] 51226749 50693658

Smallest eigenvalues:
 [1]  0.48503699  0.43655895  0.40992494  0.38106473  0.34250827  0.32877577
 [7]  0.28788444  0.21054488  0.16162259 -0.03885352

Largest  eigenvalues:
 [1] 64206663 59447133 57262210 55571173 54493701 53059324 51848335 51729715
 [9] 51275121 50839147

Smallest eigenvalues:
 [1]   0.4441993   0.4173982   0.4049454   0.3850415   0.3815862   0.3424496
 [7]   0.3171507   0.2675028  -0.3561928 -33.5318669

Largest  eigenvalues:
 [1] 66225916 60488782 57869109 57080502 55102329 53714415 53090096 51956956
 [9] 51913401 51097694

Smallest eigenvalues:
 [1]  0.4457368  0.3469112  0.3111173  0.2777945  0.2741597  0.2596741
 [7] -0.1852783 -0.4284197 -3.5392829 -4.9668615

Largest  eigenvalues:
 [1] 65313613 59957328 57855888 56466579 55224343 54015896 52719527 52402783
 [9] 52395980 51834450

Smallest eigenvalues:
 [1]  0.3377719  0.3016237  0.2998872  0.2683010  0.2435994  0.2341296
 [7] -0.6551704 -0.7253914 -1.4010014 -9.6362314

Largest  eigenvalues:
 [1] 62368185 59927158 57522380 55937590 54214348 54102724 52385871 52107340
 [9] 51047245 50735455

Smallest eigenvalues:
 [1]   0.260392160   0.246198173   0.186251639   0.137679517   0.081803619
 [6]   0.044102629   0.018894230   0.005853617  -0.990973008 -17.603513577

Largest  eigenvalues:
 [1] 62908863 60733371 57767519 55569707 55207542 53982085 52193411 51845545
 [9] 51372746 51224998

Smallest eigenvalues:
 [1]  0.6131991  0.5135985  0.5011057  0.4633477  0.3946598  0.3463550
 [7]  0.3091917  0.2928958  0.2560634 -1.0221547

Largest  eigenvalues:
 [1] 65238470 61076332 57875594 56809465 55393005 53901856 52814122 52722993
 [9] 52182180 51926616

Smallest eigenvalues:
 [1]  0.5355943  0.4957699  0.4848498  0.4499409  0.4378068  0.3363424
 [7]  0.2886285  0.2509242  0.2167049 -0.1989357

Largest  eigenvalues:
 [1] 65458743 60026275 57834345 56593570 54697921 53062377 52831881 51795006
 [9] 51477791 50890314

Smallest eigenvalues:
 [1]   0.4387782   0.4277284   0.4100086   0.3495594   0.3489280   0.2971214
 [7]   0.1925726   0.1919807  -0.5387739 -21.0813380

Largest  eigenvalues:
 [1] 65004417 60376581 57702056 56532773 55130848 53414412 52714241 52001861
 [9] 51906824 50990053

Smallest eigenvalues:
 [1]  0.5256431  0.4572065  0.4491234  0.4113677  0.3850087  0.3790004
 [7]  0.3171255  0.1960669  0.1807790 -1.9247137

Largest  eigenvalues:
 [1] 62940405 60269618 57575250 55412373 54921097 53843621 51914001 51808395
 [9] 51081605 50929350

Smallest eigenvalues:
 [1]  0.6205814  0.5906973  0.5541414  0.5475933  0.4521749  0.3755399
 [7]  0.2649637  0.2049598  0.1841806 -0.8680196

Largest  eigenvalues:
 [1] 64353659 60059015 56872269 55844029 55007882 53352383 51725673 51651644
 [9] 51422861 50519991

Smallest eigenvalues:
 [1]   0.12920234   0.07653261   0.06371167  -0.04779952  -0.34083850
 [6]  -1.92409911  -9.72468340 -27.61676598 -33.29934368 -44.89290360

Largest  eigenvalues:
 [1] 65180621 60207937 56484016 56340252 55208204 53330429 52327657 52303894
 [9] 52194607 51147638

Smallest eigenvalues:
 [1]  0.37429053  0.34924468  0.34516069  0.34213494  0.28880090  0.09359304
 [7]  0.07296078  0.05012915 -1.28637025 -3.38288881

Largest  eigenvalues:
 [1] 62689806 59049125 56601700 55003811 54732128 53093561 51879078 51489399
 [9] 50876470 50486287

Smallest eigenvalues:
 [1]  0.47232773  0.45977329  0.43119076  0.36240963  0.32969283  0.25910272
 [7]  0.23378894  0.02993916 -0.18171418 -0.24359475

Largest  eigenvalues:
 [1] 62234920 59332481 56892529 54813651 54477956 52900682 51874847 51266706
 [9] 50945506 50799773

Smallest eigenvalues:
 [1]  0.4153222  0.3721074  0.3648583  0.3597596  0.3279138  0.2510410
 [7]  0.2327371  0.1508180  0.1263878 -0.7126174

Largest  eigenvalues:
 [1] 63577332 60097602 57111281 55502187 55245232 53909106 52332234 51916698
 [9] 51393220 51173762

Smallest eigenvalues:
 [1]  0.5033041  0.5028158  0.3602542  0.3423207  0.3097934  0.2378690
 [7]  0.2302833  0.1502926 -1.0370043 -5.8579513

Largest  eigenvalues:
 [1] 64680500 60901910 57293572 56249877 55814252 54005386 52474461 52274526
 [9] 51954039 51479185

Smallest eigenvalues:
 [1]  0.4363476  0.4250772  0.3885742  0.3249050  0.2703968  0.2699337
 [7]  0.2582783 -0.1438690 -0.3453970 -0.7135927

Largest  eigenvalues:
 [1] 64614830 60386060 57820301 56550732 55390296 53923850 52997069 52582632
 [9] 52169874 51713304

Smallest eigenvalues:
 [1]  0.4570453  0.4069215  0.3449191  0.3265189  0.3156249  0.2754068
 [7]  0.2434499  0.1960337 -0.2192655 -2.0999734

Largest  eigenvalues:
 [1] 64012457 60461494 57354408 56073168 55690807 54014159 52241063 52112263
 [9] 52017083 50998877

Smallest eigenvalues:
 [1]  0.4798902  0.4523935  0.3724019  0.3239674  0.2783808  0.2624360
 [7]  0.2622589  0.1560630  0.1261194 -0.1911510

Largest  eigenvalues:
 [1] 63582006 60115770 57810428 55284706 55250052 53883565 52254894 52162502
 [9] 51444836 51278298

Smallest eigenvalues:
 [1]  0.473308256  0.401127285  0.334910641  0.322614510  0.286410878
 [6]  0.283300887  0.194000008  0.047672795 -0.004845634 -0.292629510

Largest  eigenvalues:
 [1] 64558938 61130217 57782812 56540130 55437595 53800198 52441661 52407814
 [9] 51749690 51345857

Smallest eigenvalues:
 [1]  0.4848754  0.4563133  0.4359468  0.3283973  0.3072911  0.2526044
 [7]  0.1913358 -0.1546851 -0.2407034 -4.5787521

Largest  eigenvalues:
 [1] 61991750 60031365 56568428 55263409 54337442 53486483 52057173 51534840
 [9] 50573657 50333762

Smallest eigenvalues:
 [1]  0.4570738  0.3474239  0.3350057  0.2766244  0.2600711  0.2315790
 [7]  0.2209667  0.1974956 -1.7134918 -5.2846710

Largest  eigenvalues:
 [1] 64274292 60140438 57252366 56165528 54930888 53579782 52358009 52237435
 [9] 52197215 51365213

Smallest eigenvalues:
 [1]  0.49670168  0.49394717  0.44829228  0.36448408  0.32831097  0.31792781
 [7]  0.10269757  0.07532116 -0.15397033 -0.20599405

Largest  eigenvalues:
 [1] 64363426 59878684 57104908 56088550 54249504 52786876 52087835 51823916
 [9] 51434253 50963480

Smallest eigenvalues:
 [1]  0.5167286  0.4824251  0.3597968  0.3111099  0.2555201  0.2021249
 [7]  0.1219693 -0.1239433 -0.8158369 -6.6270137

Largest  eigenvalues:
 [1] 63320238 60817045 57641719 56159222 55196536 54326377 52965386 52316766
 [9] 51996043 51352786

Smallest eigenvalues:
 [1]  0.50290442  0.47585084  0.47098028  0.40679262  0.33466914  0.31840766
 [7]  0.30616957  0.25841052  0.02244975 -1.47613820

Largest  eigenvalues:
 [1] 65447523 60485006 57435826 56876586 55352013 53730149 52920697 52447010
 [9] 51860555 51438062

Smallest eigenvalues:
 [1]  0.3383644  0.2979536  0.2618785  0.2103490  0.2046308  0.1647281
 [7] -0.2224727 -4.2857895 -6.4515612 -8.6066024

Largest  eigenvalues:
 [1] 66507608 61108059 58847356 57035193 55712819 54346549 53014014 52925881
 [9] 52581974 52269794

Smallest eigenvalues:
 [1]  0.4252840  0.3423662  0.3336869  0.3323679  0.2306571  0.2033730
 [7]  0.1020442 -0.2578452 -1.5659658 -5.8674456

Largest  eigenvalues:
 [1] 66077594 59809813 56904559 56805066 54488160 52998364 52539768 51375897
 [9] 51336507 50597457

Smallest eigenvalues:
 [1]  0.63793933  0.52631474  0.43413163  0.41457364  0.32760467  0.32722992
 [7]  0.29616832  0.17152286  0.05353258 -0.46194262

Largest  eigenvalues:
 [1] 63828026 60126248 57351873 55447429 54739545 53282513 51977171 51636795
 [9] 51497797 50927279

Smallest eigenvalues:
 [1]  0.5222351  0.4562282  0.4485056  0.4196149  0.4015466  0.3842206
 [7]  0.3312612  0.2452085  0.2279085 -0.7680761

Largest  eigenvalues:
 [1] 64024180 61105254 57827067 56250724 55873003 54252140 52567359 52415834
 [9] 52111082 51355014

Smallest eigenvalues:
 [1]  0.5519751  0.4872064  0.4747355  0.4578739  0.4470574  0.4217565
 [7]  0.2450505  0.1807670  0.0219168 -4.1126368

Largest  eigenvalues:
 [1] 63577667 59716110 57128273 55359317 55340230 53770377 52120032 52087750
 [9] 51340085 51059569

Smallest eigenvalues:
 [1]   0.1186554   0.0825284   0.0529728  -0.0372975  -0.1339336  -0.5006408
 [7]  -0.6340608  -5.3942508  -9.0506397 -10.7815102

Largest  eigenvalues:
 [1] 60197593 59660633 57177402 55554625 53771355 53535568 51798011 51774512
 [9] 50876604 50181561

Smallest eigenvalues:
 [1]  0.6035463  0.5954294  0.5759948  0.5109591  0.4127615  0.2858684
 [7]  0.2626945  0.2203413 -0.7094681 -0.9064164

Largest  eigenvalues:
 [1] 65283980 60389947 57340141 56593202 55224555 53487125 52489125 52288459
 [9] 52051476 51226028

Smallest eigenvalues:
 [1]   0.33051335   0.32947440   0.32208165   0.28144278   0.20115887
 [6]   0.10026024   0.02786063  -1.57545617  -5.72180767 -13.01099703

Largest  eigenvalues:
 [1] 66766159 60644655 58073269 57145833 55261515 53464085 53400369 52299392
 [9] 52034857 51386274

Smallest eigenvalues:
 [1]   0.1787263   0.1694780  -0.1508300  -0.1618422  -0.2092064  -2.6735940
 [7] -10.8811268 -13.9918489 -16.1152760 -45.2920170

Largest  eigenvalues:
 [1] 64181573 60385359 57681995 55624559 55139120 53978694 52483650 52397406
 [9] 51458610 51359352

Smallest eigenvalues:
 [1]   0.55709940   0.44304761   0.43967077   0.24651467   0.21007720
 [6]   0.07587060   0.03942532  -0.06699987  -1.22521144 -13.42529864

Largest  eigenvalues:
 [1] 63738121 60120180 57069934 55617674 55327418 53629248 52393111 52082738
 [9] 51650625 51243038

Smallest eigenvalues:
 [1]  0.31741735  0.29445243  0.26649249  0.15290198  0.14590069  0.01748872
 [7] -0.02409168 -0.97643113 -2.48616229 -2.69990715

Largest  eigenvalues:
 [1] 64645061 60039385 56551220 56093698 54579275 52924085 52139720 51588420
 [9] 51466508 50635687

Smallest eigenvalues:
 [1]   0.1898011   0.1779258  -0.2048827  -0.3105301  -0.3244568  -0.6612220
 [7]  -0.7574761  -9.0586112 -12.3224468 -45.5009116

Largest  eigenvalues:
 [1] 63169532 61208265 57581156 56074674 55009955 54392361 52306164 52170824
 [9] 51041471 50923017

Smallest eigenvalues:
 [1]  0.4469115  0.4369492  0.3852842  0.3410604  0.2868728  0.2702469
 [7]  0.1745803 -0.0855023 -0.3849818 -0.9510035

Largest  eigenvalues:
 [1] 65252960 60425611 58126205 56877061 54898749 53225959 52740829 52410286
 [9] 51893976 51624976

Smallest eigenvalues:
 [1]  0.5096993  0.4690237  0.3976463  0.3880216  0.3637760  0.3054254
 [7]  0.2829234  0.2599532  0.1933149 -0.7891419

Largest  eigenvalues:
 [1] 65924624 59684389 56611975 56340959 54443394 52705533 52350657 51798634
 [9] 51530241 51042740

Smallest eigenvalues:
 [1]  -0.1306257  -0.2182491  -0.4359008  -0.5852863  -1.1135423  -1.6209949
 [7]  -1.8196521  -2.2606164  -2.4056539 -11.1826519

Largest  eigenvalues:
 [1] 63929336 60765465 57684461 56001098 55794429 54214258 52600603 52521789
 [9] 51943063 51675518

Smallest eigenvalues:
 [1]  0.3996114  0.3851469  0.3834856  0.3747796  0.3739012  0.2204755
 [7] -0.6547359 -0.7969780 -3.7007032 -4.6063026

Largest  eigenvalues:
 [1] 65111569 59930882 57508501 56327488 54775501 53097587 52410190 52366181
 [9] 51636071 51499959

Smallest eigenvalues:
 [1]  0.49717037  0.44398068  0.33357902  0.32290876  0.16551153  0.11560995
 [7]  0.01621756 -0.31879867 -0.43762964 -6.27493168

Largest  eigenvalues:
 [1] 64756233 59566271 57041714 55570610 54146153 52653235 52048032 51750849
 [9] 51214058 51075972

Smallest eigenvalues:
 [1]  0.5280886  0.5229860  0.5163932  0.4758649  0.4746665  0.4543488
 [7]  0.3745868  0.2968540  0.2602990 -0.5961865

Largest  eigenvalues:
 [1] 64009321 60606589 57143668 56323018 55377409 53661104 52287254 52082333
 [9] 52009968 51226181

Smallest eigenvalues:
 [1]  0.42972082  0.37327617  0.32616719  0.25645898  0.25346892  0.20537717
 [7]  0.07521011 -0.02827733 -0.11018006 -0.51743350

Largest  eigenvalues:
 [1] 61290100 60031369 57133066 55819832 53867922 53851609 52174240 51635254
 [9] 50746817 50707498

Smallest eigenvalues:
 [1]   0.4838751   0.4833004   0.4393723   0.3841969   0.2933796   0.2815018
 [7]   0.2175510   0.1997441  -1.7149451 -28.3217400

Largest  eigenvalues:
 [1] 63829585 59968574 57081574 55657127 55174927 53322796 52153221 51690406
 [9] 51555364 51042939

Smallest eigenvalues:
 [1]  0.46707631  0.46191817  0.36168906  0.29191823  0.28113160  0.27180736
 [7]  0.19479707  0.04415995 -0.18954797 -1.97918844

Largest  eigenvalues:
 [1] 64718511 59452673 56622443 55988099 54291841 52823758 52016166 51700274
 [9] 51213750 50847463

Smallest eigenvalues:
 [1]  0.4660506  0.4599969  0.4131064  0.3923726  0.3892344  0.3143654
 [7]  0.2647937  0.2221240 -0.1185449 -3.4275015

Largest  eigenvalues:
 [1] 63537445 60421480 57546608 55664746 55451003 54147554 52344905 52314703
 [9] 51575202 51251961

Smallest eigenvalues:
 [1]  0.4056294  0.3800859  0.3677871  0.3472109  0.2619507  0.2334085
 [7]  0.1778901  0.1465146 -0.3718325 -0.6810458

Largest  eigenvalues:
 [1] 65145399 61156549 58473966 56551354 55873371 54296463 53116771 52557560
 [9] 52053291 51930585

Smallest eigenvalues:
 [1]  0.4047533  0.3961447  0.3761853  0.3121273  0.3105423  0.2957181
 [7]  0.2280731  0.2215193 -0.7267893 -1.1710817

Largest  eigenvalues:
 [1] 64978227 59900672 57844393 56155312 55024515 53940857 52191911 52158163
 [9] 51779626 51200255

Smallest eigenvalues:
 [1]  0.5094213  0.4887179  0.4350756  0.3718631  0.3454801  0.3173984
 [7]  0.2981974  0.2455020  0.1727210 -1.0740660

Largest  eigenvalues:
 [1] 64660658 59901449 57277046 55567244 54947603 53478410 52105215 51708121
 [9] 51680084 51284710

Smallest eigenvalues:
 [1]   0.23666775   0.19696834   0.16535025   0.13610663   0.07894434
 [6]  -0.06924628  -0.15111873  -2.95676465 -12.11895385 -12.66048797

Largest  eigenvalues:
 [1] 63078323 58732346 56016653 55248847 53883715 52688534 51431821 51127713
 [9] 50889641 50050161

Smallest eigenvalues:
 [1]  0.4052114  0.3977633  0.3518903  0.3464258  0.3031983  0.2768000
 [7]  0.2580313  0.2407707  0.1873606 -2.9965878

Largest  eigenvalues:
 [1] 65124315 60438801 57102924 57043930 54950138 53450674 52805348 52546452
 [9] 52017693 51660801

Smallest eigenvalues:
 [1]  0.5477875  0.4588957  0.4520199  0.3379817  0.2525528  0.2217774
 [7]  0.1773967  0.1738130  0.1545247 -0.2604269

Largest  eigenvalues:
 [1] 63736110 60366337 57321776 55295173 55274215 53485717 52936781 51827820
 [9] 51765377 51497498

Smallest eigenvalues:
 [1]  0.4816732  0.4739031  0.4259841  0.4072189  0.3362325  0.2803447
 [7]  0.1677723  0.1128676 -0.6205316 -1.3516641

Largest  eigenvalues:
 [1] 65095020 59765952 57366970 56114894 54864578 53368385 52159709 52067841
 [9] 51932334 51221450

Smallest eigenvalues:
 [1]   0.29010428   0.24140761   0.20818745   0.11323732   0.02074865
 [6]  -0.33961604 -13.07879631 -16.28979150 -56.76642877 -70.64630226

Largest  eigenvalues:
 [1] 63027284 59421479 56231444 54706048 54562277 53028310 51814327 51507339
 [9] 50830466 50597701

Smallest eigenvalues:
 [1]  0.5647435  0.3920006  0.3366998  0.2980104  0.2973342  0.2718065
 [7]  0.2709506 -0.1080825 -1.0100542 -1.1747386

Largest  eigenvalues:
 [1] 62408256 59614678 57393694 55353284 54565459 53588408 52406147 51886748
 [9] 50863848 50740281

Smallest eigenvalues:
 [1]  0.57144900  0.52921040  0.52911305  0.50753726  0.48910617  0.45276255
 [7]  0.37900531  0.07620250  0.05655370 -0.01034054

Largest  eigenvalues:
 [1] 65419041 59907847 57169638 56226242 54652356 52926350 52404559 51574323
 [9] 51552065 50761521

Smallest eigenvalues:
 [1]  0.371271890  0.330851213  0.307232654  0.281531137  0.256668163
 [6]  0.232274056  0.193993701  0.182034178 -0.005417974 -0.302951598

Largest  eigenvalues:
 [1] 63789800 59241096 57039615 55103653 54506807 53149607 51400099 51336439
 [9] 51092612 50372391

Smallest eigenvalues:
 [1]  0.4909831  0.4549253  0.4099944  0.3741369  0.3719137  0.2222549
 [7]  0.1747840 -0.3199870 -4.0824018 -4.3992507

Largest  eigenvalues:
 [1] 63554601 60075734 56807171 55074291 54931844 53146499 51787747 51057811
 [9] 51009623 50725826

Smallest eigenvalues:
 [1]  0.57592619  0.54454884  0.50724665  0.36937398  0.36003625  0.31825666
 [7]  0.25611902  0.23308721  0.22615272 -0.04615426

Largest  eigenvalues:
 [1] 63053855 60229365 56868888 55576619 55183520 53737069 52080177 51891840
 [9] 51300620 50879257

Smallest eigenvalues:
 [1]  0.5589331  0.4863285  0.4112946  0.3783604  0.3362585  0.2128650
 [7]  0.1215538 -0.2453996 -0.4138166 -1.0953834

Largest  eigenvalues:
 [1] 64953052 60249766 57455140 56518763 55019934 53460661 52457286 52097709
 [9] 51611383 50985717

Smallest eigenvalues:
 [1]  0.5972178  0.5456131  0.4455389  0.4226966  0.3205695  0.3148668
 [7]  0.2679887  0.2527282  0.1654921 -0.5227497

Largest  eigenvalues:
 [1] 65243761 60006447 56832069 56368450 54727375 53024001 52441960 51826070
 [9] 51778153 51063630

Smallest eigenvalues:
 [1]   0.38359621   0.36222014   0.35961793   0.26874270   0.20798768
 [6]   0.08574142  -0.41520101  -5.17263069 -11.23711291 -38.95989049

Largest  eigenvalues:
 [1] 62789801 59712578 56427323 54950722 54868390 52852027 51819028 51118818
 [9] 50854511 50411281

Smallest eigenvalues:
 [1]  0.4909796  0.4570228  0.4066567  0.3032244  0.2554636  0.2424323
 [7]  0.2384851 -0.4434140 -0.8030490 -2.3378398

Largest  eigenvalues:
 [1] 67150421 60669272 58591803 57408161 55274280 53620116 53564825 52896289
 [9] 52227571 52064083

Smallest eigenvalues:
 [1]  0.5579982  0.5051204  0.3622174  0.3388242  0.2910276  0.2906055
 [7]  0.2526001  0.1288093  0.1058786 -0.9665361

Largest  eigenvalues:
 [1] 65983704 60976055 58410422 57315994 55543214 54136413 53258475 52768257
 [9] 52473207 51747584

Smallest eigenvalues:
 [1]  0.4335797  0.4310832  0.3973678  0.3264764  0.2949178  0.2167845
 [7]  0.1722916  0.1245493  0.1232390 -0.3697616

Largest  eigenvalues:
 [1] 63363120 60481686 57178352 55545719 55256142 53928166 52441585 52338007
 [9] 51405894 51281093

Smallest eigenvalues:
 [1]  0.5092447  0.4580002  0.4432456  0.3791556  0.2967002  0.2387923
 [7]  0.2172654  0.1813795 -0.1203716 -0.3629448

Largest  eigenvalues:
 [1] 63005277 59507447 56539402 54936544 54658541 52937044 51505806 51095008
 [9] 50982621 50339473

Smallest eigenvalues:
 [1]  0.46291563  0.38719190  0.31786026  0.29318455  0.19211782  0.16450483
 [7] -0.04082186 -0.12421561 -0.83118975 -2.12806154

Largest  eigenvalues:
 [1] 65394117 60275985 57693786 56521421 55051914 53605746 52458415 52410567
 [9] 52337765 51609474

Smallest eigenvalues:
 [1]  0.44524083  0.33245889  0.32462086  0.25437299  0.24604660  0.23578911
 [7]  0.17555370  0.09603666 -0.01507374 -0.19263204

Largest  eigenvalues:
 [1] 64906064 59519019 57160557 55722279 54727460 53363251 51797701 51737353
 [9] 51250806 50731940

Smallest eigenvalues:
 [1]  0.41492594  0.29416226  0.28393718  0.28006142  0.18150681  0.14976376
 [7]  0.14608236  0.07471617 -0.77893733 -1.07189272

Largest  eigenvalues:
 [1] 64983449 60648684 57972259 55649599 55561426 54057784 53003278 52137233
 [9] 52052877 51781663

Smallest eigenvalues:
 [1]   0.4577545   0.4522391   0.4027851   0.3863218   0.3476765   0.3327155
 [7]   0.2706671   0.2129754  -1.0122043 -20.5550455

Largest  eigenvalues:
 [1] 63515113 60002132 57141020 55851145 55311790 53615514 51988878 51967686
 [9] 51778499 50941847

Smallest eigenvalues:
 [1]  0.54853294  0.50670621  0.43630769  0.42127703  0.39077436  0.28047300
 [7]  0.27437091  0.27193397  0.25827140 -0.09679595

Largest  eigenvalues:
 [1] 65329281 60762509 57832429 56852817 55367283 53742499 52927568 52432303
 [9] 52172398 51360320

Smallest eigenvalues:
 [1]  0.5483294  0.5379973  0.5170185  0.3726293  0.3230770  0.3121718
 [7]  0.2450974  0.2203398  0.0599361 -5.3187898

Largest  eigenvalues:
 [1] 62669562 60249016 56921224 55580776 54825988 53797765 52224272 51661710
 [9] 51005158 50788887

Smallest eigenvalues:
 [1]   0.30186246   0.25588873   0.22552097   0.17886503   0.04501903
 [6]  -0.17855591  -0.48106412 -10.43718676 -13.43292393 -24.39000393

Largest  eigenvalues:
 [1] 62345266 59068683 56452822 54424568 54355514 52693592 51603877 51499862
 [9] 50607549 50361774

Smallest eigenvalues:
 [1]  0.5029969  0.4924368  0.4343908  0.4127689  0.3936988  0.3684727
 [7]  0.3423737  0.2358618 -0.1057755 -0.2538911

Largest  eigenvalues:
 [1] 64414116 60106720 57646132 56283123 54645963 53203514 52327673 51834114
 [9] 51693769 51057981

Smallest eigenvalues:
 [1]  0.5258422  0.4687241  0.4557539  0.4278174  0.3596955  0.3399936
 [7]  0.3066862  0.1886756 -0.2935807 -0.4541939

Largest  eigenvalues:
 [1] 65254733 60385691 57041037 56303551 55570412 53723274 52300271 52221783
 [9] 51738451 51113930

Smallest eigenvalues:
 [1]   0.238454453   0.095073277  -0.007738026  -0.161267824  -0.368006568
 [6]  -1.702313950  -6.342835540 -18.344036839 -23.197898678 -95.354781700

Largest  eigenvalues:
 [1] 65296510 60911543 57177145 57000834 55917603 53967696 53321942 52893030
 [9] 51963347 51883159

Smallest eigenvalues:
 [1]  0.4991829  0.4818742  0.3902265  0.3703390  0.3133894  0.2937669
 [7]  0.1900952  0.1659271  0.1239934 -0.5915255

Largest  eigenvalues:
 [1] 64302211 60716873 57685295 56023991 55870578 54208739 52796191 52538021
 [9] 52020759 51807013

Smallest eigenvalues:
 [1]  0.429156932  0.368938493  0.325209364  0.241678838  0.226363620
 [6]  0.153614750 -0.003838937 -0.130597834 -1.006863253 -2.150462474

Largest  eigenvalues:
 [1] 62477984 59853835 57105826 55674597 54204036 53824487 52107679 51568295
 [9] 50698970 50496817

Smallest eigenvalues:
 [1]    0.2789917    0.2225079    0.1954517    0.1855275   -0.2659694
 [6]   -0.6825136   -0.7343493   -1.7496139   -6.4743192 -100.3148702

Largest  eigenvalues:
 [1] 66884428 60727530 57939227 56612360 55508821 53538982 52925127 52178014
 [9] 52109953 51010463

Smallest eigenvalues:
 [1]  0.5461506  0.4823923  0.4672295  0.3512405  0.3175798  0.2802527
 [7]  0.2663688  0.2644027  0.2258517 -0.4020982

Largest  eigenvalues:
 [1] 62906218 60603242 57310859 55776414 55097754 54178427 52751712 51888506
 [9] 51265792 50969062

Smallest eigenvalues:
 [1]  0.4625740  0.4010580  0.3619648  0.3291956  0.3288281  0.2895016
 [7]  0.2553185  0.2263961  0.2109011 -3.3883164

Largest  eigenvalues:
 [1] 64932886 60317744 57475822 56630719 55104380 53516737 52474525 52437673
 [9] 52419629 51452034

Smallest eigenvalues:
 [1]  0.52715344  0.43580318  0.38113151  0.32608084  0.31390926  0.19302616
 [7] -0.05792133 -0.93230301 -1.91622521 -6.09469851

Largest  eigenvalues:
 [1] 64517255 60109472 57331116 56545376 54876978 53172348 52340385 52301442
 [9] 51780712 51186017

Smallest eigenvalues:
 [1]  0.44887669  0.42603683  0.41961486  0.41196201  0.37011495  0.17941008
 [7]  0.14942029  0.14904827  0.05206293 -1.94679354

Largest  eigenvalues:
 [1] 64203103 60492865 57359657 56044722 55344547 53440895 52741323 52071351
 [9] 51698724 51591883

Smallest eigenvalues:
 [1]  0.3892820  0.3487393  0.3113848  0.2719389  0.2204615  0.0496663
 [7] -0.2384710 -0.5021606 -0.5821858 -3.1487417

Largest  eigenvalues:
 [1] 65609042 60671337 58168512 56122139 55410158 53825258 52993446 52289341
 [9] 52052802 51959624

Smallest eigenvalues:
 [1]  0.3921902  0.3769315  0.3519380  0.3496981  0.2686873  0.2389682
 [7]  0.1381529  0.1366931 -0.9824289 -1.0151289

Largest  eigenvalues:
 [1] 65782954 60798656 58210469 56374832 55633437 54264241 52434761 52415451
 [9] 52353673 51677285

Smallest eigenvalues:
 [1]  0.59710702  0.54076646  0.52405931  0.49091527  0.42684775  0.39801605
 [7]  0.27760095  0.14651228  0.11536004 -0.02958352

Largest  eigenvalues:
 [1] 64891688 60407884 57291069 55306151 55149069 53551103 52079719 51520547
 [9] 51514934 51198273

Smallest eigenvalues:
 [1]  0.53794929  0.42607518  0.30905173  0.26351827  0.21458911  0.02477885
 [7] -0.02717911 -0.16207734 -1.02056580 -2.80488081

Largest  eigenvalues:
 [1] 63291348 59431319 56748974 55163999 54910435 53023954 51818178 51532302
 [9] 51263653 50697319

Smallest eigenvalues:
 [1]  0.5318254  0.4674420  0.3899673  0.3229714  0.2784848  0.2699827
 [7]  0.1655744 -0.1108428 -0.1673049 -1.1428309

Largest  eigenvalues:
 [1] 64448618 60730551 57304818 56627205 55459424 53505813 52740090 52501294
 [9] 51901187 51070646

Smallest eigenvalues:
 [1]  0.25243659  0.21358580  0.19323473  0.18336026  0.09014207 -0.71495101
 [7] -1.16325950 -2.01383008 -4.18354226 -5.26476507

Largest  eigenvalues:
 [1] 65518080 59796194 57316053 56510531 55031019 53501384 52611474 52060676
 [9] 51870141 50819031

Smallest eigenvalues:
 [1]  0.4910755  0.4891466  0.4774769  0.4365560  0.4104876  0.3207398
 [7]  0.3188411  0.3007056  0.2665099 -0.2975243

Largest  eigenvalues:
 [1] 64208698 59919816 57112887 55732158 55158474 53411081 52265271 51740662
 [9] 51638936 50902639

Smallest eigenvalues:
 [1]  0.5101966  0.4951504  0.4665691  0.3619481  0.3521903  0.3331943
 [7]  0.2803387 -0.3407573 -1.5429698 -2.1064550

Largest  eigenvalues:
 [1] 67419690 60898653 58684381 57775396 55279604 53791756 53763943 52741421
 [9] 52232406 51983087

Smallest eigenvalues:
 [1]  0.5696144  0.5590046  0.4389156  0.3974480  0.3645191  0.3583544
 [7]  0.3416514  0.2737678  0.1813640 -1.8833488

Largest  eigenvalues:
 [1] 64871755 60282387 57177814 56218951 55325217 53843399 52221401 52102718
 [9] 52018948 50934637

Smallest eigenvalues:
 [1]  0.4693469  0.4518112  0.3918816  0.3859981  0.3344764  0.3247012
 [7]  0.2740529  0.2253304  0.1303382 -0.0675637

Largest  eigenvalues:
 [1] 65381241 59405266 56627087 56373903 54257151 52803392 52403884 51544328
 [9] 51286517 50622072

Smallest eigenvalues:
 [1]  0.5149883  0.4299325  0.4092290  0.3678656  0.3144539  0.2852062
 [7]  0.2502052 -0.2123847 -0.5578747 -1.5390840

Largest  eigenvalues:
 [1] 64785318 60554602 57631317 56480150 55190970 53384658 52500148 52281630
 [9] 52105357 51159596

Smallest eigenvalues:
 [1]  0.4722795  0.4650883  0.4566886  0.4523340  0.4111263  0.4048655
 [7]  0.3561046  0.3181576  0.3020069 -0.2281016

Largest  eigenvalues:
 [1] 64963433 60252594 57667626 56279449 55156992 53719120 52367111 52129632
 [9] 51905101 51220596

Smallest eigenvalues:
 [1]  0.4813249  0.4633643  0.4425030  0.3960609  0.3827651  0.3703349
 [7]  0.3567444  0.3300237 -0.2133325 -3.0614927

Largest  eigenvalues:
 [1] 63039208 59986948 57170072 55602980 55163735 53530057 51909456 51679701
 [9] 51416241 50544673

Smallest eigenvalues:
 [1]  0.33992788  0.33117354  0.24444898  0.16244912  0.16041558  0.02198482
 [7] -0.03019142 -0.04202999 -0.69409640 -4.92509489

Largest  eigenvalues:
 [1] 64303371 60012434 57103694 55855808 55827790 53966460 52150433 51788493
 [9] 51760883 50690858

Smallest eigenvalues:
 [1]  0.3739392  0.3400950  0.3374348  0.2752155  0.2492474  0.2432026
 [7]  0.2187203  0.2043097 -3.0246086 -9.9196261

Largest  eigenvalues:
 [1] 64510963 60626035 57711355 55719739 55574296 54148691 52370501 52177869
 [9] 51655977 51564711

Smallest eigenvalues:
 [1]  0.5550998  0.4613133  0.3985648  0.3393245  0.3329940  0.3010023
 [7]  0.2456954  0.1834303 -0.5305284 -2.3738032

Largest  eigenvalues:
 [1] 66580830 59676158 57142087 56878847 54361913 53231395 52558753 51759258
 [9] 51380248 51058168

Smallest eigenvalues:
 [1]  0.4774911  0.4439654  0.4332345  0.3126872  0.3014802  0.2551789
 [7]  0.1868672  0.1186505 -2.1765488 -4.3838795

Largest  eigenvalues:
 [1] 63389818 59813482 57254308 55899256 54896559 53372822 52739198 52192275
 [9] 51700891 51484188

Smallest eigenvalues:
 [1]   0.43328845   0.38719455   0.37674980   0.27752984   0.12302446
 [6]  -0.07760758  -0.11254720  -0.41678797  -3.89305747 -14.39757724

Largest  eigenvalues:
 [1] 63721875 59221417 56626464 55014390 54261307 52626148 51366186 51048924
 [9] 51001995 50472366

Smallest eigenvalues:
 [1]  0.5049877  0.4139814  0.3794518  0.3507782  0.3320662  0.2714831
 [7]  0.2431447  0.2112054  0.1881777 -0.2357201

Largest  eigenvalues:
 [1] 63363523 59721126 57030640 55540033 54812756 53299844 51787395 51676671
 [9] 51585476 50791837

Smallest eigenvalues:
 [1]  0.4198794  0.3204345  0.3035517  0.2641293  0.2438497  0.2095091
 [7]  0.1592699  0.1364110 -1.1454457 -4.0666950

Largest  eigenvalues:
 [1] 65093158 59097482 56547614 56075054 53901870 52596559 52102653 51245021
 [9] 51099102 50486599

Smallest eigenvalues:
 [1]  0.5227194  0.5059859  0.4981923  0.4457535  0.3767528  0.3616820
 [7]  0.2974851  0.2890158 -0.4473132 -2.1675098

Largest  eigenvalues:
 [1] 66617715 61003702 58140449 57788429 55209434 53823945 53382298 52434736
 [9] 52113933 51524019

Smallest eigenvalues:
 [1]  0.445328417  0.385286421  0.364609395  0.315363511  0.273160561
 [6]  0.261115992  0.254419890  0.203082302 -0.004028773 -1.052138807

Largest  eigenvalues:
 [1] 65084793 60246996 57372672 56263051 55367276 53722296 52323883 52022610
 [9] 51834624 51014821

Smallest eigenvalues:
 [1]  0.4341606  0.3577792  0.3255446  0.3157514  0.2818044  0.2334308
 [7]  0.2146404 -0.4799234 -1.6754531 -4.5124258

Largest  eigenvalues:
 [1] 63383427 60232910 57210838 55661666 55578067 53675023 51953631 51771568
 [9] 51471919 51237151

Smallest eigenvalues:
 [1]  0.42093704  0.37580775  0.31111732  0.29431373  0.27486582  0.24140553
 [7]  0.19546482  0.03669958 -0.14103699 -5.23249640

Largest  eigenvalues:
 [1] 65359462 60576357 57823392 56572610 56182118 54262181 52595117 52410399
 [9] 51955369 51251053

Smallest eigenvalues:
 [1]   0.2729783   0.2706867   0.2384592   0.2278426   0.1235578  -0.4504019
 [7]  -0.5971150  -1.4395688 -16.3249884 -34.0914851

Largest  eigenvalues:
 [1] 64901160 59759172 56958042 56667693 54905439 53217128 52489484 51370122
 [9] 51198887 50426340

Smallest eigenvalues:
 [1]  0.4554501  0.3550554  0.3425412  0.3238883  0.2681186  0.2454067
 [7] -0.1319494 -0.3589444 -1.5479449 -8.7067886

Largest  eigenvalues:
 [1] 63402451 59613515 56936391 54913542 54746845 52954454 51685464 51163980
 [9] 51013426 50560135

Smallest eigenvalues:
 [1]  0.50499464  0.50237240  0.46944764  0.45110610  0.28366685  0.26981990
 [7]  0.12573600 -0.01493711 -0.43155697 -9.48172877

Largest  eigenvalues:
 [1] 64984141 60068182 57095392 55869088 54885385 53134114 52120017 51964467
 [9] 51894852 51237814

Smallest eigenvalues:
 [1]  0.43274085  0.40635116  0.39121924  0.38072803  0.33036984  0.28694404
 [7]  0.21678863  0.20260673  0.06202214 -1.07354130

Largest  eigenvalues:
 [1] 64923661 61194443 58218019 56469070 56263877 54855320 53132086 52796651
 [9] 52185622 51983742

Smallest eigenvalues:
 [1]   0.48516217   0.36710366   0.29781240   0.20398797  -0.07905503
 [6]  -0.36319719  -0.37410108  -1.24833610  -2.03155426 -24.59923755

Largest  eigenvalues:
 [1] 65748158 60418040 57699642 56553541 55557636 53669555 52679027 52323301
 [9] 52193404 51390377

Smallest eigenvalues:
 [1]  0.5499865  0.4208013  0.4102624  0.3910351  0.3840838  0.2929361
 [7]  0.2620767  0.1673236  0.1459602 -1.1357819

Largest  eigenvalues:
 [1] 65232715 60516047 57818024 56383629 55534259 54121014 52830329 52455888
 [9] 52364252 51829765

Smallest eigenvalues:
 [1]  0.24334952  0.22008136  0.20946134  0.20289071  0.19768708 -0.01684957
 [7] -0.05938816 -0.07341618 -1.40394549 -3.74934048

Largest  eigenvalues:
 [1] 68040001 60681448 58564870 57737275 54968708 53959572 53753965 52351765
 [9] 51793378 51688121

Smallest eigenvalues:
 [1]  0.4822019  0.4618066  0.3679673  0.3482136  0.3172875  0.3096675
 [7]  0.2920842  0.2557456  0.2378626 -0.1069289

Largest  eigenvalues:
 [1] 64715112 60386260 57290028 56280337 54909910 53360729 52496448 51746698
 [9] 51714526 50854797

Smallest eigenvalues:
 [1]  0.40366129  0.35584743  0.34893782  0.26607788  0.25617216  0.24545336
 [7]  0.23088991  0.07835972 -0.06808716 -0.71303065

Largest  eigenvalues:
 [1] 64418227 60272024 57538448 55416779 55135472 53764506 52055857 51945465
 [9] 51643290 51106653

Smallest eigenvalues:
 [1]  0.6458670  0.5290819  0.4215005  0.3536802  0.3200041  0.2503895
 [7]  0.2296752  0.1531097 -0.1155864 -0.5435428

Largest  eigenvalues:
 [1] 63183821 59985908 57502172 55322395 55038142 53752840 52348876 51810737
 [9] 51198202 50840139

Smallest eigenvalues:
 [1]   0.4640593   0.4377243   0.3644144   0.3194029   0.3104610   0.2795312
 [7]   0.2055138   0.1923308  -1.2375955 -12.4058702

Largest  eigenvalues:
 [1] 64573106 59936877 56722379 55809260 55104462 53406175 52353098 51918984
 [9] 51852662 51219078

Smallest eigenvalues:
 [1]  0.45384324  0.37035798  0.35794837  0.32435794  0.25690769  0.25328091
 [7]  0.24230546  0.05948428 -0.75149526 -1.32151493

Largest  eigenvalues:
 [1] 64449102 60377059 57220185 55480173 55462660 53830333 52192780 51873629
 [9] 51413374 51156962

Smallest eigenvalues:
 [1]  0.49027024  0.44953124  0.42905935  0.42731675  0.36738142  0.30615057
 [7]  0.24320575  0.21787247  0.16608311 -0.08800963

Largest  eigenvalues:
 [1] 63324737 59538915 56864243 55083026 55073825 53210917 51888727 51500722
 [9] 51158414 50660139

Smallest eigenvalues:
 [1]  0.5442891  0.5004407  0.4789799  0.4641114  0.3300991  0.3097456
 [7]  0.3088163  0.2767147  0.2209505 -0.8225658

Largest  eigenvalues:
 [1] 64463616 59933708 57098043 55853022 54863078 53391108 52313894 51896564
 [9] 51627284 51003963

Smallest eigenvalues:
 [1]  0.4654656  0.4138306  0.3295331  0.2914700  0.2825199  0.2504557
 [7]  0.2406395  0.2264968  0.1826636 -4.7170459

Largest  eigenvalues:
 [1] 66806578 60182174 57652106 57160939 54902998 53537384 53148556 52223214
 [9] 52068645 51477767

Smallest eigenvalues:
 [1]  0.49404084  0.43808708  0.37417089  0.35002741  0.34270305  0.30349633
 [7]  0.28832401  0.18733932 -0.04115719 -0.38155206

Largest  eigenvalues:
 [1] 65596407 60748616 57948171 56464715 55692419 54062004 53442958 52657923
 [9] 52140380 51994919

Smallest eigenvalues:
 [1]  0.43767714  0.41360798  0.29450200  0.26490822  0.24130288  0.20592951
 [7]  0.16103586  0.07000476 -0.41737411 -0.50971827

Largest  eigenvalues:
 [1] 67168498 60566866 57849403 57404401 54764190 53469202 53123933 52272941
 [9] 51948122 51711059

Smallest eigenvalues:
 [1]  0.4287099  0.4282514  0.3973804  0.3892213  0.3123146  0.2358853
 [7]  0.1612999  0.1605497 -0.2688335 -5.8299995

Largest  eigenvalues:
 [1] 65084274 59743409 56896469 56346631 54535488 52725316 52411718 51643999
 [9] 51561855 50930849

Smallest eigenvalues:
 [1]  0.3082562  0.3047844  0.2716003  0.2579050  0.1788843 -0.2576115
 [7] -0.3452661 -0.9506603 -2.0562081 -2.6868315

Largest  eigenvalues:
 [1] 65264885 60778802 57708336 56415326 55899069 54367923 52810124 52405618
 [9] 52093863 51653800

Smallest eigenvalues:
 [1]  0.59600416  0.53213548  0.51288707  0.47686931  0.46248450  0.38031461
 [7]  0.30797385  0.30478171  0.20292123 -0.01065626

Largest  eigenvalues:
 [1] 65765198 60987537 58210608 56764277 55471310 53732148 52709991 52519562
 [9] 52020629 51685092

Smallest eigenvalues:
 [1]  0.6034738  0.5556320  0.5199809  0.4999030  0.4861337  0.4641957
 [7]  0.4211815  0.3063336  0.2672209 -0.2760835

Largest  eigenvalues:
 [1] 64124588 59773195 56768950 55984895 54821312 53177997 51973039 51811308
 [9] 51628959 50833276

Smallest eigenvalues:
 [1]   0.4404908   0.4034500   0.3996555   0.3893506   0.3052125   0.2917697
 [7]   0.1438516  -0.3118468  -9.3989921 -18.2183983

Largest  eigenvalues:
 [1] 65500943 60219216 57519340 56635008 54742896 53386022 52744574 51496580
 [9] 51475777 50514245

Smallest eigenvalues:
 [1]  0.46474102  0.37507310  0.36475399  0.28321383  0.23768977  0.23375274
 [7]  0.19428444  0.05959832  0.04432313 -6.34832757

Largest  eigenvalues:
 [1] 61708688 59864826 57140470 56000404 54333436 53803108 52122637 51134929
 [9] 50551509 50525734

Smallest eigenvalues:
 [1]  0.4706150  0.4617676  0.4283637  0.4041858  0.3622399  0.3478138
 [7]  0.2470418  0.2353118 -0.6615252 -1.0302431

Largest  eigenvalues:
 [1] 65180634 60288309 58247009 56440038 55256285 54039406 52539085 52509700
 [9] 52187060 51768085

Smallest eigenvalues:
 [1]  0.47066771  0.38953935  0.35319067  0.29865405  0.04963312  0.01243067
 [7] -0.12960261 -0.13251663 -1.29890621 -2.15787959

Largest  eigenvalues:
 [1] 65055322 59994988 56704071 56240372 54695048 53018451 52309600 52188075
 [9] 51422350 51171086

Smallest eigenvalues:
 [1]  0.42271475  0.37708931  0.36209363  0.33430741  0.28253021  0.24862574
 [7]  0.20156792  0.15752430  0.08164249 -3.32906415

Largest  eigenvalues:
 [1] 61367940 59582945 56825009 55424000 53504078 53409756 51673331 50917345
 [9] 50245675 50109295

Smallest eigenvalues:
 [1]   0.28327777   0.27753930   0.10578123   0.07314426  -0.16387648
 [6]  -0.88582894  -1.55372743  -2.32373572  -2.52625439 -27.40042386

Largest  eigenvalues:
 [1] 63004957 60612180 57156802 55952653 55483519 54309703 52438970 52367865
 [9] 51399196 51253812

Smallest eigenvalues:
 [1]  0.47750982  0.46956939  0.44915818  0.42281053  0.35592319  0.19446157
 [7]  0.18962537  0.16803872  0.08330244 -0.32227640

Largest  eigenvalues:
 [1] 65523492 60063624 56901120 56376583 55001407 53157168 52437940 52200364
 [9] 51999228 51485916

Smallest eigenvalues:
 [1]   0.4571964   0.3238459   0.2648202   0.2493922   0.2049719   0.2019953
 [7]   0.1837542  -0.5546926  -2.1066588 -21.2173276

Largest  eigenvalues:
 [1] 65229683 60393280 57768877 56105495 54799568 53196929 52388765 52113475
 [9] 51972804 51710292

Smallest eigenvalues:
 [1]   0.41078896   0.35949319   0.34406070   0.32722415   0.31474933
 [6]   0.29921865   0.27754639   0.09137449  -0.02184615 -29.39202358

Largest  eigenvalues:
 [1] 63022377 59484776 57100237 55226959 55194210 53428889 51724593 51475606
 [9] 51288230 50596320

Smallest eigenvalues:
 [1]  0.36847322  0.34207286  0.33981044  0.27570306  0.25959508  0.22660283
 [7]  0.17982102  0.03736938 -0.33792894 -2.94218894

Largest  eigenvalues:
 [1] 64995722 60254030 57290980 55896512 55322786 53625187 51823965 51548462
 [9] 51526877 50883196

Smallest eigenvalues:
 [1]  0.4955103  0.4726134  0.4609949  0.3370033  0.3052478  0.3018187
 [7]  0.2919358  0.2790933  0.2225502 -0.4303885

Largest  eigenvalues:
 [1] 61920249 59872713 56871954 55567620 54250349 53663278 52162575 51672359
 [9] 50790756 50459394

Smallest eigenvalues:
 [1]  0.48895418  0.46394416  0.45855480  0.42888069  0.41184146  0.31492873
 [7]  0.28350104  0.27625885  0.09075314 -3.54530943

Largest  eigenvalues:
 [1] 64043044 60509385 57318820 55474611 55434749 53804844 52156129 51656538
 [9] 51607360 50997015

Smallest eigenvalues:
 [1]  0.452059327  0.450230083  0.399109587  0.240694255  0.173602166
 [6]  0.154327437  0.066358713 -0.008891906 -1.682021539 -3.384752104

Largest  eigenvalues:
 [1] 63903868 60786594 57278680 56008697 55397039 53990673 52489251 52194596
 [9] 51931905 51254613

Smallest eigenvalues:
 [1]   0.3655935   0.3329792   0.2606046   0.2589456   0.2511102   0.2165988
 [7]   0.2043469  -0.6491771  -8.5410615 -16.9960753

Largest  eigenvalues:
 [1] 64497420 61351850 57931601 56981107 56359736 55256138 53113711 52663058
 [9] 52255885 51664821

Smallest eigenvalues:
 [1]  0.46277828  0.45676796  0.44092611  0.43662052  0.35244114  0.28151719
 [7]  0.23070772  0.19887279  0.04933185 -1.02341151

Largest  eigenvalues:
 [1] 65890518 59920846 57251140 57034471 54819032 53363671 52921575 52189240
 [9] 52064594 51554353

Smallest eigenvalues:
 [1]   0.11801268   0.09489184   0.08466386   0.07295297  -0.22823110
 [6]  -0.63592599  -1.93349065  -6.46042397 -17.86811655 -67.45496709

Largest  eigenvalues:
 [1] 63867038 59435600 56543078 54968586 54542654 52832065 51947736 51299224
 [9] 51285669 51006173

Smallest eigenvalues:
 [1]  0.5278092  0.4939030  0.4748969  0.4338467  0.4239038  0.4017272
 [7]  0.3793102  0.3614124  0.3346325 -0.5934390

Largest  eigenvalues:
 [1] 63959375 60847791 57545913 56281084 55855382 54118737 52261688 52190027
 [9] 52085476 51105563

Smallest eigenvalues:
 [1]  0.6247623  0.5476715  0.4598102  0.4455974  0.4411331  0.4318708
 [7]  0.3728331  0.2579648 -0.1275022 -0.1724734

Largest  eigenvalues:
 [1] 64797134 60195553 57625071 56073197 55273474 53481629 52518988 52242795
 [9] 51812093 51410050

Smallest eigenvalues:
 [1]  0.5584616  0.5545359  0.4930952  0.4839450  0.3540002  0.3452527
 [7]  0.3301492  0.3117685  0.2383850 -0.1593142

Largest  eigenvalues:
 [1] 63363949 59670131 57190772 55369679 55204815 53698423 52031428 51669022
 [9] 51246827 50811008

Smallest eigenvalues:
 [1]  0.47844117  0.41895707  0.40023332  0.39309687  0.35261705  0.33232005
 [7]  0.05061357  0.01728149 -0.14966521 -4.74192526

Largest  eigenvalues:
 [1] 64413604 59608540 56700461 56022953 54331782 52694243 52069234 51614090
 [9] 51250684 50674572

Smallest eigenvalues:
 [1]  0.5676876  0.5214993  0.4597463  0.3925009  0.3615232  0.3507187
 [7]  0.2664203  0.1855388  0.1679822 -0.6563396

Largest  eigenvalues:
 [1] 65042474 60765130 57521496 56683838 55783312 53960441 52919359 52613443
 [9] 52462212 51773650

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	7.595585	0.8824614	15.19461	0	2.738447	6.767316

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

HR ~ alt + n + acc + PM1

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- HR_fd
covariates <- list(altitude = altitude_fd, 
                   noise = noise_fd,
                   acceleration = acceleration_fd,
                   pollution = pollution1_fd)
path_plot <- 'figures/model_HR_alt_noise_acc_PM1_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 80, norder = 4, lambda = 1e4),
                     noise = list(nbetabasis = 80, norder = 4, lambda = 1e4),
                     acceleration = list(nbetabasis = 80, norder = 4, lambda = 1e4),
                     pollution = list(nbetabasis = 80, norder = 4, lambda = 1e4))

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, 
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 19.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Warning message in `^.fd`((outcome - yhatfd), 2):
"The maximum error exceeds the tolerance level."
Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 664 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Smallest eigenvalues:
 [1]  0.3603906  0.3206480  0.2860769  0.2596945  0.2094575  0.1474205
 [7]  0.1147731 -0.1408713 -0.1589878 -3.8942672

Largest  eigenvalues:
 [1] 64042812 60125820 57559805 55670773 55051760 53392896 52138209 51717479
 [9] 51678901 51142828

Smallest eigenvalues:
 [1]  0.19308764  0.17015664  0.10711512  0.02288223 -0.01647957 -0.01698404
 [7] -0.02461813 -0.18648999 -0.18929676 -2.45392676

Largest  eigenvalues:
 [1] 63355450 61056600 57701327 55871095 55332918 53938763 52739427 52427972
 [9] 51869486 51615887

Smallest eigenvalues:
 [1]  0.313184927  0.299904415  0.297226800  0.272611956  0.223798356
 [6]  0.129874123  0.067220822 -0.005984975 -0.153001156 -0.633852607

Largest  eigenvalues:
 [1] 64140129 61112687 58366275 55856481 55741450 54327511 53206043 52322060
 [9] 52089966 51897926

Smallest eigenvalues:
 [1]  0.486435822  0.484210632  0.414051726  0.353098383  0.346720503
 [6]  0.259123560  0.251768800 -0.006308419 -0.043910305 -0.102562167

Largest  eigenvalues:
 [1] 61984148 60501986 57601754 55831981 54968196 54066883 52461370 52415988
 [9] 51222636 51000972

Smallest eigenvalues:
 [1]  0.3567004  0.3285938  0.2976389  0.2334785  0.2046435  0.1983599
 [7]  0.1705519  0.1184595 -0.1281541 -3.2064522

Largest  eigenvalues:
 [1] 65163173 59818161 57293665 56025018 54719041 53144375 52121514 51967281
 [9] 51426274 51120415

Smallest eigenvalues:
 [1]  0.41800093  0.41103957  0.37141810  0.28186811  0.27306749  0.14039522
 [7]  0.05665045 -0.02675393 -0.10474338 -0.33093004

Largest  eigenvalues:
 [1] 64358283 60638162 57254916 56045643 55652612 53846201 52740030 52017768
 [9] 51714901 51420528

Smallest eigenvalues:
 [1]  0.2635689  0.1968254  0.1840918  0.1463388  0.1367938  0.0774332
 [7] -0.1700209 -0.1777492 -0.3643735 -0.4571581

Largest  eigenvalues:
 [1] 65013751 60998681 57648795 56151025 55480723 53867210 52962816 52135892
 [9] 52042929 51761050

Smallest eigenvalues:
 [1]  0.34805612  0.31317840  0.23050060  0.22377275  0.18881466 -0.05365539
 [7] -0.12786940 -0.30029511 -0.38798873 -0.65147113

Largest  eigenvalues:
 [1] 64870413 59853259 56521056 56464943 54495022 52690414 52475124 52167009
 [9] 51688408 51233785

Smallest eigenvalues:
 [1]  0.4924669167  0.4224823921  0.4110749524  0.3006899051  0.2739084512
 [6]  0.2118511766  0.2073970513  0.0566545630  0.0004435585 -1.9697097632

Largest  eigenvalues:
 [1] 63897554 59811350 57221227 55815994 54681379 53175611 52229504 51781375
 [9] 51653218 51043701

Smallest eigenvalues:
 [1]  0.37594417  0.35853443  0.33685754  0.32689900  0.23091090  0.22691332
 [7]  0.22173925  0.10436881  0.06168631 -0.03016414

Largest  eigenvalues:
 [1] 64507451 60409949 58002489 55634486 55321207 54073815 52718494 52110591
 [9] 51872357 51712245

Smallest eigenvalues:
 [1]  0.44564453  0.40144457  0.35814751  0.33064016  0.20256703  0.06430269
 [7] -0.43919089 -0.45225889 -1.04595515 -3.72937176

Largest  eigenvalues:
 [1] 64699010 60039590 57230094 55798586 55200344 52971868 52186125 51956598
 [9] 51697452 51235547

Smallest eigenvalues:
 [1]  0.3637690  0.3179382  0.2953825  0.2815649  0.2708426  0.1716318
 [7]  0.1256518  0.0709207 -0.2944240 -1.8981729

Largest  eigenvalues:
 [1] 63315355 59864465 57107461 55193265 54822933 53603761 52141302 52028246
 [9] 51338200 51002270

Smallest eigenvalues:
 [1]  0.38703956  0.38204369  0.35914554  0.27981298  0.27351546  0.21683480
 [7]  0.20852930 -0.05007726 -0.21218630 -1.18122172

Largest  eigenvalues:
 [1] 64864962 59719156 57151947 56535418 54774457 53303421 52543399 52172525
 [9] 51483342 50767655

Smallest eigenvalues:
 [1]  0.5666210  0.5128652  0.5047648  0.4344818  0.3820561  0.3682778
 [7]  0.2593738  0.2163635  0.1474606 -0.0161257

Largest  eigenvalues:
 [1] 65018802 59485575 56759327 55961013 54888526 53236899 52142138 51950984
 [9] 51851831 51205014

Smallest eigenvalues:
 [1]  0.49674605  0.38986244  0.36977487  0.32981922  0.22408674  0.21679872
 [7]  0.14659607  0.09302246 -0.08805735 -0.11807157

Largest  eigenvalues:
 [1] 66291866 59307802 57238030 56639429 54034094 53259521 52543575 51326778
 [9] 51117772 50519245

Smallest eigenvalues:
 [1]  0.5048780  0.5018486  0.4783975  0.4409971  0.4168265  0.3654423
 [7]  0.2558727  0.1582258 -0.1423267 -0.2183561

Largest  eigenvalues:
 [1] 63345416 60087174 56783771 55243839 54976033 53456167 51999856 51371631
 [9] 50839683 50520652

Smallest eigenvalues:
 [1]  0.3680907  0.2673715  0.2556593  0.2264717  0.2032561  0.1806324
 [7]  0.1578470  0.1348485 -0.1274604 -0.5267096

Largest  eigenvalues:
 [1] 66512102 60534115 57855623 57260735 55043218 53384080 53184007 52933113
 [9] 51654632 51496812

Smallest eigenvalues:
 [1]  0.46250142  0.40812451  0.38320941  0.23381370  0.21528419  0.12381999
 [7]  0.10875845  0.07737656  0.06233337 -0.79995766

Largest  eigenvalues:
 [1] 65753544 60501423 56960768 56753694 55112839 53464936 52724815 52234591
 [9] 52020426 51263068

Smallest eigenvalues:
 [1]  0.48720891  0.47571582  0.45112471  0.39529391  0.33727289  0.27785494
 [7]  0.15250768  0.02060553 -0.07968460 -0.71683640

Largest  eigenvalues:
 [1] 63421109 59880816 57059970 55351813 54886550 53781939 52421157 51800205
 [9] 50989232 50887761

Smallest eigenvalues:
 [1]  0.39905433  0.36072808  0.34246557  0.30407559  0.29587872  0.27107999
 [7]  0.24143192  0.11505289  0.11430622 -0.06455022

Largest  eigenvalues:
 [1] 64281762 61489955 58090710 56617451 55655382 54025692 52788376 52530737
 [9] 52474244 51781334

Smallest eigenvalues:
 [1]  0.4524249  0.4297710  0.3758639  0.3483349  0.3256069  0.2992669
 [7]  0.2661505  0.2370527  0.1072519 -0.1315416

Largest  eigenvalues:
 [1] 64822507 61097914 58013734 56414784 56408389 54708214 53058937 52587644
 [9] 52315629 51706456

Smallest eigenvalues:
 [1]  0.30172964  0.25823254  0.15310404  0.09629276  0.09252563  0.01557363
 [7] -0.06069795 -0.11263539 -0.43452943 -1.44370508

Largest  eigenvalues:
 [1] 64743454 60218965 56999694 55926177 54883767 53329324 51982796 51929633
 [9] 51562484 50890426

Smallest eigenvalues:
 [1]  0.49313171  0.43804805  0.40373882  0.32104682  0.27865145  0.26023728
 [7]  0.18798723  0.16612590  0.07420535 -0.06207839

Largest  eigenvalues:
 [1] 63228762 60339728 57141445 55692928 54834423 53103843 51918880 51757665
 [9] 51683771 50766304

Smallest eigenvalues:
 [1]  0.3815686  0.2937906  0.2934616  0.2672913  0.2637593  0.2198001
 [7]  0.2107763  0.1004381 -0.4090973 -0.5188172

Largest  eigenvalues:
 [1] 63894586 59758694 57239506 55185835 54421974 52959164 51919518 51354950
 [9] 51113528 51070084

Smallest eigenvalues:
 [1]  0.34347383  0.27432736  0.26188890  0.23710049  0.22722438  0.21810667
 [7]  0.19475320  0.01777969 -0.18448097 -0.26251265

Largest  eigenvalues:
 [1] 65754532 60415101 57841584 56729040 55100359 53409275 52978023 52750692
 [9] 51987324 51898316

Smallest eigenvalues:
 [1]  0.4341985  0.3725930  0.3666928  0.3291824  0.2923235  0.2614658
 [7]  0.1960324  0.1268017  0.1227838 -1.4700311

Largest  eigenvalues:
 [1] 64976715 59836961 57158468 56027573 55025189 53202778 52093152 52054413
 [9] 51493984 51140531

Smallest eigenvalues:
 [1]  0.49515698  0.44302564  0.35624174  0.34921851  0.33763801  0.29688016
 [7]  0.26949354  0.14490958 -0.08477671 -1.05720891

Largest  eigenvalues:
 [1] 63539838 59124913 56986340 55537837 54439466 52891167 51600459 51493504
 [9] 51429997 50568226

Smallest eigenvalues:
 [1]  0.43287209  0.39230530  0.33789149  0.31164282  0.26393407  0.19947962
 [7] -0.03676008 -0.07383353 -0.08369749 -0.22410323

Largest  eigenvalues:
 [1] 61127531 59035791 56117928 54820812 54126598 52912263 51797545 50841255
 [9] 50128339 49932966

Smallest eigenvalues:
 [1] -0.2460616 -0.3330930 -0.3729782 -0.3737812 -0.4331279 -0.5176597
 [7] -0.5487857 -0.9669094 -1.1436436 -1.2282288

Largest  eigenvalues:
 [1] 64858128 61061489 58209202 55631681 55550754 54216186 52454133 51974642
 [9] 51671098 51419047

Smallest eigenvalues:
 [1]  0.27058774  0.23880427  0.23389710  0.20867380  0.17934001  0.02470653
 [7] -0.01126291 -0.21387908 -0.34756716 -0.76965295

Largest  eigenvalues:
 [1] 64842719 61059995 57733046 56630744 55598746 54004868 52775192 52599737
 [9] 52376831 51802623

Smallest eigenvalues:
 [1]  0.39886268  0.30092224  0.25846460  0.24828442  0.21635403  0.11846062
 [7]  0.09696379 -0.05399715 -1.18493062 -1.22707519

Largest  eigenvalues:
 [1] 64505280 60140247 56638533 56268165 55292871 53292063 52537867 52240039
 [9] 52193336 51205387

Smallest eigenvalues:
 [1]  0.468809909  0.374803091  0.341744479  0.286649767  0.249555276
 [6]  0.189182536  0.142985110 -0.009777275 -0.622729528 -1.012807441

Largest  eigenvalues:
 [1] 64029117 58805802 56461250 55821379 53978132 52250512 51751027 51256342
 [9] 51020191 49960559

Smallest eigenvalues:
 [1]  0.424019349  0.324891136  0.238578223  0.228276122  0.226693893
 [6]  0.206355120  0.186955433  0.149452847  0.003521582 -7.045044203

Largest  eigenvalues:
 [1] 61832975 59825418 56886563 55066069 54669400 53472166 52120498 51468919
 [9] 50728614 50525906

Smallest eigenvalues:
 [1]  0.26833906  0.22044811  0.21640131  0.21348019  0.07544258  0.04953039
 [7] -0.12830040 -0.17947132 -1.00590867 -2.90901045

Largest  eigenvalues:
 [1] 66492448 60572966 57389874 56426197 55331903 53686182 52545385 52417101
 [9] 51793282 51658011

Smallest eigenvalues:
 [1]  0.43086981  0.35695808  0.34527069  0.34409043  0.25809766  0.24956918
 [7]  0.22633378  0.18869623  0.04441534 -0.06619720

Largest  eigenvalues:
 [1] 64569776 60746734 58209546 55780995 55604053 54234904 52757165 52437905
 [9] 51782170 51522448

Smallest eigenvalues:
 [1]  0.3199920  0.3085092  0.2815040  0.2192651  0.2166413  0.1703417
 [7]  0.1068566 -0.1781967 -0.2262937 -2.1929220

Largest  eigenvalues:
 [1] 65075273 60567053 57749733 55895980 55826053 54154201 52434478 52240629
 [9] 52204402 51355481

Smallest eigenvalues:
 [1]  0.36679593  0.36204198  0.30321159  0.27852106  0.20601523  0.09675696
 [7]  0.02474611 -0.08693992 -0.22011251 -1.60236497

Largest  eigenvalues:
 [1] 63877916 59888506 57013986 55192226 55033924 53438740 52166670 51471107
 [9] 51344018 51183333

Smallest eigenvalues:
 [1]  0.474959591  0.388621819  0.357229674  0.342993411  0.324167216
 [6]  0.310567632  0.241170437  0.013774104 -0.006679943 -0.073915400

Largest  eigenvalues:
 [1] 65237018 60365372 57467544 56411339 54843198 53060364 52541326 52121609
 [9] 51296529 50886352

Smallest eigenvalues:
 [1]  0.34471929  0.32909510  0.30661962  0.25509392  0.24737358  0.20364714
 [7]  0.06887637  0.05206281 -0.10369626 -2.43385066

Largest  eigenvalues:
 [1] 63171106 59821566 56965008 55146968 54994103 53372462 51709603 51671283
 [9] 51149930 50895599

Smallest eigenvalues:
 [1]  0.48916970  0.39957389  0.38312140  0.35914591  0.25344685  0.21311593
 [7]  0.18543280  0.12980339  0.03028597 -0.77720909

Largest  eigenvalues:
 [1] 65238373 59942593 57167130 57130370 54517661 53085943 52858254 52016865
 [9] 51906367 51073233

Smallest eigenvalues:
 [1]  0.37306304  0.32342526  0.32011327  0.17822441  0.14853715  0.14105478
 [7] -0.06471892 -0.22865453 -0.57631561 -0.71568892

Largest  eigenvalues:
 [1] 65070191 60984772 58054948 56780020 55345357 53402084 53005991 52656621
 [9] 51832038 51704852

Smallest eigenvalues:
 [1]  0.28908031  0.24141226  0.22387002  0.15346420  0.10963183  0.07682236
 [7] -0.03741547 -0.04481323 -0.79968007 -0.82843491

Largest  eigenvalues:
 [1] 64853322 60580673 58070284 56409408 55069526 53499647 52708025 52469870
 [9] 52087559 51785470

Smallest eigenvalues:
 [1]  0.33057720  0.28530559  0.27569552  0.22232186  0.13690152  0.02835007
 [7] -0.10745943 -0.36032917 -0.40872622 -1.11880970

Largest  eigenvalues:
 [1] 64155923 59585147 56853874 54875791 54761907 53058820 51286058 51238972
 [9] 51113988 50490770

Smallest eigenvalues:
 [1]  0.39960852  0.23095879  0.21918600  0.16759046  0.08511106  0.06018156
 [7] -0.03117794 -0.05202401 -0.09417116 -1.33545675

Largest  eigenvalues:
 [1] 63335509 59835216 56962529 55206734 54747277 53152608 51682359 51488730
 [9] 51309686 50888761

Smallest eigenvalues:
 [1]  0.5364285  0.5353717  0.4451344  0.4384927  0.4352319  0.3925692
 [7]  0.3231796  0.2993528  0.2874640 -0.2740327

Largest  eigenvalues:
 [1] 64168402 60433535 57581693 55838796 55364991 53658423 51735558 51697195
 [9] 51564242 50652737

Smallest eigenvalues:
 [1]  0.54477934  0.53961058  0.46571162  0.40663906  0.37828691  0.34767162
 [7]  0.20242885  0.10694160  0.01386924 -0.32716346

Largest  eigenvalues:
 [1] 62134351 59525841 56632421 55230589 54338034 53394068 51681453 51589397
 [9] 50455817 50289707

Smallest eigenvalues:
 [1]  0.44576428  0.32286257  0.31535376  0.25187381  0.14262545  0.12887404
 [7]  0.06061520  0.04429567 -0.05580773 -2.15177198

Largest  eigenvalues:
 [1] 63505411 59554332 56760102 55289636 55039486 53369357 52378995 51839392
 [9] 51441216 51216217

Smallest eigenvalues:
 [1]  0.5205121  0.5028372  0.4369018  0.3663844  0.3630000  0.3339224
 [7]  0.3291279  0.2937270  0.2668510 -0.4076816

Largest  eigenvalues:
 [1] 63812606 59626039 57210590 55512293 54681728 52916285 51692881 51525854
 [9] 51044999 50389901

Smallest eigenvalues:
 [1]  0.37353636  0.31628203  0.24671127  0.23271970  0.21987027  0.12945540
 [7] -0.01279438 -0.20582004 -0.29160393 -0.86838223

Largest  eigenvalues:
 [1] 64246167 60069298 57089796 56026719 55078598 53558221 52425139 51965156
 [9] 51934191 51448378

Smallest eigenvalues:
 [1]  0.387618700  0.350842220  0.313729781  0.274074025  0.230364909
 [6]  0.201045632  0.191965046  0.005931078 -0.145759565 -0.261922357

Largest  eigenvalues:
 [1] 64812748 61049897 58348316 56108538 55789309 54391289 52461537 52307812
 [9] 52019069 51537906

Smallest eigenvalues:
 [1]  0.35843234  0.35473116  0.33890849  0.32846012  0.31521429  0.28887962
 [7]  0.22239760  0.01641749 -0.23299799 -0.32896698

Largest  eigenvalues:
 [1] 65476519 60479513 57689154 56575188 55216963 53689845 52491133 52169096
 [9] 51982746 51247026

Smallest eigenvalues:
 [1]  0.46052563  0.43961626  0.41741332  0.40072946  0.30383083  0.25091436
 [7]  0.19061881  0.16642050  0.07783223 -0.13221950

Largest  eigenvalues:
 [1] 65440331 60869551 57965413 56422599 55596541 54095370 52633987 52530999
 [9] 52022117 51526187

Smallest eigenvalues:
 [1]  0.48360484  0.47577667  0.42888151  0.42256623  0.34681360  0.34478007
 [7]  0.27721432  0.25140540  0.22366972 -0.03321141

Largest  eigenvalues:
 [1] 65390979 60730666 57959144 56619766 56027558 54435551 52608311 52367810
 [9] 52286101 51354269

Smallest eigenvalues:
 [1]  0.3373224  0.3266732  0.2598420  0.2295445  0.2081416  0.1724380
 [7]  0.1444689 -0.5320565 -0.6962719 -0.7924707

Largest  eigenvalues:
 [1] 66333537 60712971 57981165 57139470 55098263 53523924 53274765 52331288
 [9] 51896990 51522859

Smallest eigenvalues:
 [1]  0.358128201  0.321289787  0.306916866  0.273582428  0.264583667
 [6]  0.191468149  0.163286958 -0.005859051 -0.391608586 -0.424768896

Largest  eigenvalues:
 [1] 63886544 60503146 57149465 55781985 55736539 54049574 52905981 52206455
 [9] 51954925 51687018

Smallest eigenvalues:
 [1]  0.48178954  0.40723983  0.39895801  0.38145384  0.31096653  0.25125948
 [7]  0.23717507  0.19727587  0.06835951 -0.09234222

Largest  eigenvalues:
 [1] 64917614 59570925 57013438 56450765 54200155 52678059 52445773 51409487
 [9] 51177865 50346307

Smallest eigenvalues:
 [1]  0.49139837  0.47513540  0.44025141  0.42538513  0.36614629  0.30053951
 [7]  0.28887771  0.07024903 -0.02697186 -0.46653374

Largest  eigenvalues:
 [1] 65266549 60192459 57627485 56337903 55479689 53456239 52604307 52102947
 [9] 51738313 51063413

Smallest eigenvalues:
 [1]  0.28076112  0.22395012  0.22355702  0.21288323  0.15382624  0.03527388
 [7] -0.13569635 -0.42121597 -0.59959270 -5.43688229

Largest  eigenvalues:
 [1] 66269055 60853321 57240954 57222216 55622334 53782052 53247162 52414815
 [9] 52221674 51469603

Smallest eigenvalues:
 [1]  0.27821730  0.19862006  0.19819928  0.13485490  0.07339599 -0.13500070
 [7] -0.28586167 -0.40306937 -0.99114765 -1.90357430

Largest  eigenvalues:
 [1] 64427041 60545555 57908962 56640833 55541517 53868869 52600700 52428444
 [9] 52259322 51271379

Smallest eigenvalues:
 [1]  0.14068416  0.09121334 -0.02220390 -0.06431161 -0.21434716 -0.26956082
 [7] -0.60929578 -1.21714060 -1.34764833 -1.48726618

Largest  eigenvalues:
 [1] 66219887 60093450 57918014 55880813 54851939 53048982 52343802 51705149
 [9] 51278967 50943662

Smallest eigenvalues:
 [1]  0.46875744  0.43413460  0.37802219  0.37219335  0.27783285  0.23231523
 [7]  0.17196609  0.15705356  0.05810619 -0.18960095

Largest  eigenvalues:
 [1] 65498045 61244736 58057107 56841727 55886177 54275404 53471337 52840763
 [9] 52377361 52076991

Smallest eigenvalues:
 [1]  0.30065156  0.28012827  0.24835356  0.24701815  0.13455353  0.12902444
 [7]  0.12729337  0.03730063 -0.78035003 -2.06242905

Largest  eigenvalues:
 [1] 63508021 59788113 56961370 55547485 54800061 53196096 51960334 51743953
 [9] 51524377 50954353

Smallest eigenvalues:
 [1]  0.29180419  0.27555984  0.24628449  0.22956510  0.20239016  0.18006428
 [7]  0.11235817  0.09156804 -0.04272696 -5.83561262

Largest  eigenvalues:
 [1] 63345500 60597202 57177419 55826058 54903460 53904659 51950536 51776875
 [9] 51023165 50725203

Smallest eigenvalues:
 [1]  0.51898108  0.51190742  0.49346421  0.45000858  0.44590826  0.40245592
 [7]  0.26890601  0.17226099  0.01089595 -0.01735811

Largest  eigenvalues:
 [1] 65450490 60164291 57661918 56539077 54888937 53282850 52370456 52311259
 [9] 51956350 51530022

Smallest eigenvalues:
 [1]  0.3058265  0.2989377  0.2661292  0.1974696  0.1739128  0.1180772
 [7]  0.1179815  0.1047524 -0.0267872 -1.6321315

Largest  eigenvalues:
 [1] 65868486 60961942 58268142 56642964 55654836 53985039 53045952 52600567
 [9] 52474029 52195419

Smallest eigenvalues:
 [1]  0.29353112  0.26421254  0.24069880  0.21331116  0.14220334  0.13595383
 [7]  0.08201721 -0.02624704 -1.37526050 -1.59779590

Largest  eigenvalues:
 [1] 66324597 60409218 57749827 56802431 55062561 53910980 52636040 52490835
 [9] 52366116 51812154

Smallest eigenvalues:
 [1]  0.3238356  0.2496848  0.2159286  0.1849888  0.1712111  0.1618124
 [7] -0.1586719 -0.2831307 -0.3315398 -0.9900699

Largest  eigenvalues:
 [1] 66198155 59954691 57371542 56871274 54652198 53037627 52860533 52456301
 [9] 51650825 51589338

Smallest eigenvalues:
 [1]  0.28030410  0.23164345  0.16569131  0.14974950  0.07352849 -0.04166859
 [7] -0.04956359 -0.38941178 -0.44200870 -0.53847499

Largest  eigenvalues:
 [1] 63973941 60192981 57661301 55427909 54774789 53571659 51624257 51540728
 [9] 51529087 50945402

Smallest eigenvalues:
 [1]  0.42430077  0.37351528  0.36916465  0.33133912  0.22922266  0.22083748
 [7]  0.14874419  0.08477195  0.06912904 -0.16018647

Largest  eigenvalues:
 [1] 64611572 60355340 57490467 56329037 55303275 53826454 52384693 52383575
 [9] 52180474 51306512

Smallest eigenvalues:
 [1]  0.50171588  0.46687751  0.45267226  0.39188347  0.34826348  0.32061463
 [7]  0.31232823  0.12021224  0.09798791 -0.13610437

Largest  eigenvalues:
 [1] 64772381 59660125 57134377 55753136 54904515 53502594 51926088 51854032
 [9] 51320852 50429195

Smallest eigenvalues:
 [1]  0.38531642  0.34042368  0.23556259  0.20364124  0.17823409 -0.04027302
 [7] -0.04702928 -0.05179629 -0.07915303 -1.30598756

Largest  eigenvalues:
 [1] 64284780 60462140 57269798 55685606 55474462 53795416 52884626 51973386
 [9] 51892705 51644598

Smallest eigenvalues:
 [1]  0.4215706  0.4121962  0.3736347  0.3310153  0.2855394  0.2404173
 [7]  0.2231569  0.2040454  0.1198840 -0.1835219

Largest  eigenvalues:
 [1] 62627336 60759937 57180116 55433331 55365360 53677334 52273855 52176674
 [9] 51348637 51157193

Smallest eigenvalues:
 [1]  0.4916969  0.4845972  0.4465242  0.4170723  0.3137256  0.3047418
 [7]  0.2508813  0.2288577  0.2121150 -0.0672257

Largest  eigenvalues:
 [1] 64235432 59578502 57258443 55447346 54628133 53072705 51695272 51402215
 [9] 51306666 50653162

Smallest eigenvalues:
 [1]  0.3842260  0.3788244  0.3093946  0.2491844  0.2410652  0.1990001
 [7]  0.1674324 -0.4061881 -0.6413068 -1.5163069

Largest  eigenvalues:
 [1] 62641300 59213911 56765481 55065029 54852673 53142059 51877363 51746645
 [9] 50950153 50613542

Smallest eigenvalues:
 [1]  0.60627072  0.59890510  0.54791023  0.44315392  0.38616628  0.35894897
 [7]  0.26408105  0.22032031  0.12442103 -0.01300647

Largest  eigenvalues:
 [1] 62810815 60171645 57072618 55771058 54808337 54115070 52447664 52203238
 [9] 51068261 50844478

Smallest eigenvalues:
 [1]  0.28762597  0.27535851  0.27197888  0.24981564  0.22488444  0.15031248
 [7]  0.02205735 -0.64347616 -0.90645808 -1.62884934

Largest  eigenvalues:
 [1] 64811016 60261258 57815952 56154256 55134026 53305000 52437683 52147419
 [9] 52080975 51590695

Smallest eigenvalues:
 [1]  0.43939866  0.38067198  0.30842538  0.29381131  0.25166320  0.14475968
 [7]  0.10947469  0.08465491 -0.13708031 -1.16591922

Largest  eigenvalues:
 [1] 65503611 60526228 57455322 56213183 55119027 53370079 52370235 52310403
 [9] 51914938 51329582

Smallest eigenvalues:
 [1]  0.114355585 -0.004635647 -0.008848434 -0.159913929 -0.164976422
 [6] -0.246746159 -0.336428536 -0.475751998 -0.693432413 -1.421451540

Largest  eigenvalues:
 [1] 63031583 59916935 57118657 55164654 54726760 53107658 52182645 51350157
 [9] 51156730 50926974

Smallest eigenvalues:
 [1]  0.45998872  0.41580810  0.39184842  0.33953891  0.33800481  0.33182469
 [7]  0.27681551  0.25551057  0.21870749 -0.02127224

Largest  eigenvalues:
 [1] 61723181 59132596 56775358 54843397 54310412 53083041 51443760 51092701
 [9] 50398566 50087078

Smallest eigenvalues:
 [1]  0.4124039  0.3006569  0.2514511  0.2511782  0.2249729  0.2143911
 [7]  0.1778251  0.1097218 -0.1895180 -0.2528983

Largest  eigenvalues:
 [1] 64547811 60215328 57630273 56368777 54897717 53369060 52518681 51626623
 [9] 51478585 50467374

Smallest eigenvalues:
 [1]  0.3579867  0.3538659  0.3065763  0.2799404  0.2398964  0.2322097
 [7]  0.1360400  0.1043339 -0.4957799 -1.1937904

Largest  eigenvalues:
 [1] 65307097 60270620 58356998 55588030 55510642 54424149 52858980 52693364
 [9] 51851792 51550041

Smallest eigenvalues:
 [1]  0.4043210  0.3438279  0.3292763  0.3054532  0.2274421  0.1681585
 [7]  0.1507635  0.1159263 -0.2828722 -0.4291482

Largest  eigenvalues:
 [1] 63682380 59316459 57318296 55877214 54162732 52832241 51785944 51713349
 [9] 51387607 50693001

Smallest eigenvalues:
 [1]  0.431394797  0.420844315  0.360916333  0.359955744  0.346086671
 [6]  0.339005585  0.285401444  0.257995076 -0.002866243 -5.545150798

Largest  eigenvalues:
 [1] 64216750 60061595 57117564 55598064 55108613 53333083 52120494 51716823
 [9] 51626127 50854276

Smallest eigenvalues:
 [1]  0.4608246  0.3841535  0.3712152  0.3627737  0.2946871  0.2719265
 [7]  0.2047346  0.1746251  0.1477002 -0.1509604

Largest  eigenvalues:
 [1] 64045586 59697654 57065280 55967590 54704728 53200363 52078906 51823622
 [9] 51804903 50923302

Smallest eigenvalues:
 [1]  0.522567142  0.508919326  0.412642972  0.352535295  0.307459818
 [6]  0.302199698  0.158631452  0.134830209  0.024603845 -0.002993484

Largest  eigenvalues:
 [1] 63177302 59624004 57131831 54773680 54626686 53134592 51864442 51348919
 [9] 50898124 50539322

Smallest eigenvalues:
 [1]  0.51385050  0.45614854  0.42400424  0.35775865  0.33238024  0.28848757
 [7]  0.24921755  0.16494337  0.02533496 -0.02961978

Largest  eigenvalues:
 [1] 61446744 59820695 56948255 56035796 54095329 53944818 52733495 51624963
 [9] 50741235 50665946

Smallest eigenvalues:
 [1]  0.46139118  0.44187490  0.39909965  0.33792925  0.31125959  0.29159161
 [7]  0.27961396  0.17456575  0.14171066 -0.03839334

Largest  eigenvalues:
 [1] 63714964 60702691 57312911 55907357 55824463 54108635 52535897 52011540
 [9] 51875612 51479550

Smallest eigenvalues:
 [1]  0.42639968  0.39559155  0.36525013  0.34761243  0.34320671  0.28718473
 [7]  0.26210578  0.21108925  0.05909535 -0.14595074

Largest  eigenvalues:
 [1] 61834668 60856656 57519513 55647639 55020232 53877479 52142949 52131096
 [9] 51248404 50990330

Smallest eigenvalues:
 [1]  0.30001491  0.29098047  0.26735308  0.20674120  0.16650157  0.12895381
 [7]  0.08717612 -0.13805674 -0.42287786 -0.51276924

Largest  eigenvalues:
 [1] 64617957 61378016 58295062 56594013 55839873 54005981 53775110 52832017
 [9] 52238143 52083503

Smallest eigenvalues:
 [1]  0.4068207  0.4065248  0.3910243  0.3167281  0.2799650  0.2734857
 [7]  0.2637625  0.2035177 -0.1255357 -4.0310711

Largest  eigenvalues:
 [1] 64923755 60501512 57783306 56311142 55204456 53720725 52398973 52116895
 [9] 52065385 51204325

Smallest eigenvalues:
 [1]  0.284458278  0.239570607  0.161864226  0.078653164  0.001354026
 [6] -0.049783775 -0.107340000 -0.436127485 -0.590370738 -1.137575036

Largest  eigenvalues:
 [1] 64891547 59770522 56935810 55457870 54649439 52996751 51960321 51644092
 [9] 51297891 51122953

Smallest eigenvalues:
 [1]  0.3988811  0.3785343  0.3597117  0.3264402  0.3187563  0.3079406
 [7]  0.2994325  0.1886132  0.1358960 -0.1118437

Largest  eigenvalues:
 [1] 65289964 60791535 57433230 57124862 55243598 53653674 52871165 52665504
 [9] 52329115 51409997

Smallest eigenvalues:
 [1]  0.42503823  0.39471310  0.26896249  0.23419675  0.23267573  0.19209878
 [7]  0.18739692 -0.06811077 -0.54508634 -0.63416543

Largest  eigenvalues:
 [1] 65320022 61025858 57394836 56222003 56006665 54116520 53056581 52540694
 [9] 52208895 51664922

Smallest eigenvalues:
 [1]  0.5547804  0.4796298  0.4590903  0.4184093  0.3740510  0.3720161
 [7]  0.3422207  0.3344018  0.2337584 -0.2264861

Largest  eigenvalues:
 [1] 64118028 60212374 57337982 56028139 55373081 53506169 52063641 51965326
 [9] 51773277 50799994

Smallest eigenvalues:
 [1]  0.29195785  0.26514031  0.22143992  0.21376256  0.16918389  0.15121911
 [7]  0.12781814  0.05062987 -0.04063535 -0.26847746

Largest  eigenvalues:
 [1] 62134203 58916993 56411820 54813421 54712013 53001419 51976627 51491648
 [9] 50715303 50466484

Smallest eigenvalues:
 [1]  0.57420020  0.53871151  0.48216025  0.44775400  0.39620996  0.39488092
 [7]  0.36739665  0.22070880  0.13224398 -0.06623388

Largest  eigenvalues:
 [1] 63968624 60037365 56660136 55413056 55287549 53582239 52220309 51450455
 [9] 51410823 50580619

Smallest eigenvalues:
 [1]  0.352742067  0.337433782  0.334528432  0.270141273  0.265758769
 [6]  0.173941368  0.162504619  0.062101215  0.006925509 -0.129423609

Largest  eigenvalues:
 [1] 64924472 59172526 56684532 56374077 54581068 53022179 52416933 51606833
 [9] 50762362 50190823

Smallest eigenvalues:
 [1]  0.397795416  0.375662603  0.335943325  0.311856821  0.294155796
 [6]  0.204684635  0.003725602 -0.216922536 -0.242593855 -2.926670356

Largest  eigenvalues:
 [1] 65461585 60376823 57493288 56042344 55495960 53954256 52660679 52163290
 [9] 51972204 51782551

Smallest eigenvalues:
 [1]  0.18194292  0.08483852 -0.06535354 -0.23098375 -0.23570552 -0.29365374
 [7] -0.43288915 -0.71670623 -0.83823223 -4.91196316

Largest  eigenvalues:
 [1] 62451671 59615497 56787975 55366325 54455170 53447420 52074444 51802714
 [9] 51036027 50681459

Smallest eigenvalues:
 [1]  0.637143917  0.538830483  0.513684301  0.504624488  0.431139853
 [6]  0.386743562  0.303686175  0.217925661  0.156696251 -0.001484799

Largest  eigenvalues:
 [1] 65111852 60550941 57706261 56389305 55355203 53864406 52454220 52406028
 [9] 52019443 51352038

Smallest eigenvalues:
 [1]  0.4381370  0.4163145  0.3968833  0.3435968  0.2781574  0.2569211
 [7]  0.1466814  0.1412468  0.1271378 -1.8012059

Largest  eigenvalues:
 [1] 63956777 60373091 57520828 55380189 55318216 53820383 52203252 52113608
 [9] 51522971 51319108

Smallest eigenvalues:
 [1]  0.4074957  0.3736822  0.3610401  0.3152661  0.2545363  0.2487171
 [7]  0.1374125  0.1346574 -0.3316199 -0.4561040

Largest  eigenvalues:
 [1] 63134456 60483048 56862999 55826770 54949694 53260382 52170498 51709374
 [9] 51536848 50733833

Smallest eigenvalues:
 [1]  0.3730152  0.3535112  0.3378832  0.3305521  0.2481641  0.2221549
 [7]  0.1935049  0.1100101 -0.1051907 -1.9676151

Largest  eigenvalues:
 [1] 61936147 59599615 56855775 54932905 54400927 53029978 51361980 51207151
 [9] 50618151 50410146

Smallest eigenvalues:
 [1]  0.46423913  0.40073847  0.36553243  0.34260564  0.32537861  0.29811718
 [7]  0.28135759  0.18887851  0.12339765 -0.04777045

Largest  eigenvalues:
 [1] 64927043 59830651 57435423 56049643 54706435 53080973 52191417 51846698
 [9] 51758212 51008885

Smallest eigenvalues:
 [1]  0.53378569  0.52429601  0.48888533  0.48028643  0.44036744  0.33179848
 [7]  0.18613807  0.11911690  0.06998202 -0.11580793

Largest  eigenvalues:
 [1] 63563802 60240938 57434281 55583602 55165952 53637103 52165471 51917817
 [9] 51678109 51046726

Smallest eigenvalues:
 [1]  0.4625514  0.4098466  0.3950050  0.3897157  0.3592403  0.1428243
 [7]  0.1260283  0.1138990 -0.1988930 -1.3626917

Largest  eigenvalues:
 [1] 64519744 59214123 56732450 54844362 54837469 53120083 52147075 51286113
 [9] 51212950 50596867

Smallest eigenvalues:
 [1]  0.44985555  0.43340665  0.39665318  0.37379911  0.29793721  0.17104380
 [7]  0.16079471  0.10643018  0.06518246 -1.59781987

Largest  eigenvalues:
 [1] 64446842 60147472 56881250 55975115 55313850 53315808 52367494 52052142
 [9] 51597967 51215915

Smallest eigenvalues:
 [1]  0.269956889  0.168703941  0.128518350  0.045044792  0.039120644
 [6]  0.003191129 -0.116530282 -0.330270907 -0.590093810 -0.851078350

Largest  eigenvalues:
 [1] 64240755 60878508 57548537 55651574 55272276 53572096 52107573 51850581
 [9] 51539419 51213731

Smallest eigenvalues:
 [1]  0.41871591  0.38195318  0.35698294  0.32602633  0.29134595  0.24158548
 [7]  0.22386232  0.19775791 -0.05521472 -2.23561446

Largest  eigenvalues:
 [1] 63191346 60076232 57326240 55869687 54709059 53356190 52177186 51715577
 [9] 51652003 51200595

Smallest eigenvalues:
 [1]  0.39243812  0.37778438  0.29793035  0.25610061  0.22433754  0.22185230
 [7]  0.01741347 -0.03202508 -0.08575769 -5.24342707

Largest  eigenvalues:
 [1] 63363168 59695982 56724347 55117036 54980511 52899753 51465013 51446686
 [9] 51224826 50449030

Smallest eigenvalues:
 [1]  0.49175672  0.40112003  0.36323426  0.29570560  0.27596625  0.23047658
 [7]  0.19690478  0.17238320  0.04136418 -0.98022697

Largest  eigenvalues:
 [1] 64944767 59798967 57647056 55922501 54627372 53456253 52215664 51699038
 [9] 51483015 50796357

Smallest eigenvalues:
 [1]  0.35680785  0.33378388  0.25902892  0.23487622  0.23211194  0.21514133
 [7]  0.16171935  0.09826078 -0.22083617 -0.80487036

Largest  eigenvalues:
 [1] 62464811 60246060 57279819 55640718 55052970 53486891 52297287 52177961
 [9] 51454446 50813074

Smallest eigenvalues:
 [1]  0.21809328  0.17766232  0.17054201  0.16118970  0.07402816  0.07078496
 [7] -0.10071888 -0.28095705 -1.46274409 -1.55358804

Largest  eigenvalues:
 [1] 63606322 59473104 56973373 54813005 54695710 53216161 51599122 51123121
 [9] 50987209 50443197

Smallest eigenvalues:
 [1]  0.36202829  0.35079600  0.24234965  0.20275350  0.16940017  0.10203958
 [7]  0.02006566 -0.04535303 -0.23270112 -3.57495525

Largest  eigenvalues:
 [1] 64980942 59705304 56925347 56302661 54872859 53152064 52460402 52262021
 [9] 51759935 51262943

Smallest eigenvalues:
 [1]  0.31840516  0.20177103  0.15939058  0.13932871 -0.02069221 -0.03142577
 [7] -0.11038247 -0.22070981 -1.09169964 -2.05762710

Largest  eigenvalues:
 [1] 65888465 59784264 57060916 56618711 54568943 53057364 52664335 52188248
 [9] 51414871 51391962

Smallest eigenvalues:
 [1]  0.46273726  0.36205484  0.22338922  0.19390587  0.18597176  0.15130079
 [7]  0.11961507 -0.06721433 -0.36030320 -1.67870313

Largest  eigenvalues:
 [1] 63818053 59417184 56343085 55084596 54632459 52934193 51713555 51286134
 [9] 51128063 50371408

Smallest eigenvalues:
 [1]  0.416692834  0.364815114  0.240203085  0.191391103  0.118741762
 [6]  0.063732697  0.004530815 -0.015170372 -0.077513604 -0.632270320

Largest  eigenvalues:
 [1] 63359283 59430167 56752892 54791207 54516702 53005746 51683104 51252831
 [9] 51073236 50643275

Smallest eigenvalues:
 [1]  0.48314931  0.39699723  0.38656114  0.36852205  0.31081783  0.29669520
 [7]  0.28052225 -0.03951312 -0.04482099 -2.32612212

Largest  eigenvalues:
 [1] 64308431 60612838 56984282 55689644 55565238 53620448 52189609 51984478
 [9] 51817341 51126469

Smallest eigenvalues:
 [1]  0.255893637  0.255496711  0.222270377  0.034376715 -0.009442275
 [6] -0.140263386 -0.433526406 -0.723518822 -1.077376241 -1.454730069

Largest  eigenvalues:
 [1] 65895119 59530534 56850827 56252136 54400012 52998113 52314320 51750849
 [9] 51363202 50943201

Smallest eigenvalues:
 [1]  0.31448537  0.31089953  0.24469739  0.18495554  0.12219551  0.02676088
 [7] -0.30076956 -0.85848804 -1.58658861 -1.85757015

Largest  eigenvalues:
 [1] 66457410 60426487 58459040 56947635 55141540 53193619 52890811 52219571
 [9] 51797093 51481297

Smallest eigenvalues:
 [1]  0.39882907  0.36988662  0.34962567  0.34640457  0.32618712  0.30297334
 [7]  0.25496569  0.19267631  0.18536449 -0.01011802

Largest  eigenvalues:
 [1] 64526635 60723027 58150356 55814539 55688479 54371589 52435290 52057851
 [9] 51923014 51186804

Smallest eigenvalues:
 [1]  0.10331314  0.09411901 -0.05479243 -0.10662159 -0.12199998 -0.31617443
 [7] -0.32968892 -0.38409834 -0.74752024 -1.24051087

Largest  eigenvalues:
 [1] 66153630 60398999 57972392 57252778 54850598 53367460 53112243 52797847
 [9] 51888651 51518140

Smallest eigenvalues:
 [1]  0.38241794  0.35423516  0.33731761  0.30472545  0.30069783  0.20922189
 [7]  0.10869108 -0.08314438 -0.15020855 -1.32186369

Largest  eigenvalues:
 [1] 63638549 60277715 57401201 56276972 55013923 53339215 52519683 52066540
 [9] 51829671 51332714

Smallest eigenvalues:
 [1]  0.49799915  0.44928913  0.44581410  0.41499356  0.33121849  0.27941617
 [7]  0.23813911  0.20386552  0.05577655 -0.06201129

Largest  eigenvalues:
 [1] 66259222 60049795 57766631 57093564 54859826 53569324 53193417 51933343
 [9] 51746823 50986621

Smallest eigenvalues:
 [1]  0.38344711  0.33708112  0.33666557  0.27678748  0.26551530  0.21773843
 [7]  0.20135358  0.05200353 -0.02940766 -0.41362848

Largest  eigenvalues:
 [1] 64948306 60119483 57028828 56571925 54897534 53300319 52546207 52486640
 [9] 51982007 51535200

Smallest eigenvalues:
 [1]  0.20179198  0.19685450  0.18101021  0.13777247 -0.03113217 -0.23597599
 [7] -0.51116234 -1.00738849 -1.38620527 -1.51914677

Largest  eigenvalues:
 [1] 65295663 60301423 57699408 56512384 54765000 53432575 52643772 52164124
 [9] 51620770 51354129

Smallest eigenvalues:
 [1]  0.5354128  0.5036787  0.4995127  0.4318419  0.3589464  0.3519149
 [7]  0.1788749  0.1578994  0.1156847 -0.2320354

Largest  eigenvalues:
 [1] 64203162 59266658 56591366 55558831 54351875 52286714 51617249 51118063
 [9] 51098441 50270800

Smallest eigenvalues:
 [1]  0.5313828  0.4991924  0.4406278  0.4039710  0.3529575  0.2939176
 [7]  0.2645401  0.0338451 -0.3570618 -4.0684087

Largest  eigenvalues:
 [1] 65487650 59825436 56828623 56436953 54550995 52546916 52259940 51470609
 [9] 51418905 50639626

Smallest eigenvalues:
 [1]  0.21519902  0.15399032  0.10489712 -0.02301297 -0.05059752 -0.12224821
 [7] -0.13170798 -0.77349678 -1.06153459 -1.88610184

Largest  eigenvalues:
 [1] 66332553 60411304 57380203 57188388 54998345 53277662 53126460 52821210
 [9] 51854920 51802795

Smallest eigenvalues:
 [1]  0.3746854  0.3275190  0.3178091  0.2250618  0.1771928  0.1572432
 [7]  0.1093535 -0.1651058 -0.3501318 -0.9610655

Largest  eigenvalues:
 [1] 64128097 59864698 56886956 55135106 54682539 53092378 51768006 51661962
 [9] 51289161 51044492

Smallest eigenvalues:
 [1]  0.39885408  0.37649569  0.36196943  0.28037889  0.26043615  0.20837866
 [7]  0.18578268  0.05003467  0.04163188 -1.45146658

Largest  eigenvalues:
 [1] 64616076 60324247 56857436 56039624 55398832 53639036 51908081 51784943
 [9] 51716899 50874203

Smallest eigenvalues:
 [1]  0.376280719  0.307968800  0.270685000  0.171366752  0.160953665
 [6]  0.108070901  0.072151884  0.020834484  0.002786508 -1.987170405

Largest  eigenvalues:
 [1] 63983121 60170079 57266457 55482300 55072229 53896826 52008947 51582188
 [9] 51111977 50789597

Smallest eigenvalues:
 [1]  0.24094082  0.16113435  0.07831721  0.04222213 -0.03530437 -0.04026649
 [7] -0.07239794 -0.12900239 -0.35897698 -0.82937782

Largest  eigenvalues:
 [1] 66149144 60763201 58175050 56352719 55258555 53761435 52584161 52274386
 [9] 51911871 51441598

Smallest eigenvalues:
 [1]  0.45072375  0.44930617  0.42707307  0.33227141  0.27608788  0.25176901
 [7]  0.05342844  0.04366002 -0.05559960 -2.35706928

Largest  eigenvalues:
 [1] 65316235 60092150 57101572 56471027 55207253 53717852 52384138 52138233
 [9] 51965542 51267309

Smallest eigenvalues:
 [1]  0.46426041  0.43155913  0.39258429  0.37299448  0.36460008  0.30936865
 [7]  0.28669020  0.17339815  0.13165021 -0.07712913

Largest  eigenvalues:
 [1] 64447110 59828114 56546209 55860706 54700493 53110423 51915110 51875719
 [9] 51444778 50799338

Smallest eigenvalues:
 [1]  0.32180708  0.30948438  0.28262209  0.22483686  0.19245215 -0.05613209
 [7] -0.09511850 -0.17865712 -0.56782904 -2.91985104

Largest  eigenvalues:
 [1] 65494462 60770984 57409712 55881813 55367889 53448261 51999398 51898515
 [9] 51631644 51150789

Smallest eigenvalues:
 [1]  0.4215955  0.3830922  0.3608919  0.3411174  0.3170894  0.3020075
 [7]  0.2732070  0.2585327  0.2136132 -0.0904391

Largest  eigenvalues:
 [1] 64170768 60128314 57281690 55445678 55411005 53774799 51903407 51567664
 [9] 51325856 50429510

Smallest eigenvalues:
 [1]  0.41027462  0.34991550  0.33201372  0.28719242  0.23969036  0.17322448
 [7]  0.08775426 -0.03237588 -0.07105975 -0.25147471

Largest  eigenvalues:
 [1] 65732569 60345982 57423459 56437619 55366065 53937114 52478352 51988905
 [9] 51832965 50614801

Smallest eigenvalues:
 [1]  0.30067100  0.25692767  0.17869120  0.14802603  0.13641694  0.11662896
 [7]  0.02789947 -0.76134603 -0.96719689 -1.04722745

Largest  eigenvalues:
 [1] 65316550 59817144 57643068 55937888 55004182 53727770 52529449 52012799
 [9] 52006955 51646610

Smallest eigenvalues:
 [1]  0.4718204  0.3725984  0.3688057  0.3619263  0.3417680  0.2895856
 [7]  0.2668145  0.2288515  0.1696846 -0.0419761

Largest  eigenvalues:
 [1] 65430252 60186549 57902544 56708130 54799905 53182629 52727318 51983730
 [9] 51787673 51207025

Smallest eigenvalues:
 [1]  0.16163110  0.10226022  0.07016115  0.01021784 -0.01938875 -0.15511759
 [7] -0.20201882 -0.28235975 -0.83649657 -1.41196324

Largest  eigenvalues:
 [1] 63589651 60474192 57779315 55120910 54979755 53748396 51942201 51879761
 [9] 51166026 50946444

Smallest eigenvalues:
 [1]  0.43652355  0.42026365  0.39998526  0.39097169  0.31227609  0.27948034
 [7]  0.26460260  0.19855633  0.06991435 -0.03640425

Largest  eigenvalues:
 [1] 65120762 60300018 58019377 55737396 55382700 53653209 52427660 52078487
 [9] 51952404 51482757

Smallest eigenvalues:
 [1]  0.365817485  0.253268375  0.245423941  0.174328665  0.139668327
 [6]  0.035727625  0.009370155 -0.049486401 -0.160140997 -0.538150752

Largest  eigenvalues:
 [1] 66174484 60557071 57955294 56600992 54988746 53595055 52667171 52608848
 [9] 51925991 51758373

Smallest eigenvalues:
 [1]  0.37421177  0.37286524  0.36146869  0.27574148  0.24273759  0.16643424
 [7]  0.16437171  0.10164275  0.03150259 -0.41895148

Largest  eigenvalues:
 [1] 66555193 61015849 57875134 57278162 56051532 54362047 53313086 53219235
 [9] 52404952 52003054

Smallest eigenvalues:
 [1]  0.42999126  0.39400374  0.32997726  0.30741752  0.29716140  0.24433894
 [7]  0.17649854  0.13992982  0.09912456 -0.68463267

Largest  eigenvalues:
 [1] 65480565 59535569 57271541 56789497 54602543 53325300 52731957 51867612
 [9] 51482190 50987039

Smallest eigenvalues:
 [1]  0.56084345  0.49043668  0.48142433  0.41932512  0.36428754  0.26911925
 [7]  0.25576346  0.21769094 -0.04888047 -3.80561657

Largest  eigenvalues:
 [1] 64832032 60105255 57402449 56089024 55128969 53440947 52201383 51955887
 [9] 51932038 50968290

Smallest eigenvalues:
 [1]  0.43845323  0.42975066  0.39989268  0.38468818  0.34356178  0.22839252
 [7]  0.20607929  0.08697602  0.07640505 -5.50472005

Largest  eigenvalues:
 [1] 63794133 60633576 57902608 56019595 55698928 54404253 52707114 52662581
 [9] 51882010 51585602

Smallest eigenvalues:
 [1]  0.4624995  0.3755231  0.3703261  0.3592630  0.3440499  0.3248258
 [7]  0.2752419  0.2409431  0.1158476 -0.7668570

Largest  eigenvalues:
 [1] 64221205 60318583 57709171 55619533 55531237 54156202 52544302 52282630
 [9] 51618503 51105844

Smallest eigenvalues:
 [1]  0.45448890  0.42029267  0.39848239  0.29456969  0.20575790  0.15607533
 [7]  0.13126174  0.08395056  0.01181098 -1.42544809

Largest  eigenvalues:
 [1] 63006324 60062214 56941706 55361428 54650641 53614751 51778485 51688758
 [9] 50917214 50820470

Smallest eigenvalues:
 [1]  0.51249200  0.45822914  0.40281296  0.39870987  0.36076613  0.35794471
 [7]  0.34564490  0.14319905  0.10718640 -0.07663943

Largest  eigenvalues:
 [1] 65176484 61281441 57663689 56588514 56289128 54564393 53434200 52573449
 [9] 52280838 51819554

Smallest eigenvalues:
 [1]  0.42829448  0.41753283  0.38087157  0.36199592  0.33765541  0.29052853
 [7]  0.26068976  0.01377166 -0.20060367 -0.87768029

Largest  eigenvalues:
 [1] 64144509 60444007 57639448 56127475 55400155 53856133 52361648 52171013
 [9] 51806209 51182076

Smallest eigenvalues:
 [1]   0.308025995   0.206761619   0.203216503   0.186286851   0.113052555
 [6]   0.076307466   0.006604131  -0.181839664  -0.291542576 -21.811795757

Largest  eigenvalues:
 [1] 65871585 59810854 57759104 56107180 54956920 53792945 52488773 52300045
 [9] 51995030 51435775

Smallest eigenvalues:
 [1]  0.4434678  0.3933192  0.3548960  0.2414716  0.2047585  0.1569187
 [7]  0.1048188 -0.1947996 -0.3046727 -0.7510127

Largest  eigenvalues:
 [1] 65753249 60422185 57651871 56907886 54849631 52897648 52848862 52433092
 [9] 51726218 51532197

Smallest eigenvalues:
 [1]  0.5779033  0.5601017  0.4521349  0.4358426  0.3057825  0.2802577
 [7]  0.2698895  0.2403582 -0.2231736 -0.2502104

Largest  eigenvalues:
 [1] 65495792 60740763 57667770 56644212 55475239 53738347 52781202 52599364
 [9] 51953171 51400325

Smallest eigenvalues:
 [1]  0.39276884  0.35729847  0.34816612  0.30998125  0.27557320  0.22853905
 [7]  0.14775489  0.11577115  0.08818914 -3.10563628

Largest  eigenvalues:
 [1] 63716726 59893907 57517720 55575251 54941132 53477474 51870779 51750287
 [9] 51570194 50904700

Smallest eigenvalues:
 [1]  0.34195849  0.24133060  0.21694165  0.19503112  0.10672832  0.02787603
 [7] -0.10118311 -0.21591306 -0.67050739 -1.28075896

Largest  eigenvalues:
 [1] 65171880 60592546 57871300 56212817 55299538 53882689 52342246 52080007
 [9] 51797614 51116417

Smallest eigenvalues:
 [1]  0.40662046  0.38647370  0.33170701  0.33162997  0.30318397  0.22392881
 [7]  0.20000899  0.08068127  0.05883845 -0.39544448

Largest  eigenvalues:
 [1] 65145845 60237238 57688219 56369463 55097132 53466215 53217061 52567880
 [9] 51852069 51605759

Smallest eigenvalues:
 [1]  0.4959148  0.4117465  0.3925934  0.3892781  0.2854885  0.2722464
 [7]  0.1915873  0.1864380 -0.1529678 -0.1771534

Largest  eigenvalues:
 [1] 64485225 60417703 57274239 55921359 55124532 53399009 51904648 51825347
 [9] 51797969 50898568

Smallest eigenvalues:
 [1]  0.6139020  0.5804288  0.5208425  0.5147206  0.4563544  0.3409322
 [7]  0.2962343  0.2506831  0.2447080 -0.6830423

Largest  eigenvalues:
 [1] 64533801 59843461 57051366 55700044 55026546 53588815 52152621 51836739
 [9] 51632093 50798520

Smallest eigenvalues:
 [1]  0.38089860  0.36074590  0.30022144  0.28137132  0.27443576  0.18334242
 [7]  0.17583582  0.16014067  0.13095374 -0.07063696

Largest  eigenvalues:
 [1] 65799156 60657443 58331932 56359963 55470306 53900753 52569202 52415561
 [9] 52330166 51790033

Smallest eigenvalues:
 [1]  0.3616097  0.3286228  0.3181877  0.3007739  0.2525987  0.2037673
 [7]  0.1977944  0.1026287 -0.5029078 -3.1767412

Largest  eigenvalues:
 [1] 65431182 59830413 57109716 56758413 54850195 52841188 52646603 52424251
 [9] 51838168 51478743

Smallest eigenvalues:
 [1]  0.4471657  0.4327267  0.3227875  0.2972009  0.2606796  0.2331267
 [7]  0.2251395  0.1442445  0.1034761 -0.6873129

Largest  eigenvalues:
 [1] 61983548 59479073 56151308 54809728 54805144 53062109 51964424 51953472
 [9] 50874982 50679640

Smallest eigenvalues:
 [1]  0.38179778  0.29670344  0.26829412  0.21802983  0.15912084  0.07662484
 [7] -0.02784264 -0.12456120 -0.57823318 -0.78838126

Largest  eigenvalues:
 [1] 65278982 61455893 58255280 57242291 55362965 53669651 53381839 52675368
 [9] 52285646 51440846

Smallest eigenvalues:
 [1]  0.4701700  0.4498259  0.4130603  0.3694225  0.3263399  0.2567731
 [7]  0.2288796  0.1915548  0.1630194 -0.6071124

Largest  eigenvalues:
 [1] 62909426 59399446 56885421 54818310 54707668 53234116 51921570 51200939
 [9] 50850083 50466636

Smallest eigenvalues:
 [1]  0.24025026  0.23284841  0.21419365  0.18911631  0.13054411  0.01454168
 [7] -0.13678224 -0.19889759 -0.32694998 -1.22316880

Largest  eigenvalues:
 [1] 64079599 59956866 57537982 55733631 54838047 53561966 51793740 51766962
 [9] 51707695 50824179

Smallest eigenvalues:
 [1]  0.41558011  0.37971485  0.23767634  0.07841913  0.07488108  0.04916357
 [7] -0.02906305 -0.08548154 -0.30606844 -2.11074582

Largest  eigenvalues:
 [1] 63827165 60265287 57422937 55607886 55498858 53761653 52625950 51818676
 [9] 51735138 51284014

Smallest eigenvalues:
 [1]  0.206281423  0.186940906  0.184822632  0.164652584  0.156494196
 [6]  0.147955263  0.058202108 -0.007530551 -0.279125147 -0.352152164

Largest  eigenvalues:
 [1] 63593910 59314045 56383037 55532901 54778798 53085053 51773136 51495649
 [9] 50830776 50198942

Smallest eigenvalues:
 [1]  0.47735267  0.38922739  0.38311668  0.37983251  0.34968656  0.28385840
 [7]  0.19040160  0.16099142 -0.08795911 -0.44315592

Largest  eigenvalues:
 [1] 64537503 60757877 57781254 55942695 55358972 53760801 52792436 52172156
 [9] 52105396 51884014

Smallest eigenvalues:
 [1]  0.36681956  0.33198055  0.33129214  0.32368534  0.24858332  0.21126190
 [7]  0.20711594  0.19122726 -0.08568089 -1.58808715

Largest  eigenvalues:
 [1] 64961779 60717350 58030721 55773400 55687200 54230392 52235425 52002581
 [9] 51934151 51336714

Smallest eigenvalues:
 [1]  0.23151387  0.16549267  0.15482562  0.08237195  0.03596431 -0.06702173
 [7] -0.37048212 -0.38894702 -1.34481634 -1.70611943

Largest  eigenvalues:
 [1] 64597605 59563841 56882993 55986066 54643173 53036149 52238462 51993337
 [9] 51601370 51022888

Smallest eigenvalues:
 [1]  0.43433141  0.41408769  0.29875081  0.29814096  0.23928795  0.23167230
 [7]  0.18174241  0.16648653 -0.06203392 -1.23436719

Largest  eigenvalues:
 [1] 64440736 60560603 57212631 56259889 55598767 53962329 52232686 52090257
 [9] 51934081 51051546

Smallest eigenvalues:
 [1]  0.3042010065  0.2028350908  0.1740175163  0.1612815640  0.1369131970
 [6]  0.0001836193 -0.0677540862 -0.2490146759 -0.4799055444 -1.0698131028

Largest  eigenvalues:
 [1] 64993726 60428037 57374522 56547352 54849189 53550509 52484664 52412518
 [9] 51789101 51646571

Smallest eigenvalues:
 [1]  0.27330582  0.23265980  0.20692219  0.12274527  0.07847066 -0.19807447
 [7] -0.25987368 -0.30761489 -0.51152650 -1.38724883

Largest  eigenvalues:
 [1] 64121480 59235452 57025321 55467561 54263155 53170667 51844510 51643615
 [9] 51464198 50938521

Smallest eigenvalues:
 [1]  0.22199018  0.21752864  0.17762979  0.16634727  0.12907103 -0.04799962
 [7] -0.09461652 -0.13949955 -0.17537962 -1.50600064

Largest  eigenvalues:
 [1] 64803510 60825577 57752098 56073264 55661494 54323780 52679780 52602585
 [9] 52017695 51827638

Smallest eigenvalues:
 [1]  0.529283596  0.519283179  0.490264063  0.434428678  0.422483895
 [6]  0.342396511  0.313743248  0.261834375  0.078963518 -0.009048804

Largest  eigenvalues:
 [1] 62319757 59863546 56791761 54995234 54701300 53307653 51698147 51593220
 [9] 50666779 50490874

Smallest eigenvalues:
 [1]   0.37679206   0.36717120   0.32350101   0.31689581   0.29871551
 [6]   0.25686390   0.25632731  -0.01333862  -0.06789774 -10.12314265

Largest  eigenvalues:
 [1] 64411516 59932779 57280277 55653920 55068576 53505755 52217133 51758458
 [9] 51549442 50961953

Smallest eigenvalues:
 [1]  0.33992151  0.33773102  0.33052832  0.24759088  0.17865735  0.16725219
 [7]  0.13009824  0.12557393  0.06940252 -0.05708416

Largest  eigenvalues:
 [1] 62687074 60046225 57096819 55454949 55099931 53311649 52429309 52254927
 [9] 51307310 51079840

Smallest eigenvalues:
 [1]  0.3734285  0.3578477  0.3031081  0.2387319  0.2306287  0.2039266
 [7]  0.1485060 -0.1171986 -0.3440188 -1.6214314

Largest  eigenvalues:
 [1] 65486043 60113924 57079185 56666044 55185757 53628727 52574929 52359392
 [9] 52009107 51585582

Smallest eigenvalues:
 [1]  0.49486609  0.47791572  0.45526315  0.38861004  0.26367715  0.24308695
 [7]  0.16907081  0.12584112  0.02471961 -0.01684104

Largest  eigenvalues:
 [1] 62945545 60794518 57637850 56261031 54882770 54402627 52808606 52517634
 [9] 51566391 51069462

Smallest eigenvalues:
 [1]  0.40440121  0.33971828  0.32780829  0.26849468  0.18441321  0.14547299
 [7]  0.03445263 -0.35447099 -0.44357899 -4.96304851

Largest  eigenvalues:
 [1] 65527053 60207613 57375006 56259761 55115688 53212988 52481602 52032514
 [9] 51617348 51241593

Smallest eigenvalues:
 [1]  0.2201364  0.1930468  0.1874791 -0.1227888 -0.1273022 -0.2719032
 [7] -0.2880179 -0.3875469 -0.4994241 -1.0144298

Largest  eigenvalues:
 [1] 65057256 61275334 57637187 56391357 56306501 54331565 53877199 52564757
 [9] 52190753 51824437

Smallest eigenvalues:
 [1]  0.4518062  0.3811479  0.3427248  0.3200841  0.2817578  0.2711405
 [7]  0.2704352  0.1788838 -0.2115723 -0.4633926

Largest  eigenvalues:
 [1] 64165066 60755183 58081525 56166649 55246195 53722459 52005370 51939202
 [9] 51843830 50931778

Smallest eigenvalues:
 [1]  0.25074725  0.20080264  0.10458999  0.08528284  0.07400013  0.01865420
 [7] -0.02934871 -0.12047732 -0.15615536 -3.60260821

Largest  eigenvalues:
 [1] 65005210 59847985 57578032 56482285 55144388 53920519 52943505 52327741
 [9] 52276216 51892719

Smallest eigenvalues:
 [1]  0.45241489  0.44066831  0.35509133  0.32710229  0.31067170  0.25264288
 [7]  0.18197227 -0.07615371 -0.23499493 -2.00386152

Largest  eigenvalues:
 [1] 65575740 59738799 56726747 56287922 54373976 52617790 52310861 51390303
 [9] 51134809 50635299

Smallest eigenvalues:
 [1]  0.4649903  0.4474241  0.4294076  0.3502424  0.3471955  0.2751184
 [7]  0.2261942  0.1726147  0.1328097 -0.3506693

Largest  eigenvalues:
 [1] 64730132 59805212 57428042 55376687 55297960 53809419 51715412 51587904
 [9] 51486614 50723969

Smallest eigenvalues:
 [1]  0.53888156  0.45745730  0.39162100  0.36546596  0.32729226  0.24969499
 [7]  0.22215482  0.09068120  0.03596904 -0.16543456

Largest  eigenvalues:
 [1] 64285560 60171025 57302773 55878871 55708304 54134687 52378623 52314474
 [9] 51809959 51710390

Smallest eigenvalues:
 [1]   0.30722470   0.26472251   0.20720361   0.17229991   0.08035100
 [6]   0.06282899  -0.13471021  -0.24564233  -0.84712211 -19.78156914

Largest  eigenvalues:
 [1] 63373225 60139956 57612673 55372237 55048578 53712521 52590324 51754877
 [9] 51208079 50960488

Smallest eigenvalues:
 [1]  0.45094110  0.43401422  0.40202821  0.37104549  0.28886965  0.28196224
 [7]  0.19893324  0.14721583  0.05688805 -0.63896127

Largest  eigenvalues:
 [1] 65752212 59703940 57233182 56738997 54613908 53095906 52639259 52129237
 [9] 51608316 51128829

Smallest eigenvalues:
 [1]  0.538572136  0.515976379  0.469945128  0.430167322  0.366027608
 [6]  0.317178642  0.142653151  0.084944324  0.041586483 -0.008741183

Largest  eigenvalues:
 [1] 64580174 60202693 57517011 55442585 55231930 53796502 52481055 52135800
 [9] 51571013 51344194

Smallest eigenvalues:
 [1]  0.36606927  0.35714062  0.29389149  0.23647287  0.21072451  0.18678329
 [7]  0.09481632 -0.06747963 -0.23553946 -1.14394497

Largest  eigenvalues:
 [1] 64461719 59735997 56821507 56081272 54957468 53379231 52166592 52112757
 [9] 51622284 51044612

Smallest eigenvalues:
 [1]  0.46249793  0.43717746  0.40706058  0.30474117  0.27275971  0.26185734
 [7]  0.22445666  0.19572387  0.03786895 -1.21038559

Largest  eigenvalues:
 [1] 63452371 59579523 57298204 55281584 54737329 53529528 52205879 51839523
 [9] 51449580 51030156

Smallest eigenvalues:
 [1]  0.44583460  0.43792066  0.38713001  0.34232814  0.32319399  0.30532744
 [7]  0.20429410  0.03224634 -0.10057823 -0.38382236

Largest  eigenvalues:
 [1] 62820107 59663631 57056598 55572069 54853961 53197441 51612340 51509818
 [9] 51435912 50413943

Smallest eigenvalues:
 [1]  0.48627473  0.48486213  0.44672818  0.33133222  0.29116410  0.24938516
 [7]  0.17885290  0.15383709  0.03918108 -0.32173457

Largest  eigenvalues:
 [1] 64044075 60455779 57302207 55913636 55661146 53944846 52678631 52321508
 [9] 52078249 51483432

Smallest eigenvalues:
 [1]  0.5002047  0.4877379  0.4363611  0.3618692  0.2871384  0.2837144
 [7]  0.2813088  0.2140507 -0.4797941 -0.9148599

Largest  eigenvalues:
 [1] 63638083 59431396 56612639 55357256 54698638 52886140 52464489 51393630
 [9] 51193909 50785635

Smallest eigenvalues:
 [1]  0.40686541  0.40339525  0.38322734  0.35472292  0.31792274  0.14749524
 [7]  0.10558648  0.01705676 -0.01633554 -1.35660784

Largest  eigenvalues:
 [1] 65858758 59719838 57339255 56055788 54743702 53212222 52241443 51955715
 [9] 51846048 50763179

Smallest eigenvalues:
 [1]  0.43457226  0.39821612  0.39522916  0.33260903  0.30360549  0.27909684
 [7]  0.09056232  0.07132009 -0.03331028 -0.15457582

Largest  eigenvalues:
 [1] 64720423 59776526 57054000 55910283 55196154 53571753 51959316 51679796
 [9] 51182446 50133327

Smallest eigenvalues:
 [1]  0.39260874  0.33435365  0.30692710  0.30182919  0.18902775  0.18174103
 [7]  0.12612453 -0.01734765 -0.23787213 -1.24284197

Largest  eigenvalues:
 [1] 63199803 60239464 57177048 55512057 54614668 53577085 51846545 51628947
 [9] 51002896 50764446

Smallest eigenvalues:
 [1]  0.50145166  0.48650096  0.38400414  0.34200567  0.24375922  0.17251154
 [7]  0.15953227  0.12035749  0.02524313 -0.77626865

Largest  eigenvalues:
 [1] 62208651 59439404 56257202 54771859 54608922 52944998 51956172 51311175
 [9] 50736905 50573517

Smallest eigenvalues:
 [1]  0.56872319  0.55253719  0.52510494  0.38457499  0.37944957  0.32946291
 [7]  0.14578330  0.06764163 -0.02156755 -0.08872731

Largest  eigenvalues:
 [1] 65497041 59685859 56909482 56792229 54671221 52837401 52798023 51602580
 [9] 51214826 50555018

Smallest eigenvalues:
 [1]  0.45195098  0.33012824  0.32135000  0.24388514  0.20623307  0.06529955
 [7]  0.04877222 -0.10096606 -0.42589629 -1.64607516

Largest  eigenvalues:
 [1] 65073717 61262736 57555699 57004377 56014142 54035441 53623577 52585375
 [9] 52541897 52021777

Smallest eigenvalues:
 [1]  0.36025654  0.26378349  0.21604217  0.21202484  0.10607797  0.08405659
 [7] -0.07731024 -0.60904395 -0.67791686 -1.48559029

Largest  eigenvalues:
 [1] 66083921 59610777 56943449 56626455 54251470 52778248 52755492 51933327
 [9] 51177987 51122943

Smallest eigenvalues:
 [1]  0.49283605  0.48350648  0.37031427  0.34334530  0.34313966  0.24508915
 [7]  0.22922330  0.02242962 -0.07046072 -0.09086812

Largest  eigenvalues:
 [1] 64279055 59176574 56610448 55358905 54514337 52907435 51709124 51318291
 [9] 50987734 50327076

Smallest eigenvalues:
 [1]  0.59273904  0.45494010  0.43849772  0.42920931  0.31278377  0.31257013
 [7]  0.26006999  0.15085641 -0.01491967 -0.18238095

Largest  eigenvalues:
 [1] 63841274 59410326 56573212 55552144 54267231 52710932 51581156 51387589
 [9] 50842338 49968115

Smallest eigenvalues:
 [1]  0.32548894  0.28259775  0.26385580  0.25170916  0.18768399  0.17611072
 [7]  0.13279673  0.05586095  0.01349406 -0.62425734

Largest  eigenvalues:
 [1] 65491052 60679702 58281654 56793204 55238631 54039033 52738094 52398507
 [9] 52174768 51299871

Smallest eigenvalues:
 [1]  0.26999467  0.24067227  0.18690195  0.17381151  0.15689405  0.06549953
 [7]  0.02325153 -0.01391736 -0.02708347 -1.39803260

Largest  eigenvalues:
 [1] 65084599 59667335 56795187 55302314 54541184 52989902 51781746 51415711
 [9] 51288702 50928691

Smallest eigenvalues:
 [1]  0.481809313  0.463455723  0.380058870  0.303092990  0.297394438
 [6]  0.296393546  0.260159155  0.245311660  0.001545766 -5.653291840

Largest  eigenvalues:
 [1] 65444898 60920182 58162050 56492742 55877988 54191029 52776147 52371895
 [9] 52288088 51327756

Smallest eigenvalues:
 [1]  0.42724661  0.36254226  0.26973931  0.24610441  0.18356294  0.17923246
 [7]  0.11800548  0.09199347 -0.04562304 -2.16147899

Largest  eigenvalues:
 [1] 64443860 59692638 56612346 55302251 54601411 53081073 51565075 51394645
 [9] 51080771 50329756

Smallest eigenvalues:
 [1]  0.127079620  0.121829523 -0.009105345 -0.098734966 -0.175533379
 [6] -0.252872943 -0.275911775 -0.311978659 -0.407907347 -2.161574917

Largest  eigenvalues:
 [1] 65166770 60394479 57775083 55548521 55184248 53636282 52218048 51709664
 [9] 51565684 51504031

Smallest eigenvalues:
 [1]  0.498621018  0.482464932  0.464719120  0.367635146  0.357574127
 [6]  0.281352521  0.156715382  0.137070219 -0.002578572 -0.026560631

Largest  eigenvalues:
 [1] 63739908 60064686 56938842 55368735 55233402 53695629 52270016 52120536
 [9] 51489855 51181683

Smallest eigenvalues:
 [1]  0.4550115  0.4339077  0.4096776  0.4083677  0.2809894  0.2704890
 [7]  0.2332062  0.1926729  0.1642633 -0.3350256

Largest  eigenvalues:
 [1] 65597075 60361315 57620003 56372938 54974286 53558960 52533581 51877096
 [9] 51684126 51062125

Smallest eigenvalues:
 [1]  0.59293228  0.58439590  0.46079415  0.45680111  0.32576455  0.30668977
 [7]  0.26509910  0.22948079  0.08844987 -0.19775837

Largest  eigenvalues:
 [1] 66080229 60433448 57848196 56491531 55229555 53883980 52610828 52405954
 [9] 51883012 51441355

Smallest eigenvalues:
 [1]  0.37981832  0.36038541  0.35522910  0.32377308  0.27366214  0.22163999
 [7]  0.17251062  0.13792477 -0.08273076 -0.55500850

Largest  eigenvalues:
 [1] 65121254 60782164 58069287 56509829 55274120 53986842 52427337 52286661
 [9] 52056309 51143008

Smallest eigenvalues:
 [1]  0.4922655  0.4512300  0.4361336  0.3612484  0.3577866  0.3213488
 [7]  0.3003183  0.2121997  0.1652579 -0.2157578

Largest  eigenvalues:
 [1] 64907340 59573935 56568121 56394720 54398209 52937925 52218787 51739831
 [9] 51448563 50468316

Smallest eigenvalues:
 [1]  0.5408972  0.5211180  0.5062630  0.4059827  0.3587215  0.3547026
 [7]  0.1936218  0.1909158  0.1808374 -0.1337813

Largest  eigenvalues:
 [1] 63808887 60205071 56991351 55354761 55284676 53747266 52290576 52010319
 [9] 51451656 51267976

Smallest eigenvalues:
 [1]  0.3447919987  0.3307802435  0.2989218221  0.2922549215  0.2223076358
 [6]  0.1546549790  0.1139861743  0.0701401505  0.0005542438 -0.0658164069

Largest  eigenvalues:
 [1] 62031393 60336994 57417077 55937013 55018472 54168102 52646816 52352086
 [9] 51505789 51012184

Smallest eigenvalues:
 [1]  0.6018108  0.5702971  0.5446860  0.4811291  0.4214358  0.4008453
 [7]  0.3032235  0.2026565  0.1251318 -0.6339919

Largest  eigenvalues:
 [1] 64140185 60661946 57032731 55678399 55601213 53980704 52335225 52178298
 [9] 51534697 51069349

Smallest eigenvalues:
 [1]  0.4444439  0.4202566  0.3568545  0.3111323  0.2645969  0.2453223
 [7]  0.1863267  0.1122573  0.1027479 -0.2382730

Largest  eigenvalues:
 [1] 65917226 60080011 57518928 57227433 54856524 53449453 53203666 52068827
 [9] 52001653 51138955

Smallest eigenvalues:
 [1]  0.36775398  0.36635231  0.28628080  0.22434271  0.14659257  0.10947501
 [7]  0.07425764 -0.13103102 -0.46137337 -8.81269989

Largest  eigenvalues:
 [1] 65632878 60315777 57704361 56882175 55055499 53485093 52860971 52488291
 [9] 52332170 51832382

Smallest eigenvalues:
 [1]  0.41436564  0.38280502  0.36637619  0.29972288  0.21380625  0.19608325
 [7]  0.13019916  0.02778648 -0.26604737 -0.36041729

Largest  eigenvalues:
 [1] 63463811 60308786 56959079 55314477 54933507 53235613 52011915 51545353
 [9] 51359442 51117125

Smallest eigenvalues:
 [1]  0.42499966  0.40481843  0.37754132  0.33857223  0.19431705  0.18293681
 [7] -0.08745294 -0.22701228 -0.22901659 -1.85418629

Largest  eigenvalues:
 [1] 64778842 59975199 57334997 56085416 54691803 53210121 52154412 52089627
 [9] 51865965 51359928

Smallest eigenvalues:
 [1]  0.43607020  0.38846239  0.37169210  0.32916283  0.26544295  0.25766863
 [7]  0.23214259  0.19554605 -0.01945274 -0.23953616

Largest  eigenvalues:
 [1] 63577978 59508908 57116957 55813181 54230290 52799328 51803495 51498936
 [9] 51095340 50431225

Smallest eigenvalues:
 [1]  0.382521787  0.303025366  0.233012294  0.222400318  0.217929149
 [6]  0.146430846  0.003283711 -0.071249471 -0.364714792 -2.076921842

Largest  eigenvalues:
 [1] 63389438 60524476 57270817 55576869 54974677 53437762 52024739 51993810
 [9] 51715772 51310069

Smallest eigenvalues:
 [1]  0.35367247  0.34057294  0.30666115  0.23073180  0.22192793  0.18926718
 [7]  0.18611158  0.05033477 -0.67011418 -1.04611634

Largest  eigenvalues:
 [1] 64474348 59593010 57349514 56989253 54446650 52950565 52602283 52560805
 [9] 51821221 51089856

Smallest eigenvalues:
 [1]  0.18523578  0.16596405  0.09903060  0.07801804  0.07507484  0.04546843
 [7]  0.01899126 -0.02363648 -0.57226297 -1.83073925

Largest  eigenvalues:
 [1] 66504444 61601941 58788573 57689326 55697108 54093670 53626734 52955438
 [9] 52543049 52223916

Smallest eigenvalues:
 [1]  0.4544503  0.4184977  0.4027554  0.3353646  0.3245670  0.2896932
 [7]  0.2108479  0.1587453  0.1257685 -0.1317678

Largest  eigenvalues:
 [1] 65259073 60189300 57816812 56136084 54910889 53332152 52055641 52008840
 [9] 51532561 51196078

Smallest eigenvalues:
 [1]  0.45254930  0.44487126  0.39384401  0.38563752  0.34448654  0.29665333
 [7]  0.19905804  0.15241638  0.00551193 -0.03876237

Largest  eigenvalues:
 [1] 65927861 60712931 57938491 56459590 55520595 53970151 52773381 52682583
 [9] 52463471 51814417

Smallest eigenvalues:
 [1]  0.410698714  0.408099959  0.243021489  0.232795109  0.127629407
 [6]  0.083217061  0.003270844 -0.155305548 -0.395444815 -2.934279357

Largest  eigenvalues:
 [1] 65876519 60353230 57619607 56827282 55201571 53869789 52895199 52133512
 [9] 52105097 51236102

Smallest eigenvalues:
 [1]  0.181022704  0.174913007  0.150845916  0.042466630 -0.009345051
 [6] -0.096044263 -0.183298468 -0.187795549 -0.836485269 -3.559519544

Largest  eigenvalues:
 [1] 62707691 59235668 56963571 54769921 54040168 53213604 51564434 51096805
 [9] 50516481 50315509

Smallest eigenvalues:
 [1]  0.165680136  0.146564132  0.112689155  0.046108623 -0.002610232
 [6] -0.023676892 -0.124903852 -0.136475594 -0.232947222 -0.383598663

Largest  eigenvalues:
 [1] 64922418 60290803 57654552 55311559 54784116 53417417 52095025 51496364
 [9] 51305503 51217163

Smallest eigenvalues:
 [1]  0.44105618  0.39454040  0.32722464  0.30564660  0.28974343  0.21912103
 [7]  0.12869477  0.02467714 -0.10971108 -2.06292443

Largest  eigenvalues:
 [1] 65484262 59849210 57211460 56312252 54694300 53293779 52426081 51836154
 [9] 51818290 51009001

Smallest eigenvalues:
 [1]  0.32180552  0.18214718  0.13225753  0.10831086  0.03874408 -0.04069816
 [7] -0.15856280 -0.24018360 -0.87680988 -1.68601624

Largest  eigenvalues:
 [1] 64515020 59466898 56478765 55719171 54747729 52889345 51884086 51712812
 [9] 51281814 50690846

Smallest eigenvalues:
 [1]  0.47174664  0.47005563  0.34241999  0.33970331  0.28957042  0.19171958
 [7]  0.04497320  0.04476324 -0.04559572 -0.31645563

Largest  eigenvalues:
 [1] 64531091 60184811 57181651 56350083 54713090 53098936 52418216 52223430
 [9] 51552641 51090515

Smallest eigenvalues:
 [1]  0.41526513  0.39880820  0.34388130  0.27121541  0.24190545  0.18419011
 [7]  0.07437829 -0.16510526 -0.21212665 -4.52041256

Largest  eigenvalues:
 [1] 62207773 59355186 55921699 54675618 54162259 52702627 51450199 50723030
 [9] 50231418 49925273

Smallest eigenvalues:
 [1]  0.37074429  0.34164873  0.30671791  0.27714647  0.22234495  0.19320356
 [7]  0.16831436  0.07345757  0.04423442 -1.44009343

Largest  eigenvalues:
 [1] 63990438 59830093 57168527 55672086 55412440 53844115 52520037 51969896
 [9] 51625410 51474002

Smallest eigenvalues:
 [1]  0.30022882  0.27236204  0.22714886  0.19124063  0.11819728  0.07276478
 [7] -0.07348596 -0.20636960 -0.21830364 -1.29573249

Largest  eigenvalues:
 [1] 64236562 59801849 56369385 55094268 54736682 52852062 51490881 51162714
 [9] 51105142 50595417

Smallest eigenvalues:
 [1]  0.09820088  0.01650463 -0.07651741 -0.13403839 -0.15289827 -0.22207786
 [7] -0.39813064 -0.48560551 -0.91696221 -3.76682158

Largest  eigenvalues:
 [1] 62954386 59115222 56085525 54841022 54356505 52832332 51992030 51445482
 [9] 50825124 50507288

Smallest eigenvalues:
 [1]  0.420085508  0.393832512  0.376946216  0.357338459  0.277455977
 [6]  0.207533793  0.080876851  0.008207197 -0.168546993 -0.398576622

Largest  eigenvalues:
 [1] 64370745 60413383 57136266 56321755 55023929 53177864 52610524 52328249
 [9] 51732811 51464329

Smallest eigenvalues:
 [1]  0.4724632  0.4370566  0.4265297  0.4231744  0.3627276  0.3252239
 [7]  0.1988408  0.1272765 -0.3075132 -0.9177189

Largest  eigenvalues:
 [1] 63308648 60185682 57366272 55834980 54989849 53201688 51978565 51913818
 [9] 51804414 50900120

Smallest eigenvalues:
 [1]  0.34648664  0.33279024  0.30633631  0.29363954  0.12753658  0.11236166
 [7] -0.01674858 -0.06218904 -0.20278956 -1.65584630

Largest  eigenvalues:
 [1] 62864323 60792602 57091288 55771527 55201640 53898426 52213670 51827805
 [9] 51245487 50946048

Smallest eigenvalues:
 [1]  0.35996701  0.34816292  0.30543824  0.28775183  0.24654443  0.22504584
 [7] -0.07327008 -0.08201719 -0.92335522 -1.33899399

Largest  eigenvalues:
 [1] 63152375 59536511 56998389 55489336 54728026 53018664 51765333 51693990
 [9] 51507978 50776270

Smallest eigenvalues:
 [1]  0.34145843  0.30525460  0.24207377  0.19609694  0.18092572  0.07296567
 [7]  0.04392425 -0.07557654 -0.20843504 -1.00644044

Largest  eigenvalues:
 [1] 64191288 60468457 57349626 55987471 55267367 53752561 52402743 52337988
 [9] 51930716 51342907

Smallest eigenvalues:
 [1]  0.16480505  0.10501115  0.09733584 -0.05264161 -0.11341967 -0.54094444
 [7] -0.62447927 -1.04296375 -1.10775942 -1.28413435

Largest  eigenvalues:
 [1] 65721208 59250519 56443440 55962739 54075474 52612083 52042557 51583471
 [9] 51297542 50731930

Smallest eigenvalues:
 [1]  0.4553532  0.4397757  0.4357501  0.2878770  0.2780496  0.2022769
 [7]  0.1498324  0.1361284  0.1015900 -0.9212881

Largest  eigenvalues:
 [1] 64679249 60718639 57771459 55864558 55720175 54153124 53002686 52082547
 [9] 51922089 51684424

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	7.531307	0.6518278	15.35903	0.465	2.692704	1.446231

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

HR ~ alt + n + speed + PM1

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- HR_fd
covariates <- list(altitude = altitude_fd, 
                   noise = noise_fd,
                   speed = speed_fd,
                   pollution = pollution1_fd)
path_plot <- 'figures/model_HR_alt_noise_speed_PM1_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     noise = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     speed = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     pollution = list(nbetabasis = 80, norder = 4, lambda = 1e3))

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, 
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 23.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Warning message in `^.fd`((outcome - yhatfd), 2):
"The maximum error exceeds the tolerance level."
Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 572 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Smallest eigenvalues:
 [1]  0.55050433  0.53256241  0.48654544  0.38000551  0.33202243  0.29621819
 [7]  0.16187231  0.14078987 -0.07034003 -0.08904212

Largest  eigenvalues:
 [1] 77833360 72433811 69511016 68086269 66300872 64557563 63233857 62652249
 [9] 62479350 61141199

Smallest eigenvalues:
 [1]  0.5412244  0.5337260  0.4357262  0.4182506  0.3881416  0.3443903
 [7]  0.3059660  0.2733733  0.2503802 -1.2558948

Largest  eigenvalues:
 [1] 76757647 73318543 69260738 67114619 67059005 65255124 62702247 62626440
 [9] 62182056 61147733

Smallest eigenvalues:
 [1]  0.5193067  0.4496392  0.3968282  0.3397934  0.3136508  0.2613941
 [7]  0.2323116  0.1967921  0.1406068 -0.2743322

Largest  eigenvalues:
 [1] 78468244 72626014 69694125 68449978 66778806 64797285 63930462 63603712
 [9] 62850940 62459966

Smallest eigenvalues:
 [1]  0.34468866  0.32021831  0.31255933  0.30876547  0.22313897  0.20452539
 [7]  0.10849901 -0.02678394 -0.24521738 -2.46405812

Largest  eigenvalues:
 [1] 77157694 73870474 69773724 67675367 67247413 65972609 63671250 63335281
 [9] 62358348 62240166

Smallest eigenvalues:
 [1]  0.4896740  0.4732335  0.4701173  0.3629771  0.3490251  0.2594458
 [7]  0.1323622  0.1005853 -0.3194762 -0.8731024

Largest  eigenvalues:
 [1] 79282261 73605326 69275792 68900141 67130452 64877079 63826134 63429073
 [9] 63143960 62163698

Smallest eigenvalues:
 [1]  0.39351702  0.32168073  0.29418720  0.15565554  0.14602426  0.13982603
 [7]  0.04342068 -0.27676117 -0.34207489 -1.72044392

Largest  eigenvalues:
 [1] 75465392 71566958 68134935 66426086 65997371 64299402 62690276 61646054
 [9] 61284674 60797550

Smallest eigenvalues:
 [1]  0.5853250  0.5295660  0.4590514  0.4474366  0.4301865  0.3775529
 [7]  0.3452556  0.2490105  0.2460635 -0.9763349

Largest  eigenvalues:
 [1] 77279787 72166896 68395283 67597868 65696280 63631743 62627451 62437772
 [9] 61800440 60756817

Smallest eigenvalues:
 [1]  0.5936902  0.5721702  0.4994369  0.4402444  0.4320499  0.4255537
 [7]  0.4044148  0.3486449  0.1886876 -3.6099993

Largest  eigenvalues:
 [1] 75975802 72899327 68982820 67141956 66127681 64770376 62202316 61953649
 [9] 61553745 60864096

Smallest eigenvalues:
 [1]  0.70127365  0.61435980  0.61046660  0.49482274  0.49357250  0.37027296
 [7]  0.31642644  0.27751581  0.08055193 -2.50509719

Largest  eigenvalues:
 [1] 77987238 73823862 69589330 67767612 67102764 65011914 62887331 62830596
 [9] 62683486 61500945

Smallest eigenvalues:
 [1]  0.5748293  0.5487580  0.4717583  0.4461822  0.3779188  0.3253492
 [7]  0.3214183  0.2483043  0.1717289 -0.2814774

Largest  eigenvalues:
 [1] 77040482 73344713 69358448 67665073 66661542 64800505 63543228 62803723
 [9] 62577633 62151441

Smallest eigenvalues:
 [1]  0.5771021  0.5649774  0.5511547  0.4714670  0.3947720  0.3835320
 [7]  0.2355225  0.1835590 -0.4674059 -0.6436282

Largest  eigenvalues:
 [1] 78368187 73064907 68970571 68580579 66422429 64577415 63480186 63007314
 [9] 62456438 61504093

Smallest eigenvalues:
 [1]  0.6203575  0.5639875  0.4805643  0.4394764  0.3923364  0.3507042
 [7]  0.3216985  0.1956973  0.1574092 -0.4715224

Largest  eigenvalues:
 [1] 77985049 72880844 69054724 68574424 65986723 64297307 63466068 62831782
 [9] 62558638 61806695

Smallest eigenvalues:
 [1]  0.44527544  0.42061535  0.38830877  0.38245969  0.32906657  0.20603643
 [7]  0.17947217  0.13179447  0.07722245 -0.85837095

Largest  eigenvalues:
 [1] 78119939 72564923 69189920 67586477 66704913 64955492 62945960 62770982
 [9] 62640721 61430230

Smallest eigenvalues:
 [1]  0.5959746  0.5408543  0.5241625  0.5105877  0.5086148  0.4984554
 [7]  0.4759609  0.4247122  0.2083826 -0.8058766

Largest  eigenvalues:
 [1] 76214867 72314659 68497350 66450934 66418714 64185016 62076139 61763088
 [9] 61701115 60720334

Smallest eigenvalues:
 [1]  0.52401028  0.49724913  0.48734768  0.45129408  0.43999226  0.40520349
 [7]  0.30748820  0.25934623  0.20358497 -0.06406239

Largest  eigenvalues:
 [1] 79426568 73743266 70159137 68764587 67142681 65355790 63970909 63939034
 [9] 63302679 62973021

Smallest eigenvalues:
 [1]  0.6588228  0.5463475  0.5355863  0.4894836  0.4351913  0.3469303
 [7]  0.3281641  0.3167582  0.3085053 -0.0465695

Largest  eigenvalues:
 [1] 76606890 72467099 68985091 67941250 65993602 64177961 62826310 62577722
 [9] 62163914 61278191

Smallest eigenvalues:
 [1]  0.44059291  0.37935961  0.33071818  0.32587899  0.29147508  0.28413418
 [7]  0.11581144  0.06103834  0.01497845 -1.26512857

Largest  eigenvalues:
 [1] 77381967 71730105 68202847 67104511 66028013 64238671 62286996 62211881
 [9] 61183800 60177009

Smallest eigenvalues:
 [1]  0.5103336  0.4925815  0.4613206  0.4486733  0.3553426  0.2700776
 [7]  0.2658374  0.2394336  0.1595794 -0.2364893

Largest  eigenvalues:
 [1] 76688563 72635813 69506089 67062396 66512681 64747988 62971768 62897015
 [9] 62290806 61711971

Smallest eigenvalues:
 [1]  0.66782273  0.58425948  0.55109872  0.54734984  0.45735486  0.42625028
 [7]  0.31454942  0.28902263  0.28009124 -0.07082533

Largest  eigenvalues:
 [1] 76496572 72602802 68670322 67309433 66753084 64560926 63186928 62468255
 [9] 62257546 61715133

Smallest eigenvalues:
 [1]  0.5199745  0.4130775  0.4101600  0.3792363  0.3167555  0.2399512
 [7]  0.1821167  0.1570986 -0.4443419 -0.4521060

Largest  eigenvalues:
 [1] 75964362 72524464 68472647 67121279 66146361 64380685 62330255 62103026
 [9] 62101038 61109529

Smallest eigenvalues:
 [1]  0.5914923  0.5014930  0.3686788  0.3570254  0.3132893  0.2763499
 [7]  0.2492538  0.2061373  0.1413934 -0.6540668

Largest  eigenvalues:
 [1] 76879680 73335645 69733528 67462648 67280318 65397243 63236041 63010438
 [9] 62422218 61994426

Smallest eigenvalues:
 [1]  0.3768560  0.3675516  0.3177338  0.2860588  0.2793688  0.2619481
 [7]  0.1743407  0.1728558  0.1706334 -0.6185908

Largest  eigenvalues:
 [1] 79011653 73255900 69574188 68350744 66803205 65060220 63532324 62822332
 [9] 62592111 61419237

Smallest eigenvalues:
 [1]  0.54377271  0.53810294  0.49180748  0.43076881  0.41986959  0.31024692
 [7]  0.22004644  0.21379538  0.07893951 -4.94836246

Largest  eigenvalues:
 [1] 76275202 73050970 69362795 67274582 67034827 65193982 62915040 62848413
 [9] 62195007 61645705

Smallest eigenvalues:
 [1]  0.67386427  0.61904324  0.55139825  0.54992412  0.50972916  0.45653835
 [7]  0.37376453  0.33818627 -0.07756398 -0.12099685

Largest  eigenvalues:
 [1] 75573170 72494355 68634885 66929348 66235218 64553658 62457016 61631814
 [9] 61457280 60808897

Smallest eigenvalues:
 [1]  0.5852783  0.4424343  0.4060084  0.3986288  0.3782321  0.3419111
 [7]  0.3350956  0.2818306  0.1333849 -1.4844796

Largest  eigenvalues:
 [1] 77455001 73409251 69747000 68069587 66934803 65349581 63010848 62950832
 [9] 62885780 61916476

Smallest eigenvalues:
 [1]  0.61067130  0.59564890  0.44528318  0.40287246  0.33257559  0.27736386
 [7]  0.25389963  0.24623060  0.17950845 -0.04802855

Largest  eigenvalues:
 [1] 77064087 73854580 69682392 68325183 67648650 66072303 63385077 63356016
 [9] 62704506 61869063

Smallest eigenvalues:
 [1]  0.49998707  0.47878998  0.31904681  0.29153507  0.27464203  0.26828693
 [7]  0.15851103  0.11926162  0.05747892 -0.28229002

Largest  eigenvalues:
 [1] 78535214 73035915 69783202 68019307 66459357 64829533 63256695 63156090
 [9] 62797589 62322318

Smallest eigenvalues:
 [1]  0.4723635  0.3912575  0.3851720  0.3414968  0.3232837  0.2842141
 [7]  0.2669647  0.1974578  0.1950401 -0.3505106

Largest  eigenvalues:
 [1] 77418887 73755864 69249846 68157358 67142982 65500067 63052892 62941243
 [9] 62641739 61670557

Smallest eigenvalues:
 [1]  0.4828237  0.4817132  0.4446093  0.4317999  0.3067970  0.2624808
 [7]  0.2278049  0.2119374  0.1027619 -0.1712094

Largest  eigenvalues:
 [1] 76086378 72846042 68789078 66383887 66327873 64569867 62583088 61842470
 [9] 61547881 61012645

Smallest eigenvalues:
 [1]  0.5271975  0.5063615  0.4562745  0.4227428  0.3839283  0.2926226
 [7]  0.2325375  0.2297640  0.2137379 -0.1613282

Largest  eigenvalues:
 [1] 77896849 72825463 69021100 67986920 66591967 64675585 63089559 62982052
 [9] 62377297 61886280

Smallest eigenvalues:
 [1]  0.36566361  0.31865925  0.30146308  0.19483654  0.18097169  0.17424625
 [7]  0.06623446  0.02375042 -0.09330488 -1.64920503

Largest  eigenvalues:
 [1] 76602624 73317207 68912482 67423260 66874147 65168007 62877797 62590343
 [9] 62052566 61615224

Smallest eigenvalues:
 [1]  0.48253825  0.38191451  0.35905960  0.28043671  0.27654467  0.25303596
 [7]  0.14123438  0.13488854 -0.04432461 -0.76955118

Largest  eigenvalues:
 [1] 78127783 73592781 68678488 68370272 66709882 64535112 63436856 62978503
 [9] 62740783 61590343

Smallest eigenvalues:
 [1]  0.53753274  0.47434338  0.47176779  0.43937919  0.43308854  0.41313197
 [7]  0.28829439  0.28217184  0.21198725 -0.07474942

Largest  eigenvalues:
 [1] 78192087 74035284 69361383 68012899 66828118 65041528 63015074 62961809
 [9] 62464416 61669655

Smallest eigenvalues:
 [1]  0.5610421  0.4957297  0.4849538  0.3511187  0.3411522  0.3139303
 [7]  0.2565304  0.2457611  0.2058332 -0.4582968

Largest  eigenvalues:
 [1] 80453923 73430251 70355570 69579319 66744585 64821438 64784183 63805645
 [9] 62781328 62269842

Smallest eigenvalues:
 [1]  0.62527641  0.61646997  0.57774377  0.45831939  0.36207668  0.32392068
 [7]  0.28420095  0.21344506  0.20367886 -0.02992591

Largest  eigenvalues:
 [1] 78959018 73483317 69975906 68414059 67086570 65178640 63613461 63582354
 [9] 63057415 62304113

Smallest eigenvalues:
 [1]  0.6535490  0.6503341  0.5825893  0.5250772  0.4696757  0.3816589
 [7]  0.3400971  0.2693848  0.2282517 -0.1262570

Largest  eigenvalues:
 [1] 76163899 73108038 68634654 66907999 66874588 64746920 62762017 62404244
 [9] 62010359 60933468

Smallest eigenvalues:
 [1]  0.42372041  0.41129005  0.40427971  0.34114189  0.33793438  0.28477815
 [7]  0.27140470  0.19954846  0.03101168 -0.21139883

Largest  eigenvalues:
 [1] 78756867 72166584 68657497 67890919 66190124 64312005 63065588 62739670
 [9] 62352902 61698804

Smallest eigenvalues:
 [1]  0.4889110  0.4670574  0.4561989  0.4361883  0.3815398  0.3720569
 [7]  0.3652966  0.2183780 -0.1898968 -1.3632109

Largest  eigenvalues:
 [1] 78571154 72905156 69415063 68076651 66440055 64937061 63171997 62771084
 [9] 62555153 61740873

Smallest eigenvalues:
 [1]  0.37861305  0.34623755  0.28731850  0.28293476  0.24525114  0.21145686
 [7]  0.20615373  0.18470773 -0.06399567 -1.38734308

Largest  eigenvalues:
 [1] 76382284 73936040 69742068 67651626 67403684 65891156 63642528 62828995
 [9] 62609597 61740626

Smallest eigenvalues:
 [1]  0.504516582  0.481783800  0.417154221  0.392213521  0.366511135
 [6]  0.345189650  0.336792801  0.215669830  0.142559533 -0.009007333

Largest  eigenvalues:
 [1] 75121904 73211474 68627346 66716859 66131307 64939846 62697589 61564480
 [9] 61104718 60669143

Smallest eigenvalues:
 [1]  0.47178434  0.46689147  0.42408490  0.29883213  0.27811200  0.20031507
 [7]  0.19424887  0.19265454 -0.08498325 -1.72120260

Largest  eigenvalues:
 [1] 79783506 74809641 70922655 69240333 67776974 66176877 64115474 64058387
 [9] 63856147 62950062

Smallest eigenvalues:
 [1]  0.42841051  0.35748851  0.35104235  0.34628557  0.32002307  0.17171505
 [7]  0.15674220  0.14793619  0.01362610 -0.08413527

Largest  eigenvalues:
 [1] 76051779 72982798 69002493 66691266 66629998 65132938 62777816 62245981
 [9] 61793328 61272084

Smallest eigenvalues:
 [1]  0.5053269  0.4669195  0.4523051  0.3586205  0.3102549  0.3076255
 [7]  0.2639822  0.2432264  0.0444544 -0.6590660

Largest  eigenvalues:
 [1] 77819523 72704247 69467221 67470467 66572792 65030782 62923634 62610545
 [9] 62590702 61438334

Smallest eigenvalues:
 [1]  0.4461113  0.4373170  0.4342049  0.3131738  0.2421742  0.1919153
 [7] -0.1656899 -0.1791776 -0.4526655 -1.8921244

Largest  eigenvalues:
 [1] 77971076 72247094 68633237 68589966 65673255 63286538 63274127 62825766
 [9] 62024065 61677701

Smallest eigenvalues:
 [1]  0.60959073  0.56045632  0.54251189  0.52708391  0.48267544  0.32515361
 [7]  0.30563307  0.10723032  0.07525862 -0.03075654

Largest  eigenvalues:
 [1] 76881138 72991010 69273163 67252713 67109028 65321977 63116920 62933591
 [9] 62108685 61624245

Smallest eigenvalues:
 [1]  0.5395889  0.4465586  0.4430413  0.3856597  0.3479056  0.3405963
 [7]  0.3242266  0.2430054  0.1203213 -0.4976387

Largest  eigenvalues:
 [1] 77596092 73632707 70044309 67475099 66745345 65431474 63047603 62726262
 [9] 62454268 61933265

Smallest eigenvalues:
 [1]  0.5162739  0.4707992  0.4466143  0.4318657  0.3449503  0.3380128
 [7]  0.3030409  0.2049623  0.1517631 -1.0239417

Largest  eigenvalues:
 [1] 77911493 72368512 69163137 68378787 66349914 64748610 63384586 62610399
 [9] 62402670 61393930

Smallest eigenvalues:
 [1]  0.6209771  0.5586180  0.5447933  0.4704432  0.4246072  0.3730246
 [7]  0.2698720  0.2310374  0.1868026 -0.4445809

Largest  eigenvalues:
 [1] 76802668 72075979 68053775 67895986 65537138 63495467 62667215 62053720
 [9] 62016796 60706000

Smallest eigenvalues:
 [1]  0.53917242  0.52364442  0.50318045  0.49074244  0.39386796  0.25189182
 [7]  0.24257973  0.17284128 -0.06541903 -0.11566226

Largest  eigenvalues:
 [1] 78178169 73481684 70147871 68791633 66947936 65308010 63547850 63393160
 [9] 63361117 62062268

Smallest eigenvalues:
 [1]  0.53531316  0.41311835  0.38000035  0.36012147  0.35002906  0.32506645
 [7]  0.31025279  0.27805186  0.06468173 -0.21606587

Largest  eigenvalues:
 [1] 78118240 72743653 69513000 67206435 66442566 64810401 62456040 62424790
 [9] 62321697 61512553

Smallest eigenvalues:
 [1]  0.34534472  0.26903293  0.26728483  0.25213307  0.21637402  0.11050141
 [7]  0.10522272  0.03568764 -0.04337439 -0.69033036

Largest  eigenvalues:
 [1] 76892843 72361285 68507388 67504949 66351923 64481874 62766663 62730446
 [9] 62451337 61728254

Smallest eigenvalues:
 [1]  0.58121399  0.47110198  0.45271145  0.45004487  0.42270916  0.39485928
 [7]  0.32562693  0.02700045 -0.07682017 -1.93117202

Largest  eigenvalues:
 [1] 76310896 71988663 68410729 66565202 66269356 64545937 62297320 62042835
 [9] 61405903 60984028

Smallest eigenvalues:
 [1]  0.45676543  0.44527826  0.39215912  0.35903114  0.34584123  0.22250206
 [7]  0.16530757  0.09010545  0.01147663 -1.33018835

Largest  eigenvalues:
 [1] 75095531 71952906 68563142 66122172 65720257 64630884 62709329 61574776
 [9] 60847417 60626242

Smallest eigenvalues:
 [1]  0.5268369  0.5253547  0.4495646  0.4423658  0.4184852  0.3685783
 [7]  0.3667439  0.2412914  0.1556810 -0.1227073

Largest  eigenvalues:
 [1] 76100395 72210466 68437501 66964931 65989060 64151053 62502850 62037942
 [9] 61930884 61124902

Smallest eigenvalues:
 [1]  0.40484377  0.39793920  0.34790528  0.31805481  0.24604047  0.22465553
 [7]  0.17961903  0.16210385  0.09696991 -0.85821771

Largest  eigenvalues:
 [1] 76507782 73157931 68700539 67384821 66631695 64840047 62518241 62485411
 [9] 62243271 61297501

Smallest eigenvalues:
 [1]  0.5516048  0.5488101  0.4782532  0.4424994  0.4374080  0.4062754
 [7]  0.3802243  0.3542188  0.3119516 -0.2950655

Largest  eigenvalues:
 [1] 77146701 72380999 68618636 67233614 66293726 64482192 62551356 62330466
 [9] 62149749 61141032

Smallest eigenvalues:
 [1]  0.47717635  0.41341230  0.37705806  0.29628191  0.25032638  0.24637906
 [7]  0.17340250 -0.01253615 -0.20420115 -0.35763236

Largest  eigenvalues:
 [1] 78599037 74052911 70071353 68619373 67013716 65359968 63599203 63425910
 [9] 63115799 62286738

Smallest eigenvalues:
 [1]  0.4698582  0.4584676  0.3625502  0.3533563  0.3204797  0.3173521
 [7]  0.3013119  0.2705705  0.2255708 -0.5698507

Largest  eigenvalues:
 [1] 78209693 72756919 68693173 67645069 66337854 64639666 62842837 62716814
 [9] 62530664 61762373

Smallest eigenvalues:
 [1]  0.44779206  0.43566215  0.34168218  0.32916163  0.32586749  0.25358317
 [7]  0.09478012 -0.13104861 -0.46889495 -0.77400065

Largest  eigenvalues:
 [1] 80983373 73569976 69927200 69216526 66743145 64753879 64327749 63180453
 [9] 63083247 62310527

Smallest eigenvalues:
 [1]  0.60888615  0.60459091  0.53468755  0.50691583  0.50219473  0.48142919
 [7]  0.42987856  0.27504740  0.07144804 -2.05436477

Largest  eigenvalues:
 [1] 77153155 73152370 69017596 67302684 66772292 65301586 62999670 62583448
 [9] 62100404 61369623

Smallest eigenvalues:
 [1]  0.52895510  0.49442599  0.48104675  0.45537924  0.34736516  0.27135971
 [7]  0.26967318  0.16084657  0.03217937 -0.81455937

Largest  eigenvalues:
 [1] 77274361 73749314 68980206 67792938 66906199 64987919 62783561 62749710
 [9] 62720216 61602799

Smallest eigenvalues:
 [1]  0.52861223  0.48861124  0.44761914  0.31506121  0.31003877  0.27424240
 [7]  0.21370409  0.19839632  0.02218377 -0.12963859

Largest  eigenvalues:
 [1] 76899967 73548428 70205726 67696032 67422512 65680919 63068549 62996275
 [9] 62573304 61658094

Smallest eigenvalues:
 [1]  0.4412637846  0.4021458286  0.3352397799  0.3020136481  0.2595983249
 [6]  0.1278242713  0.1114825481  0.0995514685 -0.0007480274 -0.9706437438

Largest  eigenvalues:
 [1] 75305121 72765104 68989948 66677045 66383655 64814612 62856081 62605236
 [9] 61759319 61269979

Smallest eigenvalues:
 [1]  0.46657352  0.37997608  0.37000797  0.25268517  0.19378856  0.16554402
 [7]  0.13818003  0.06135697 -0.21252654 -0.48520943

Largest  eigenvalues:
 [1] 78111223 73351079 69642694 68807010 66758053 64730898 63500882 63185421
 [9] 63006764 61920670

Smallest eigenvalues:
 [1]  0.64935658  0.64072863  0.50601624  0.48834324  0.48359208  0.43185791
 [7]  0.34494965  0.27843737  0.12514701 -0.06596242

Largest  eigenvalues:
 [1] 77653081 73196163 69244050 67038671 66965760 65027059 63054388 62340578
 [9] 62136939 61763364

Smallest eigenvalues:
 [1]  0.37397266  0.36474379  0.33165730  0.31943787  0.26674836  0.24388061
 [7]  0.22712632  0.22567748  0.02903477 -0.12074796

Largest  eigenvalues:
 [1] 77192291 72821900 69320856 67528601 66627303 64950272 62531135 62525489
 [9] 62240820 61028107

Smallest eigenvalues:
 [1]  0.5392415  0.5018866  0.4681729  0.4210981  0.4128392  0.2235284
 [7]  0.2005025  0.1542450  0.1411396 -0.4116996

Largest  eigenvalues:
 [1] 76236441 73513879 68753236 67366333 67073354 65157224 63019944 62999863
 [9] 62387108 61709371

Smallest eigenvalues:
 [1]  0.47067317  0.45587766  0.41450008  0.41180087  0.37041416  0.31865170
 [7]  0.30156645  0.24869087  0.09840674 -1.45738032

Largest  eigenvalues:
 [1] 78625495 73943120 70053826 67900037 67528669 65723528 63232622 63095219
 [9] 63024978 61809164

Smallest eigenvalues:
 [1]  0.49035567  0.46403231  0.46030065  0.41631453  0.39330579  0.32607545
 [7]  0.27186241  0.16009162  0.12545506 -0.03469129

Largest  eigenvalues:
 [1] 75754326 72633080 68543620 66902312 66570848 64579859 62459999 62265668
 [9] 61811048 60952404

Smallest eigenvalues:
 [1]  0.5398690  0.5337990  0.4551504  0.4133656  0.3830911  0.3224970
 [7]  0.2961641  0.2927599  0.2107947 -0.4301329

Largest  eigenvalues:
 [1] 76011933 72759279 68805530 67430964 65945013 64178365 62742387 62344299
 [9] 62061291 61507686

Smallest eigenvalues:
 [1]  0.5939107  0.5496027  0.5430406  0.5197949  0.4425005  0.4355064
 [7]  0.4294090  0.2908245  0.2724754 -2.2176092

Largest  eigenvalues:
 [1] 77413898 72315803 68538406 67219119 66374923 64622331 62449201 62317798
 [9] 61872895 60933781

Smallest eigenvalues:
 [1]  0.5369338  0.5282296  0.3907041  0.3614953  0.3385366  0.3300459
 [7]  0.2953671  0.2750601 -1.4669558 -3.9988135

Largest  eigenvalues:
 [1] 77219137 72343277 68637272 67328812 65963346 64082986 62486022 62316023
 [9] 61930033 60880881

Smallest eigenvalues:
 [1]  0.4142293  0.4035843  0.3052835  0.2849635  0.1726516  0.1083813
 [7] -0.1880029 -0.2041266 -0.2573278 -2.5245213

Largest  eigenvalues:
 [1] 77433652 73456762 69012646 67534088 67324165 65224541 63070684 62750628
 [9] 62538916 61607362

Smallest eigenvalues:
 [1]  0.4221675  0.4113480  0.3930594  0.3746244  0.2771734  0.1951779
 [7]  0.1224577  0.1107408 -0.4173752 -5.1942842

Largest  eigenvalues:
 [1] 78127798 72408071 68784249 68317234 65645803 63809997 63389613 61746248
 [9] 61665710 60511450

Smallest eigenvalues:
 [1]  0.44308815  0.37342399  0.35375460  0.25680067  0.18955281  0.15217654
 [7]  0.08022281  0.07096196 -0.11677683 -2.32595269

Largest  eigenvalues:
 [1] 75469703 73117869 68682190 66832167 66793529 64570801 62548250 62233732
 [9] 61884019 61083913

Smallest eigenvalues:
 [1]  0.56346443  0.55503063  0.49899161  0.48856436  0.47968829  0.47249497
 [7]  0.38707996  0.28378114  0.06293197 -1.08068189

Largest  eigenvalues:
 [1] 77917674 72863760 68776013 67666951 65836530 63944199 62708812 62299124
 [9] 62141814 61241046

Smallest eigenvalues:
 [1]  0.49084275  0.39420319  0.30362793  0.28679473  0.25313097  0.23911682
 [7]  0.21345937  0.17107179  0.08149994 -0.62999759

Largest  eigenvalues:
 [1] 77288711 72935714 69468388 67443297 66381396 64889352 62801701 62505797
 [9] 62315728 61235107

Smallest eigenvalues:
 [1]  0.5259478  0.4960631  0.4397647  0.3904451  0.3842165  0.3791179
 [7]  0.3566501  0.2939234  0.2539997 -0.2633033

Largest  eigenvalues:
 [1] 79269402 73253894 70130360 69228123 66144359 64262989 64226383 62763002
 [9] 62681195 61485402

Smallest eigenvalues:
 [1]  0.5875704  0.5791915  0.5432155  0.4957099  0.4836447  0.3999043
 [7]  0.3810816  0.3335534  0.2872577 -4.8400558

Largest  eigenvalues:
 [1] 77799495 72663782 69436910 67941288 66491539 64461592 62947637 62896994
 [9] 62811459 61738942

Smallest eigenvalues:
 [1]  0.5576461  0.4978513  0.4297535  0.3962712  0.3585189  0.3076665
 [7]  0.2889435  0.2823608  0.1092095 -0.1328825

Largest  eigenvalues:
 [1] 78758288 73995560 69556351 69023946 67109005 65072259 63889386 63260724
 [9] 63113737 61944731

Smallest eigenvalues:
 [1]  0.46112632  0.44435734  0.42251972  0.29146883  0.29132954  0.24225346
 [7]  0.18044426  0.07978961 -0.89466780 -1.56549320

Largest  eigenvalues:
 [1] 78063315 72578398 68681560 67917398 66463991 64665735 63005270 62897881
 [9] 62785928 61764655

Smallest eigenvalues:
 [1]  0.57240816  0.56308732  0.50883246  0.50231902  0.42581645  0.40998954
 [7]  0.33292717  0.32940473  0.28866679 -0.04808187

Largest  eigenvalues:
 [1] 77409563 73125107 68973620 67631870 66693053 64613172 62822764 62573552
 [9] 62443090 61102096

Smallest eigenvalues:
 [1]  0.4391791  0.3818668  0.3096826  0.3021444  0.2835909  0.2828333
 [7]  0.2625952  0.2236139  0.1998042 -4.7503656

Largest  eigenvalues:
 [1] 78790445 72778588 69023574 68301885 66402769 64670038 63227362 62320534
 [9] 61884988 61095223

Smallest eigenvalues:
 [1]  0.57913374  0.57233952  0.47368403  0.40336224  0.36699524  0.34711919
 [7]  0.30289895  0.16496625  0.08726118 -0.04250618

Largest  eigenvalues:
 [1] 76777460 72725437 69307654 67540522 67150182 65402113 63048511 62751375
 [9] 62524140 61356749

Smallest eigenvalues:
 [1]  0.56560520  0.54824738  0.38209648  0.31009612  0.26685413  0.23989876
 [7]  0.08325651 -0.07290181 -0.44716777 -3.71661430

Largest  eigenvalues:
 [1] 75815132 72685190 68316372 66621151 66460553 64474652 62346917 62011299
 [9] 61709544 60672364

Smallest eigenvalues:
 [1]  0.5085805  0.4511928  0.3903523  0.3236891  0.3016539  0.2422886
 [7]  0.1332402  0.1244244  0.0847495 -0.0216849

Largest  eigenvalues:
 [1] 76996633 73493556 69461115 67539468 67170144 65171259 63122729 62869575
 [9] 62695229 61693950

Smallest eigenvalues:
 [1]  0.44120920  0.39339443  0.37504544  0.28969713  0.28796913  0.20753454
 [7]  0.19918180  0.16882218  0.05465016 -0.82452239

Largest  eigenvalues:
 [1] 78163800 72813736 69359576 68001799 66691651 65042677 63146372 63142900
 [9] 62827565 61852691

Smallest eigenvalues:
 [1]  0.617619693  0.607399444  0.585992566  0.584248216  0.570915035
 [6]  0.488495903  0.361012994  0.268844625  0.004517985 -0.110975565

Largest  eigenvalues:
 [1] 77765798 72529640 68313254 67574197 65971805 64079464 62560910 62103770
 [9] 61985712 60867424

Smallest eigenvalues:
 [1]  0.49791580  0.42858258  0.41856716  0.34348125  0.34320007  0.29930628
 [7]  0.22130627  0.11641306  0.03357146 -0.07973467

Largest  eigenvalues:
 [1] 77071222 73384443 69879048 67128201 66838548 65103819 63095360 62882015
 [9] 62472171 62106800

Smallest eigenvalues:
 [1]  0.56331037  0.48432183  0.44766832  0.35688816  0.31167840  0.29389868
 [7]  0.27011621  0.16106373  0.06863595 -0.28255588

Largest  eigenvalues:
 [1] 75160003 71911892 67840389 66365889 65775111 63891334 62482308 61333487
 [9] 61179947 60216015

Smallest eigenvalues:
 [1]  0.5900622  0.5458285  0.5292158  0.4826307  0.4531926  0.2855408
 [7]  0.2518647  0.2512229  0.1130998 -2.1437523

Largest  eigenvalues:
 [1] 78780594 72607505 68342437 67795706 66117146 63961777 62946644 62115656
 [9] 62026870 61063362

Smallest eigenvalues:
 [1]  0.58861946  0.49640218  0.43775227  0.42612548  0.39857828  0.30424909
 [7]  0.28018261  0.10328813  0.03197308 -0.25670430

Largest  eigenvalues:
 [1] 77427337 71816789 68831165 66818233 65837571 64172204 62740240 62334261
 [9] 62047765 61263721

Smallest eigenvalues:
 [1]  0.56689404  0.48850955  0.46939879  0.34963593  0.33034713  0.29036723
 [7]  0.26425258  0.17036773  0.06080502 -0.97775593

Largest  eigenvalues:
 [1] 77534749 73612076 69884162 67921779 67367274 65658338 63126119 63065810
 [9] 62797875 61977944

Smallest eigenvalues:
 [1]  0.6019600  0.5864450  0.5741068  0.5360648  0.4351847  0.4127963
 [7]  0.4102074  0.3936848  0.1670804 -0.2264092

Largest  eigenvalues:
 [1] 76260796 73009611 68736599 66711711 66412668 64823934 62175142 61750840
 [9] 61405641 60366456

Smallest eigenvalues:
 [1]  0.4409786  0.4111338  0.3186108  0.3071264  0.2950198  0.2814946
 [7]  0.1922572  0.1591420 -0.1500812 -1.1966799

Largest  eigenvalues:
 [1] 76265530 72209777 68865885 66217759 66172428 64507541 62504952 61820144
 [9] 61502691 60943276

Smallest eigenvalues:
 [1]  0.5642905  0.5095889  0.4971675  0.4878429  0.4122527  0.3813373
 [7]  0.3761242  0.2741862  0.1263883 -1.1254294

Largest  eigenvalues:
 [1] 80569601 73498846 69629049 69609463 66611171 64780602 64678186 63054462
 [9] 62351974 61795270

Smallest eigenvalues:
 [1]  0.4165391  0.4061869  0.3801803  0.3758458  0.3492932  0.3094795
 [7]  0.2949535  0.2807042 -0.0446970 -1.1192370

Largest  eigenvalues:
 [1] 77753404 71851585 68407970 67847595 65548043 63902492 62890705 61850894
 [9] 61827038 60803865

Smallest eigenvalues:
 [1]  0.23580639  0.18449458  0.04556393 -0.07006873 -0.11100463 -0.12889717
 [7] -0.30172450 -0.78758416 -1.91594761 -2.27607093

Largest  eigenvalues:
 [1] 77463285 72682369 68455940 66715950 66508523 64493809 62148304 62083714
 [9] 61509947 60480488

Smallest eigenvalues:
 [1]  0.42480957  0.38230947  0.36170997  0.34639133  0.28592913  0.26116859
 [7]  0.23132756  0.15846357  0.03461095 -1.02061837

Largest  eigenvalues:
 [1] 78972912 73753321 69913122 69324787 66804428 64928578 64055176 63003238
 [9] 62852595 61379146

Smallest eigenvalues:
 [1]  0.5188156  0.4869317  0.4624479  0.4432447  0.4414182  0.3905045
 [7]  0.3713981  0.2250883  0.2144155 -0.2394167

Largest  eigenvalues:
 [1] 79279739 73093688 69066838 67842352 66316280 64535821 63032728 62541785
 [9] 62086213 61388374

Smallest eigenvalues:
 [1]  0.5805323  0.3862634  0.3670794  0.3152899  0.2883731  0.2795393
 [7]  0.2485552  0.2365054 -0.0322109 -0.2993613

Largest  eigenvalues:
 [1] 77880808 72725815 69544808 67528551 66549866 64842371 62599739 62575413
 [9] 62484803 61641779

Smallest eigenvalues:
 [1]  0.42296303  0.39789931  0.35138867  0.31732080  0.30924156  0.25076722
 [7]  0.25069625  0.19087366 -0.03506752 -0.07986408

Largest  eigenvalues:
 [1] 77658976 73205022 69691871 67960144 66421848 64935479 63127203 62678803
 [9] 62625332 61612506

Smallest eigenvalues:
 [1]  0.5231114  0.4885183  0.4756620  0.4338424  0.4213640  0.3910881
 [7]  0.3731172  0.3541567  0.3254599 -0.1442809

Largest  eigenvalues:
 [1] 77634579 74569619 69517185 68228571 67805852 65733503 63649713 63283406
 [9] 62887977 61914440

Smallest eigenvalues:
 [1]  0.46825758  0.41001124  0.39826089  0.35338986  0.19811679  0.19510919
 [7]  0.17650116  0.07220242 -0.08088277 -1.17307476

Largest  eigenvalues:
 [1] 76756107 73605860 69925933 67745143 67166340 65653043 63274565 63191222
 [9] 62606971 62189851

Smallest eigenvalues:
 [1]  0.61404251  0.59563550  0.54559627  0.53695696  0.48206830  0.43228333
 [7]  0.31985793  0.13353889 -0.02976476 -0.09610230

Largest  eigenvalues:
 [1] 76436547 73364426 68851775 67485648 67153334 65063053 63063983 62791114
 [9] 62387669 61586475

Smallest eigenvalues:
 [1]  0.6368985  0.5992832  0.5298476  0.5252220  0.4081237  0.3937257
 [7]  0.3368829  0.3278955  0.2221071 -0.1225472

Largest  eigenvalues:
 [1] 78786428 73228843 69764036 67829182 66631214 64828976 63187796 62833134
 [9] 62752870 62031575

Smallest eigenvalues:
 [1]  0.6034882  0.5622188  0.5527781  0.4696642  0.4495244  0.3468501
 [7]  0.2752957  0.2652741  0.2441000 -0.9947116

Largest  eigenvalues:
 [1] 76136307 73385784 69679216 67816752 66291656 65776054 63042418 62801364
 [9] 61608940 61392461

Smallest eigenvalues:
 [1]  0.6614102  0.5622234  0.4988345  0.4871921  0.4594174  0.3883313
 [7]  0.3646422  0.3596251  0.2796611 -0.5140386

Largest  eigenvalues:
 [1] 77287175 73210031 69393766 67633693 66760161 65149125 62715912 62660124
 [9] 62546000 61202066

Smallest eigenvalues:
 [1]  0.45113533  0.31167135  0.23957183  0.22823710  0.21656046  0.19917037
 [7]  0.19746384  0.17195608  0.01762304 -3.66413946

Largest  eigenvalues:
 [1] 78153112 74250472 69579670 67958038 67934422 65686324 64010624 63238870
 [9] 62997561 62307720

Smallest eigenvalues:
 [1]  0.4428171  0.3386460  0.3271099  0.3078645  0.2770213  0.2396184
 [7]  0.2125655  0.2103045  0.0510398 -0.1143580

Largest  eigenvalues:
 [1] 75962506 73574452 69204811 67123065 67096864 65373454 62951476 62666350
 [9] 61991785 61382775

Smallest eigenvalues:
 [1]  0.4788231  0.3958568  0.3691574  0.3422451  0.3113427  0.3099296
 [7]  0.2567396  0.2322446  0.2243544 -1.5490367

Largest  eigenvalues:
 [1] 76294750 72606221 69194034 66852446 66146795 64790943 62623308 62113617
 [9] 61906546 60894250

Smallest eigenvalues:
 [1]  0.3932003  0.3822624  0.2838283  0.2732697  0.2700669  0.2583313
 [7]  0.2225064  0.1801301  0.1490531 -0.8078267

Largest  eigenvalues:
 [1] 75909093 72717956 69219321 67262170 66110932 65089804 62689428 62120018
 [9] 61366950 61208515

Smallest eigenvalues:
 [1]  0.653822298  0.547785579  0.544422903  0.482389915  0.416249122
 [6]  0.388129221  0.320381895  0.296084028 -0.002701621 -0.202626325

Largest  eigenvalues:
 [1] 77175254 72619515 68697195 66656285 66551738 64701016 62405511 62378784
 [9] 61790609 61339649

Smallest eigenvalues:
 [1]  0.53805211  0.52310086  0.51480711  0.44434781  0.34135233  0.32900681
 [7]  0.31333002  0.05509160  0.05057911 -0.13531371

Largest  eigenvalues:
 [1] 79290068 72489841 69135627 68867761 65843308 64028619 63970212 62425821
 [9] 62073776 61213946

Smallest eigenvalues:
 [1]  0.5731632  0.5621653  0.4422420  0.3415889  0.2869506  0.2798386
 [7]  0.2171453  0.1695872 -0.3088695 -2.6463412

Largest  eigenvalues:
 [1] 77002304 73169061 69333926 67669040 67494706 65392622 63242620 63068306
 [9] 62664227 61755188

Smallest eigenvalues:
 [1]  0.4866866  0.4732881  0.4692815  0.3272880  0.3114048  0.2442588
 [7]  0.2112379  0.1919694  0.1912410 -0.2096386

Largest  eigenvalues:
 [1] 76802814 72995127 68904226 66913591 66888311 64892519 63338202 62334215
 [9] 62169367 62012067

Smallest eigenvalues:
 [1]  0.54168339  0.51492056  0.49215215  0.48313743  0.40801997  0.34566312
 [7]  0.25437909  0.08720135  0.01184963 -0.40672102

Largest  eigenvalues:
 [1] 76738709 72492713 68304976 66459158 66139108 64304907 62481815 61849896
 [9] 61541475 60715281

Smallest eigenvalues:
 [1]  0.59422875  0.54765128  0.43647906  0.42889650  0.34781227  0.34371081
 [7]  0.33752622  0.19671603  0.17768952 -0.06990113

Largest  eigenvalues:
 [1] 79515958 72959497 70224055 67890661 66785833 64899071 63358694 63111499
 [9] 62870705 62002546

Smallest eigenvalues:
 [1]  0.379250925  0.352382197  0.291887880  0.226144928  0.180574337
 [6]  0.167773321  0.081935654 -0.008258228 -1.603749107 -3.951294003

Largest  eigenvalues:
 [1] 77605872 73646713 69116494 67640191 67117824 65249860 62817406 62709710
 [9] 62672017 61116528

Smallest eigenvalues:
 [1]  0.5439338  0.5086563  0.5040921  0.3478505  0.3075325  0.2226177
 [7]  0.1989941  0.1726739  0.1107143 -3.4974201

Largest  eigenvalues:
 [1] 77850545 73165436 69702503 67760699 66741289 65091200 63316654 62985319
 [9] 62833767 61872835

Smallest eigenvalues:
 [1]  0.3872133  0.3687104  0.3294288  0.3177236  0.1733053  0.1713076
 [7]  0.1547694  0.0922867 -0.2280324 -1.3032510

Largest  eigenvalues:
 [1] 75366867 71380151 67943990 66148025 65807121 64374438 62716088 61301821
 [9] 61001013 60514629

Smallest eigenvalues:
 [1]  0.3905634  0.3704986  0.3524538  0.3509479  0.2984183  0.2698907
 [7]  0.1789072  0.1175717 -0.5745736 -1.0216216

Largest  eigenvalues:
 [1] 77138439 72574859 68912307 67106992 66802229 65057912 62838001 62137101
 [9] 62099146 61336521

Smallest eigenvalues:
 [1]  0.512608489  0.463687837  0.390407122  0.385917345  0.379095724
 [6]  0.375592065  0.331197253  0.321957394  0.244113622 -0.003397504

Largest  eigenvalues:
 [1] 77442569 73103416 69048494 67955201 66682735 64982715 62718646 62500266
 [9] 62097532 61009960

Smallest eigenvalues:
 [1]  0.64807655  0.59362882  0.57008654  0.56957219  0.49588229  0.41817972
 [7]  0.41464411  0.32462628  0.26399870 -0.05003109

Largest  eigenvalues:
 [1] 78883203 73460068 69560661 68546682 66822170 64723024 63613382 63473926
 [9] 62474684 61711092

Smallest eigenvalues:
 [1]  0.54558508  0.50753203  0.40975616  0.39230917  0.36221065  0.32815604
 [7]  0.27085496  0.25340695  0.07968162 -0.02581307

Largest  eigenvalues:
 [1] 78258221 73888749 70199984 68292358 66794885 65290275 63389264 63221732
 [9] 62684859 61893222

Smallest eigenvalues:
 [1]  0.5946218  0.5020848  0.4803186  0.4758547  0.4383129  0.4248227
 [7]  0.3893174  0.3137578  0.1961756 -0.1769507

Largest  eigenvalues:
 [1] 78157728 73293276 69113388 68449311 66757270 64661385 63409632 62660965
 [9] 62546629 61362084

Smallest eigenvalues:
 [1]  0.51784275  0.47465287  0.39471867  0.37467349  0.36192549  0.27385162
 [7]  0.23877685  0.22242167  0.08843524 -0.11657658

Largest  eigenvalues:
 [1] 76137846 72530144 68826374 66463363 66431514 64812217 62443842 62207630
 [9] 61748431 60997144

Smallest eigenvalues:
 [1]  0.6335119  0.4482552  0.4443160  0.4352408  0.4347628  0.4338516
 [7]  0.2572862  0.1995757  0.1645509 -0.7597067

Largest  eigenvalues:
 [1] 79100255 73650071 69822202 68676300 66968180 65175732 63811355 63207373
 [9] 62746681 62102726

Smallest eigenvalues:
 [1]  0.424242081  0.381771450  0.369927507  0.318038870  0.302561677
 [6]  0.252094052  0.204688963  0.160558092 -0.007016862 -0.425280753

Largest  eigenvalues:
 [1] 75475984 72260806 68587102 66254981 66092394 64482786 62390454 61887300
 [9] 61030723 60756095

Smallest eigenvalues:
 [1]  0.60732390  0.47654025  0.39272312  0.36503256  0.32383390  0.21054712
 [7]  0.18168489  0.17763563  0.04821269 -0.89859070

Largest  eigenvalues:
 [1] 77444673 73180115 69612109 67503067 67111461 65294823 63503125 63287374
 [9] 62533953 62293359

Smallest eigenvalues:
 [1]  0.63537171  0.58361521  0.50900256  0.45650631  0.41422482  0.31998696
 [7]  0.31354813  0.29442810  0.23267037 -0.02179254

Largest  eigenvalues:
 [1] 78348604 73400596 70109961 67809934 67430546 65892228 63524756 63228926
 [9] 62979895 62207051

Smallest eigenvalues:
 [1]  0.71403417  0.63169834  0.52851899  0.51838754  0.48714279  0.45832461
 [7]  0.37180565  0.34834287  0.08639388 -0.02537194

Largest  eigenvalues:
 [1] 77089287 72517406 68560387 67490415 66194984 64226423 62557354 62370431
 [9] 61889377 60708265

Smallest eigenvalues:
 [1]  0.5561950  0.4940294  0.4197982  0.3556398  0.3081623  0.2629303
 [7]  0.2209056  0.2207962  0.1061034 -0.6377883

Largest  eigenvalues:
 [1] 77711272 73733625 70065973 67646860 67512603 66210261 63709492 63218166
 [9] 62664969 62163537

Smallest eigenvalues:
 [1]  0.3860705  0.3017566  0.2264116  0.1501360  0.1384508  0.1251060
 [7]  0.1070625  0.0268163 -0.1506807 -0.2326486

Largest  eigenvalues:
 [1] 74829898 72046528 68652648 67405727 65403028 65205342 63436229 61924215
 [9] 61169553 61070315

Smallest eigenvalues:
 [1]  0.6222086  0.5692506  0.5194139  0.4304063  0.3843781  0.3639545
 [7]  0.2800696  0.2344509  0.2278835 -1.4740686

Largest  eigenvalues:
 [1] 76978447 73023212 69646903 67402839 67087318 65203727 63080172 63067332
 [9] 62530120 61761270

Smallest eigenvalues:
 [1]  0.56005307  0.49448898  0.42479411  0.41008631  0.33622247  0.32297986
 [7]  0.18350642  0.09914597 -0.03587974 -3.62056726

Largest  eigenvalues:
 [1] 78883296 74197628 69790020 68553894 67385265 65274494 63933112 63666201
 [9] 62871260 62342541

Smallest eigenvalues:
 [1]  0.53400353  0.46389788  0.42076565  0.37511738  0.34801570  0.26929821
 [7]  0.26035183  0.24019392  0.22532802 -0.04512077

Largest  eigenvalues:
 [1] 78343413 73505308 69894118 68126356 67282577 65597415 64063539 63224748
 [9] 63212522 62655273

Smallest eigenvalues:
 [1]  0.5937502  0.5404256  0.4705270  0.4627922  0.4072046  0.3297166
 [7]  0.3123015  0.1937314  0.1492728 -0.1010974

Largest  eigenvalues:
 [1] 77065069 73563738 70032609 67310861 67033510 65406908 63383889 63139497
 [9] 62606798 62130782

Smallest eigenvalues:
 [1]  0.4828148  0.3907461  0.3639922  0.3611642  0.3496244  0.3289970
 [7]  0.2980622  0.2353663  0.2211265 -0.5727577

Largest  eigenvalues:
 [1] 78257025 73164929 69561379 68334250 66368222 65027147 63273473 62687783
 [9] 62368170 61427819

Smallest eigenvalues:
 [1]  0.4728710  0.4586556  0.4149114  0.4029525  0.3346516  0.3011435
 [7]  0.1800176  0.1387795  0.0118461 -0.8114178

Largest  eigenvalues:
 [1] 77628906 73405687 69510169 67913743 67202519 65472942 63612263 63168614
 [9] 62703582 62075609

Smallest eigenvalues:
 [1]  0.6101223  0.5680907  0.5276110  0.4674018  0.4574974  0.3935130
 [7]  0.3873984  0.2507839  0.1910051 -0.3275738

Largest  eigenvalues:
 [1] 78041992 73244927 69371595 68039403 67216725 65055741 63386192 63203365
 [9] 62800800 62104435

Smallest eigenvalues:
 [1]  0.63580334  0.57989306  0.47218193  0.46540855  0.40600048  0.34239513
 [7]  0.33955572  0.18737824  0.06358133 -0.17945200

Largest  eigenvalues:
 [1] 77859725 73575235 69405833 68078511 66760414 64932989 62940994 62738567
 [9] 62575689 61472237

Smallest eigenvalues:
 [1]  0.4484417  0.3736445  0.3588141  0.3487862  0.3230052  0.3159369
 [7]  0.2344544  0.1331244 -0.2035580 -2.0140574

Largest  eigenvalues:
 [1] 78700511 73592656 69533151 67975934 66804175 64988935 63061251 62874714
 [9] 62307879 61696484

Smallest eigenvalues:
 [1]  0.42969097  0.37649904  0.32953453  0.26879063  0.26206248  0.15468292
 [7]  0.15113522  0.08440772 -0.06491986 -0.35192571

Largest  eigenvalues:
 [1] 75692201 73448299 69590133 68351001 66219662 66055551 63610227 62822700
 [9] 61639198 61344042

Smallest eigenvalues:
 [1]  0.5042810  0.4236652  0.4065005  0.3964352  0.3739095  0.3444603
 [7]  0.2693778  0.2653005  0.2297315 -0.3884519

Largest  eigenvalues:
 [1] 77155261 72539793 69250173 67926819 66329224 64424568 62915333 62635906
 [9] 62481406 61531767

Smallest eigenvalues:
 [1]  0.49168582  0.44511370  0.44113008  0.42213586  0.35589466  0.32327593
 [7]  0.25261458  0.22836430 -0.03718705 -0.32728381

Largest  eigenvalues:
 [1] 75632067 72783182 68743555 67575557 66314284 65541295 63360283 61907494
 [9] 61346053 61154631

Smallest eigenvalues:
 [1]  0.5754385  0.5284635  0.5122090  0.4266025  0.3964567  0.3258635
 [7]  0.3229003  0.2932079  0.2706647 -0.3307973

Largest  eigenvalues:
 [1] 76273297 73188051 68835157 66577962 66160661 64817159 62394719 62226057
 [9] 61418985 60972459

Smallest eigenvalues:
 [1]  0.4316791  0.4301878  0.4294169  0.4209674  0.3489428  0.3017923
 [7]  0.2438169  0.1551130  0.1524928 -0.1097878

Largest  eigenvalues:
 [1] 76796472 73058723 69081596 66801540 66754274 64839715 63134292 62528694
 [9] 62082844 61914747

Smallest eigenvalues:
 [1]  0.52693423  0.42705024  0.38814423  0.33278257  0.22822342  0.20926477
 [7]  0.19002762 -0.09751184 -0.15372031 -0.85328667

Largest  eigenvalues:
 [1] 78206428 73818672 70015033 67645889 67365166 65319066 63773753 63312352
 [9] 62957854 62486697

Smallest eigenvalues:
 [1]  0.5346416  0.5065598  0.4619060  0.3966006  0.3412903  0.2634656
 [7]  0.2554226  0.2450997 -0.3910511 -0.4462226

Largest  eigenvalues:
 [1] 74811730 72075892 68380355 66495942 65952974 64216149 62561081 62312758
 [9] 61240852 61166290

Smallest eigenvalues:
 [1]  0.6764752  0.5722619  0.5525329  0.5152314  0.4612097  0.2178576
 [7]  0.2056087  0.2001281  0.0693849 -0.2792403

Largest  eigenvalues:
 [1] 75411431 73468368 69206157 67795269 66390033 65740601 63375192 63141253
 [9] 61792418 61554280

Smallest eigenvalues:
 [1]  0.61958873  0.47505559  0.45934819  0.43075196  0.40352850  0.36104174
 [7]  0.34576566  0.26638340  0.24576449 -0.04670816

Largest  eigenvalues:
 [1] 76385710 73635296 68949514 67278367 67100741 65181825 62886132 62620811
 [9] 62169196 61566930

Smallest eigenvalues:
 [1]  0.43851264  0.43052135  0.40936852  0.34033719  0.23375146  0.17150987
 [7]  0.03583367 -0.01091468 -1.58063976 -5.34231098

Largest  eigenvalues:
 [1] 76367503 72071484 67956823 66047230 66045958 64214099 62211047 62041353
 [9] 61214424 61082679

Smallest eigenvalues:
 [1]  0.5379096  0.5047268  0.3660185  0.3403853  0.2793852  0.2646597
 [7]  0.2399460  0.2164335  0.1727535 -0.1641470

Largest  eigenvalues:
 [1] 74407904 72311339 68923313 66291952 66205309 64455215 62471934 62332369
 [9] 61322164 61148691

Smallest eigenvalues:
 [1]  0.6329424  0.6321771  0.6111984  0.5425904  0.5185075  0.4791763
 [7]  0.4058807  0.2314654  0.1938446 -0.1626324

Largest  eigenvalues:
 [1] 75395840 72177689 68087365 66497674 66326170 64194774 62292133 62172689
 [9] 61332746 60786486

Smallest eigenvalues:
 [1]  0.52140079  0.47864039  0.47176709  0.40635498  0.36266667  0.26839433
 [7]  0.24524689  0.14545060  0.04393903 -0.19839482

Largest  eigenvalues:
 [1] 76315724 73052585 68704411 67785933 66714240 64583243 62709020 62624962
 [9] 62558368 61173891

Smallest eigenvalues:
 [1]  0.37495057  0.34634444  0.33256559  0.30153222  0.28124835  0.23766733
 [7]  0.23112482  0.22683800  0.20653937 -0.05645087

Largest  eigenvalues:
 [1] 78322768 72043838 68954446 67750771 66055037 64330911 62791647 62310125
 [9] 62184150 61406664

Smallest eigenvalues:
 [1]  0.46671237  0.44859994  0.44787846  0.39241518  0.30106268  0.26946639
 [7]  0.16228008  0.15265390 -0.03588098 -0.86799539

Largest  eigenvalues:
 [1] 77811691 72687101 68643073 68057620 66488840 64202955 63335451 62663561
 [9] 62588523 61486338

Smallest eigenvalues:
 [1]  0.5738878  0.5212360  0.5026136  0.4937408  0.4736657  0.3469288
 [7]  0.3262566  0.2486761  0.1451266 -1.3156564

Largest  eigenvalues:
 [1] 76823527 71984241 68405254 66851240 65815352 63922274 62160381 61951557
 [9] 61186924 60412151

Smallest eigenvalues:
 [1]  0.56686551  0.51874500  0.50717794  0.39833543  0.34924779  0.34638839
 [7]  0.33816218  0.30676061  0.06802969 -0.28199406

Largest  eigenvalues:
 [1] 76694909 72760935 68669257 67173003 66158832 64467593 62413275 62019350
 [9] 61540983 60484878

Smallest eigenvalues:
 [1]  0.60699465  0.49105293  0.45285170  0.43007205  0.40741436  0.37120272
 [7]  0.30887573  0.25304342  0.22924822 -0.02335191

Largest  eigenvalues:
 [1] 75630329 72039281 68460823 66440300 66342896 64577474 62533060 61872744
 [9] 61537119 60921486

Smallest eigenvalues:
 [1]  0.47430805  0.42336787  0.37840012  0.37463387  0.25035398  0.23057415
 [7]  0.16635048  0.11260586  0.07523869 -0.11008967

Largest  eigenvalues:
 [1] 76811195 72636970 69644068 67371222 66856558 65161956 62894580 62664372
 [9] 62385395 61542000

Smallest eigenvalues:
 [1]  0.56192331  0.52523709  0.47296856  0.44851631  0.42596966  0.38270716
 [7]  0.33885588  0.26087053 -0.03636955 -0.12855814

Largest  eigenvalues:
 [1] 79316301 72270075 69483623 68262428 65986177 63947730 63495571 62697827
 [9] 61949502 61577226

Smallest eigenvalues:
 [1]  0.5214146  0.4373091  0.4238392  0.4169651  0.3998511  0.3966686
 [7]  0.3821218  0.3608148  0.0233280 -2.1786051

Largest  eigenvalues:
 [1] 79051855 72459514 69001420 68565304 65829869 64081239 63605455 62321077
 [9] 61778802 60965545

Smallest eigenvalues:
 [1]  0.4238450  0.3850903  0.3806719  0.3628110  0.3259736  0.3090765
 [7]  0.2435713  0.2337977  0.1739058 -0.8904169

Largest  eigenvalues:
 [1] 79534900 72920690 69579358 68982976 66146969 64307659 64114858 62624933
 [9] 62103010 61323642

Smallest eigenvalues:
 [1]  0.4417435  0.4086389  0.4033034  0.2792020  0.2675175  0.2356599
 [7]  0.2091957  0.1563795  0.1335076 -0.2107113

Largest  eigenvalues:
 [1] 77184360 72696971 69159634 67501565 66896864 64890073 63539650 62803729
 [9] 62572832 62017221

Smallest eigenvalues:
 [1]  0.6624453  0.6303578  0.6196134  0.5564708  0.5177692  0.4249571
 [7]  0.3867329  0.1604138  0.1172345 -0.3902365

Largest  eigenvalues:
 [1] 77040916 72650381 68943252 66814516 66741803 64929454 62693032 62587944
 [9] 62011911 61268522

Smallest eigenvalues:
 [1]  0.45798793  0.45633148  0.37774876  0.37496777  0.37379365  0.30929490
 [7]  0.28899159  0.24799622  0.08377336 -1.11258283

Largest  eigenvalues:
 [1] 78900277 73629670 69700503 68582907 66982432 65361294 63576306 62950253
 [9] 62664983 61636778

Smallest eigenvalues:
 [1]  0.6305051  0.4387054  0.4292747  0.4200145  0.3931072  0.2590602
 [7]  0.2176671  0.2016262 -1.0875164 -1.0981275

Largest  eigenvalues:
 [1] 79705027 74033302 70491431 69229768 67045618 64924497 64247923 64116563
 [9] 62920660 62655285

Smallest eigenvalues:
 [1]  0.48787339  0.44564366  0.37283063  0.34702816  0.28345017  0.19014642
 [7]  0.11991021  0.10696743  0.07180644 -0.55819769

Largest  eigenvalues:
 [1] 78053710 73620655 70112814 67536802 67209654 65754262 63633056 63034544
 [9] 62891633 62083419

Smallest eigenvalues:
 [1]  0.5082068  0.4633876  0.4389805  0.4332896  0.3487568  0.3288734
 [7]  0.3228620  0.2322629  0.1382711 -0.3830972

Largest  eigenvalues:
 [1] 77648812 73413537 69064868 67527692 66770882 64888663 63106793 62497552
 [9] 62287741 61387221

Smallest eigenvalues:
 [1]  0.47420501  0.47380065  0.44095983  0.36480024  0.21259658  0.20787040
 [7]  0.17738861  0.15967101  0.01472700 -0.02465229

Largest  eigenvalues:
 [1] 75704414 73851577 69597385 67979518 66366150 65747858 63231503 63199302
 [9] 61770625 61616543

Smallest eigenvalues:
 [1]  0.53666510  0.53570212  0.50662900  0.43048219  0.35490832  0.32411047
 [7]  0.27259041  0.17336792  0.13486057 -0.04425019

Largest  eigenvalues:
 [1] 76495627 72438441 69061634 66776847 66702609 64915012 63071417 62293055
 [9] 62002643 61154225

Smallest eigenvalues:
 [1]  0.60835550  0.54886199  0.54013265  0.49849366  0.46269301  0.42102675
 [7]  0.38400003  0.25060351  0.11637300 -0.08452492

Largest  eigenvalues:
 [1] 76732649 73587269 68994652 67363126 67252504 65238214 62985757 62814645
 [9] 62194421 61700367

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	7.229381	0.846894	16.34333	0	2.066983	4.269703

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

HR ~ alt + n + steps + PM1

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- HR_fd
covariates <- list(altitude = altitude_fd, 
                   noise = noise_fd,
                   steps = steps_fd,
                   pollution = pollution1_fd)
path_plot <- 'figures/model_HR_alt_noise_steps_PM1_N200'
basis_params <- list(beta_0 = list(nbetabasis = 80, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     noise = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     steps = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     pollution = list(nbetabasis = 80, norder = 4, lambda = 1e3))

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, 
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 19.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Warning message in `^.fd`((outcome - yhatfd), 2):
"The maximum error exceeds the tolerance level."
Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 596 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Smallest eigenvalues:
 [1]  0.55687112  0.53569714  0.50426534  0.45079293  0.45007921  0.44912612
 [7]  0.37583368  0.11103673 -0.01388968 -0.18580991

Largest  eigenvalues:
 [1] 65128131 60301836 57485971 56558063 54933725 53240486 52519780 51979198
 [9] 51733698 50890918

Smallest eigenvalues:
 [1]  0.414116763  0.387579473  0.378678563  0.371295928  0.338374686
 [6]  0.313321104  0.309448258  0.141811756 -0.009306981 -0.171816604

Largest  eigenvalues:
 [1] 65341506 59947236 56968613 56278473 54917796 52984859 52496682 52442448
 [9] 51434141 51384566

Smallest eigenvalues:
 [1]  0.60644245  0.56121131  0.46256413  0.44032827  0.40697927  0.39444046
 [7]  0.34290363  0.26409122 -0.04566527 -0.05932885

Largest  eigenvalues:
 [1] 64108753 60186149 57621320 55732571 55114963 53453615 52195941 51772330
 [9] 51733262 51207729

Smallest eigenvalues:
 [1]  0.48783042  0.42729969  0.38378504  0.37758830  0.25824490  0.23982461
 [7]  0.18355483  0.12728013 -0.03011679 -1.07840210

Largest  eigenvalues:
 [1] 63422861 61109891 57765317 55934410 55395763 53999215 52790295 52485817
 [9] 51927114 51676842

Smallest eigenvalues:
 [1]   0.504267900   0.492722818   0.380579481   0.280285809   0.271283633
 [6]   0.245279758   0.195201247   0.003416523  -4.279198071 -21.485173449

Largest  eigenvalues:
 [1] 63416652 59658973 56681350 55377681 54971927 53668047 51955144 51631036
 [9] 51085226 50712610

Smallest eigenvalues:
 [1]   0.34925108   0.23008916   0.16079795   0.10828240   0.05681264
 [6]  -0.40148557  -0.69321495  -1.33484111  -3.94585907 -11.27616806

Largest  eigenvalues:
 [1] 65232586 59878722 57362752 56087718 54785082 53209734 52179158 52031762
 [9] 51479028 51186894

Smallest eigenvalues:
 [1]  0.440997342  0.412429781  0.342110671  0.304887786  0.296257523
 [6]  0.228656580  0.085959578  0.043035705  0.007661383 -1.736909097

Largest  eigenvalues:
 [1] 64426087 60693580 57322693 56107975 55716697 53909241 52800435 52075424
 [9] 51767150 51484123

Smallest eigenvalues:
 [1]  0.4501320  0.4365989  0.3779659  0.3536999  0.3382276  0.3345129
 [7]  0.2565055  0.1977048  0.1957531 -0.2255753

Largest  eigenvalues:
 [1] 65080896 61056860 57712812 56213345 55545358 53927770 53021143 52197053
 [9] 52103791 51815280

Smallest eigenvalues:
 [1]  0.47344605  0.36370195  0.33513862  0.32476445  0.32233421  0.31500958
 [7]  0.22047040 -0.09114835 -0.29602937 -1.21915111

Largest  eigenvalues:
 [1] 65352723 60563253 58131699 56782109 55181753 53954780 52680551 52488068
 [9] 52252395 51853720

Smallest eigenvalues:
 [1]  0.4894155  0.4355029  0.4241096  0.3421384  0.3161329  0.2843101
 [7]  0.2772782  0.2072198  0.1968273 -1.9607034

Largest  eigenvalues:
 [1] 65224104 60201985 57300745 56341612 55372381 53829466 52422928 52384924
 [9] 52252523 51382684

Smallest eigenvalues:
 [1]  0.40695360  0.36038905  0.29562369  0.29225967  0.24687806  0.18989229
 [7] -0.09093593 -1.11431836 -1.59614066 -3.75925425

Largest  eigenvalues:
 [1] 64938209 59906516 56584057 56532929 54557191 52752711 52532100 52226467
 [9] 51736859 51295520

Smallest eigenvalues:
 [1]  0.4959405  0.4659263  0.3764014  0.3534696  0.2896080  0.2246971
 [7]  0.2135307  0.2127684 -0.3342576 -0.4500901

Largest  eigenvalues:
 [1] 63963617 59864066 57282662 55877880 54742138 53232050 52281182 51838132
 [9] 51710608 51106206

Smallest eigenvalues:
 [1]  0.38111495  0.31020414  0.29966429  0.23838408  0.21337859  0.20601348
 [7]  0.08933640  0.07373036 -0.13328462 -4.00107803

Largest  eigenvalues:
 [1] 64574769 60469970 58072464 55696716 55386346 54136136 52779784 52164945
 [9] 51936786 51768649

Smallest eigenvalues:
 [1]  0.55800055  0.53222857  0.47901164  0.45327221  0.40111130  0.29574129
 [7]  0.28865336  0.21698533 -0.01837324 -0.08723218

Largest  eigenvalues:
 [1] 64763631 60091526 57289727 55859550 55257864 53031663 52245414 52011088
 [9] 51747918 51298262

Smallest eigenvalues:
 [1]   0.44555950   0.35855589   0.34644380   0.34254610   0.31386154
 [6]   0.30381877   0.16489995  -0.02806064  -0.62321588 -10.73542989

Largest  eigenvalues:
 [1] 65098445 60496720 57916559 56530651 55892263 54401973 52598333 52311894
 [9] 52193945 51413150

Smallest eigenvalues:
 [1]  0.42884363  0.41326134  0.35288602  0.31155545  0.30340781  0.28770810
 [7]  0.19576906  0.14889819  0.05327519 -0.39449121

Largest  eigenvalues:
 [1] 64308146 61317997 57541652 56335300 56265408 54379653 53956661 52376686
 [9] 52147255 52016770

Smallest eigenvalues:
 [1]  0.4977455  0.4652190  0.3768249  0.3524583  0.2692991  0.2287106
 [7]  0.2221596  0.1675569  0.1574845 -5.5116755

Largest  eigenvalues:
 [1] 63381151 59922187 57170124 55257217 54884088 53663842 52200231 52078116
 [9] 51400733 51059013

Smallest eigenvalues:
 [1]  0.4074224  0.3968622  0.3530963  0.2555267  0.2474881  0.2263166
 [7]  0.2006830  0.1595939 -1.6013676 -5.5512470

Largest  eigenvalues:
 [1] 64932740 59777837 57214617 56597890 54838139 53365041 52598440 52224892
 [9] 51547044 50832763

Smallest eigenvalues:
 [1]  0.5220158  0.4689755  0.4232338  0.2780233  0.2505749  0.2480184
 [7]  0.2270590  0.1189813 -0.6327994 -2.5670336

Largest  eigenvalues:
 [1] 65084496 59542378 56827508 56021559 54950602 53297069 52200860 52005525
 [9] 51899353 51268144

Smallest eigenvalues:
 [1]   0.2373609   0.2035308   0.1836030   0.1749543  -0.7485899  -1.2278123
 [7]  -3.4175991  -4.4915799  -4.5950425 -29.3420945

Largest  eigenvalues:
 [1] 66361761 59369288 57301796 56711763 54099806 53316077 52608739 51390608
 [9] 51170823 50586295

Smallest eigenvalues:
 [1]   0.50033964   0.45222152   0.40967222   0.32697790   0.10749068
 [6]   0.08785149  -0.80741622  -1.44425650  -1.64350508 -10.49660788

Largest  eigenvalues:
 [1] 63411882 60145516 56848071 55306598 55038747 53516827 52047792 51431854
 [9] 50892719 50584103

Smallest eigenvalues:
 [1]  0.31150923  0.24619425 -0.03639436 -0.13244920 -0.14563683 -0.34485592
 [7] -0.82018803 -0.96012485 -1.31702944 -2.22271195

Largest  eigenvalues:
 [1] 66582209 60594525 57924544 57325979 55106941 53443545 53250426 52996640
 [9] 51720950 51555079

Smallest eigenvalues:
 [1]  0.42886063  0.31631996  0.23713970  0.17590678  0.17500220  0.05010624
 [7]  0.04544901 -0.01995707 -0.02289414 -3.01281466

Largest  eigenvalues:
 [1] 65822252 60558361 57030909 56817179 55176836 53528394 52780736 52295592
 [9] 52069992 51326101

Smallest eigenvalues:
 [1]  0.447146989  0.324025542  0.230563255  0.184923170  0.143353772
 [6]  0.022862673  0.008039507 -2.121552625 -4.611530489 -6.806283202

Largest  eigenvalues:
 [1] 63486616 59936176 57126829 55413115 54947221 53841226 52468866 51859666
 [9] 51046936 50944832

Smallest eigenvalues:
 [1]  0.5142570  0.4758353  0.4264181  0.3762573  0.3063389  0.2692648
 [7]  0.2392225  0.2137642  0.1945631 -0.6363635

Largest  eigenvalues:
 [1] 64350185 61545702 58157471 56681847 55718662 54089246 52847029 52583822
 [9] 52530699 51844875

Smallest eigenvalues:
 [1]  0.4374744  0.3992590  0.3849865  0.3492341  0.3307163  0.2983505
 [7]  0.2186151  0.2003982  0.1124304 -0.7832771

Largest  eigenvalues:
 [1] 64890640 61154660 58079071 56477370 56474882 54768964 53110028 52649256
 [9] 52373044 51770007

Smallest eigenvalues:
 [1]  0.56421538  0.55752709  0.55664422  0.52688970  0.47180185  0.45960272
 [7]  0.42816317  0.24870440  0.09815254 -0.19587481

Largest  eigenvalues:
 [1] 65254606 60332741 57564846 56789798 54984187 53174178 52694222 51836743
 [9] 51564777 50801067

Smallest eigenvalues:
 [1]  0.4205212  0.3674697  0.3267711  0.3218011  0.2654311  0.2497190
 [7]  0.2466122  0.1998852 -0.7425969 -0.7772123

Largest  eigenvalues:
 [1] 64812466 60273890 57064084 55990185 54948271 53392165 52032082 51987480
 [9] 51623529 50953563

Smallest eigenvalues:
 [1]   0.35707207   0.32921013   0.27030210   0.26479053  -0.01234182
 [6]  -0.34181885  -3.10642187  -3.94843410  -9.80614986 -20.53973229

Largest  eigenvalues:
 [1] 63297274 60393515 57209411 55756904 54896577 53166682 51970749 51817363
 [9] 51740014 50828502

Smallest eigenvalues:
 [1]  0.5175133  0.4495037  0.4493913  0.4063343  0.3834703  0.3451151
 [7]  0.2864278  0.2171597  0.2043953 -0.9392579

Largest  eigenvalues:
 [1] 63962432 59816902 57302680 55249458 54486613 53023524 51980301 51414788
 [9] 51170903 51131405

Smallest eigenvalues:
 [1]  0.50530142  0.41933493  0.40986760  0.27762105  0.25989676  0.24079429
 [7]  0.15032521  0.02589387 -0.56884545 -4.70105351

Largest  eigenvalues:
 [1] 65182516 59415329 56789268 55701408 54775762 53196347 51916299 51662484
 [9] 51476359 50698181

Smallest eigenvalues:
 [1]   0.32356859   0.27967519   0.24517137   0.14298235   0.12618440
 [6]  -0.04201492  -4.11753473  -7.15476213 -14.51420748 -23.34458119

Largest  eigenvalues:
 [1] 65820940 60471866 57911199 56791327 55161976 53472017 53040179 52805807
 [9] 52048815 51956339

Smallest eigenvalues:
 [1]  0.37316140  0.36300033  0.25392025  0.25376290  0.25240567  0.20462237
 [7]  0.03507761 -0.73317526 -1.04810045 -1.89526955

Largest  eigenvalues:
 [1] 63260942 60530009 57808460 55825974 55100184 54463211 52809452 52497301
 [9] 51469800 51179138

Smallest eigenvalues:
 [1]  0.29226497  0.25172135  0.22835484  0.17392128  0.07286766 -0.28217109
 [7] -0.41373482 -0.83910045 -0.85686019 -1.20358330

Largest  eigenvalues:
 [1] 65044269 59895276 57226892 56088957 55088512 53265286 52149720 52113740
 [9] 51545297 51205620

Smallest eigenvalues:
 [1]  0.4478490  0.4189495  0.3725930  0.3474046  0.3211359  0.2678841
 [7]  0.2567332  0.1185031  0.1022033 -0.6812989

Largest  eigenvalues:
 [1] 63606247 59186747 57049402 55599175 54504143 52953180 51656158 51552367
 [9] 51481831 50633547

Smallest eigenvalues:
 [1]   0.366817117   0.308699385   0.302670629   0.103656940  -0.008364085
 [6]  -0.054458435  -0.241645060  -1.013964921 -27.473403519 -53.823053513

Largest  eigenvalues:
 [1] 61191986 59094498 56176233 54883639 54187020 52970589 51843654 50897582
 [9] 50181656 49987469

Smallest eigenvalues:
 [1]  0.37929030  0.28229472  0.27060161  0.23332496  0.13353378  0.01769273
 [7] -0.04359874 -0.52088314 -3.14103586 -3.45004325

Largest  eigenvalues:
 [1] 64928846 61126488 58270512 55700657 55616981 54281038 52518675 52031029
 [9] 51731769 51485685

Smallest eigenvalues:
 [1]  0.44207729  0.39741612  0.39478884  0.31490376  0.27290942  0.18846113
 [7]  0.03118364 -0.37961401 -0.62435106 -7.57848891

Largest  eigenvalues:
 [1] 63037909 60635596 57433418 55560252 55485423 54186659 52550081 52127120
 [9] 51418896 51024559

Smallest eigenvalues:
 [1]  0.3757570  0.3734703  0.3075687  0.2105842  0.1971154  0.1915167
 [7]  0.1705802  0.1499399  0.1365020 -0.3246430

Largest  eigenvalues:
 [1] 63090313 60402108 57302651 55505550 55259369 53643226 52820723 51995209
 [9] 51644508 51427010

Smallest eigenvalues:
 [1]  0.5004582363  0.4677769404  0.4175565730  0.3934018498  0.3446933755
 [6]  0.3339203213  0.3123174852  0.1966392916 -0.0006498299 -0.1149381748

Largest  eigenvalues:
 [1] 64910078 61114409 57800651 56693335 55662039 54066405 52832887 52658092
 [9] 52430728 51864759

Smallest eigenvalues:
 [1]  0.42893636  0.42508809  0.28301472  0.26806698  0.26663556  0.15846928
 [7]  0.04607751 -0.17602037 -0.61911520 -0.69753981

Largest  eigenvalues:
 [1] 62456339 59522829 56222054 55441612 54462673 52726942 51877080 51563276
 [9] 51051773 50272218

Smallest eigenvalues:
 [1]  0.4894173  0.4633274  0.4321226  0.3420420  0.3268126  0.3031480
 [7]  0.2112384  0.1694344  0.1211073 -0.4119919

Largest  eigenvalues:
 [1] 64663687 60013593 57632066 56035560 55360168 53925969 52236725 52167398
 [9] 51994886 51504129

Smallest eigenvalues:
 [1]  0.5727118  0.4790871  0.4767965  0.3858702  0.3735021  0.3611180
 [7]  0.3558342  0.3087649  0.2924612 -0.7861576

Largest  eigenvalues:
 [1] 64583895 60680502 57781192 56258924 55770917 54208541 52430470 52244122
 [9] 52232199 51350791

Smallest eigenvalues:
 [1]  0.29338469  0.27420392  0.13254373  0.09721057  0.04793512  0.02019989
 [7] -0.02937095 -0.81876192 -1.06515388 -3.32199415

Largest  eigenvalues:
 [1] 64571381 60191796 56704498 56329417 55352128 53351106 52584919 52297363
 [9] 52247966 51266410

Smallest eigenvalues:
 [1]  0.38422846  0.29566629  0.29526793  0.21934122  0.17661412  0.15617584
 [7]  0.11950021 -0.02736394 -1.21608458 -6.66204627

Largest  eigenvalues:
 [1] 64096711 58864039 56525972 55883897 54040246 52311477 51805215 51308204
 [9] 51082181 50019992

Smallest eigenvalues:
 [1]  0.4306284  0.4281921  0.4254483  0.4215927  0.3606504  0.2962655
 [7]  0.2712279  0.2479106  0.2145853 -0.1993490

Largest  eigenvalues:
 [1] 61898313 59884704 56945231 55130839 54731281 53531303 52169263 51525367
 [9] 50789389 50582759

Smallest eigenvalues:
 [1]  0.4200911  0.4082382  0.3926899  0.3717099  0.2662142  0.2190207
 [7]  0.1680343  0.1418466 -0.9401058 -3.7003649

Largest  eigenvalues:
 [1] 66559080 60630818 57455306 56486817 55395057 53745658 52602166 52477638
 [9] 51847353 51721052

Smallest eigenvalues:
 [1]  0.3885635  0.3335561  0.3165416  0.3067927  0.2583692  0.2180735
 [7]  0.1945838  0.1756398 -0.5093009 -0.5216461

Largest  eigenvalues:
 [1] 64637448 60799634 58274546 55843795 55666532 54296734 52808288 52501305
 [9] 51839164 51584826

Smallest eigenvalues:
 [1]  0.62921028  0.61213362  0.55685992  0.55663502  0.48811402  0.42769164
 [7]  0.37711107  0.24052497  0.08135995 -0.30148987

Largest  eigenvalues:
 [1] 65307649 60424549 57535552 56476860 54908540 53127783 52600814 52184804
 [9] 51353414 50953242

Smallest eigenvalues:
 [1]  0.4940349  0.4148464  0.4017195  0.3607420  0.3544056  0.3437997
 [7]  0.3300890  0.2178246  0.1822510 -0.7168477

Largest  eigenvalues:
 [1] 63237064 59881546 57025049 55212974 55055675 53431689 51760286 51728149
 [9] 51207105 50956947

Smallest eigenvalues:
 [1]  0.4339095  0.3762701  0.3644910  0.3296540  0.3066297  0.2596743
 [7]  0.2540064  0.2046422 -3.5255256 -6.1202354

Largest  eigenvalues:
 [1] 65307576 60002497 57237961 57194643 54581906 53149487 52914004 52078957
 [9] 51958575 51138392

Smallest eigenvalues:
 [1]  0.5409622  0.4566514  0.4437517  0.4334861  0.4111928  0.2600885
 [7]  0.2229195  0.1329756  0.0141318 -1.2802341

Largest  eigenvalues:
 [1] 65138502 61041128 58122737 56844557 55408092 53466789 53063749 52713232
 [9] 51888007 51770388

Smallest eigenvalues:
 [1]  0.529785916  0.523294080  0.512311540  0.448145987  0.386795870
 [6]  0.352477961  0.333146952  0.263928439  0.253707046 -0.008032498

Largest  eigenvalues:
 [1] 64300050 60671379 57693389 56130887 55818194 54529858 52926283 52112752
 [9] 52003261 51453048

Smallest eigenvalues:
 [1]  0.43807672  0.36899806  0.34642450  0.26440199  0.24571534  0.12937061
 [7]  0.01600913 -0.35984653 -0.82246332 -1.44659688

Largest  eigenvalues:
 [1] 64922702 60638583 58137692 56473698 55134241 53563983 52770642 52529513
 [9] 52142465 51851146

Smallest eigenvalues:
 [1]  0.5464070  0.5408620  0.4847972  0.4526939  0.3574238  0.3560562
 [7]  0.3387780  0.2565086  0.1040409 -0.4622915

Largest  eigenvalues:
 [1] 65285620 59864009 56941939 56453727 54809409 52833551 52428444 52106885
 [9] 51591950 51179410

Smallest eigenvalues:
 [1]  0.5795934  0.5231061  0.4924282  0.4198396  0.3977189  0.3756215
 [7]  0.3230170  0.3163818  0.2793956 -0.1175031

Largest  eigenvalues:
 [1] 64237753 60497364 57646620 55903064 55433126 53721747 51793706 51755625
 [9] 51620744 50719989

Smallest eigenvalues:
 [1]  0.4442047  0.4383072  0.3958422  0.3793990  0.3267505  0.2727223
 [7]  0.2713087  0.1411989 -0.7821975 -2.1247937

Largest  eigenvalues:
 [1] 62786351 60124673 56979890 55306766 54960093 53261006 51987015 51973627
 [9] 51098465 50979871

Smallest eigenvalues:
 [1]  0.52077886  0.49876598  0.48560069  0.41178838  0.37660218  0.33909050
 [7]  0.25761768  0.18956798  0.09143721 -0.12658351

Largest  eigenvalues:
 [1] 62200625 59586788 56697758 55295604 54399359 53454450 51729831 51645731
 [9] 50513054 50345127

Smallest eigenvalues:
 [1]  0.4833877  0.4487874  0.3642969  0.3582604  0.3234725  0.2850042
 [7]  0.2837291  0.1549455  0.1166377 -1.6427620

Largest  eigenvalues:
 [1] 63570500 59615578 56824923 55350516 55104913 53428982 52434907 51888519
 [9] 51501994 51273157

Smallest eigenvalues:
 [1]  0.4610588  0.4476073  0.4152041  0.2880318  0.2828920  0.2346105
 [7]  0.2121308 -0.2061981 -0.8369581 -5.1849205

Largest  eigenvalues:
 [1] 65592710 60421501 57753963 56935015 54685234 53285151 53002233 52118460
 [9] 51496817 51157625

Smallest eigenvalues:
 [1]  0.4749086  0.4583713  0.4416734  0.4012094  0.2871016  0.2540906
 [7]  0.2431543  0.2330525  0.2182223 -1.0845595

Largest  eigenvalues:
 [1] 64313503 60130081 57156629 56088696 55145242 53619070 52484156 52017336
 [9] 51992416 51510113

Smallest eigenvalues:
 [1]  0.40661740  0.39977450  0.35001365  0.28207737  0.26227096  0.23448724
 [7]  0.21981857  0.21588404  0.08300476 -5.32097231

Largest  eigenvalues:
 [1] 64882170 61110112 58412171 56173023 55855630 54455208 52515092 52370432
 [9] 52076450 51603479

Smallest eigenvalues:
 [1]  0.4028769  0.3611067  0.3268382  0.2607294  0.2589110  0.1960836
 [7]  0.1926653  0.1755897  0.1153372 -2.1516945

Largest  eigenvalues:
 [1] 65543612 60537830 57751143 56637878 55279459 53752519 52545734 52220830
 [9] 52047836 51312755

Smallest eigenvalues:
 [1]  0.496872340  0.314472066  0.303361469  0.299760573  0.223741512
 [6]  0.180105937 -0.009718017 -0.233019380 -1.574875006 -1.806591585

Largest  eigenvalues:
 [1] 62791170 59691242 56940123 55314304 54901898 53682569 52143773 52116159
 [9] 51077011 50897653

Smallest eigenvalues:
 [1]   0.40291080   0.40079374   0.34784687   0.29734893   0.20029571
 [6]   0.13859035   0.08521309  -0.02655003  -1.10552199 -17.82229237

Largest  eigenvalues:
 [1] 64991724 59869275 56727952 56509970 55008326 53378814 52416319 51948472
 [9] 51719625 51019982

Smallest eigenvalues:
 [1]  0.47215332  0.43549486  0.42841373  0.34674341  0.32663521  0.31044831
 [7]  0.29070554  0.26323988  0.15073677 -0.02575701

Largest  eigenvalues:
 [1] 64615516 60407232 57838657 56351142 55284822 53969586 52292664 52224104
 [9] 52047168 51225406

Smallest eigenvalues:
 [1]  0.5690613  0.5205353  0.4330237  0.3823208  0.3110412  0.2667287
 [7]  0.2504866  0.2403642  0.2242317 -1.5732473

Largest  eigenvalues:
 [1] 65510103 60931571 58035151 56486548 55663633 54159916 52696003 52589097
 [9] 52078788 51592138

Smallest eigenvalues:
 [1]  0.3825955193  0.3465771545  0.3266057443  0.2917143789  0.2804264278
 [6]  0.2161354287  0.1955692611  0.1806341677  0.0001922657 -1.9903300286

Largest  eigenvalues:
 [1] 65877671 59820381 57162904 56583631 54712230 53427067 52631425 51977859
 [9] 51857543 51158048

Smallest eigenvalues:
 [1]  0.4631269  0.4420274  0.4352148  0.4124177  0.3447332  0.2811365
 [7]  0.2540594  0.2386270  0.2346326 -0.3102671

Largest  eigenvalues:
 [1] 65459730 60789418 58025229 56682454 56094863 54497776 52666601 52422671
 [9] 52350156 51419882

Smallest eigenvalues:
 [1]  0.55595527  0.42255741  0.38889732  0.37790478  0.36312972  0.33262057
 [7]  0.29156613  0.22392322 -0.08571046 -1.89131944

Largest  eigenvalues:
 [1] 66402625 60769644 58049245 57203154 55161122 53588053 53333340 52393701
 [9] 51952523 51588469

Smallest eigenvalues:
 [1]   0.32334565   0.31470741   0.30558009   0.25747671   0.22075442
 [6]   0.16445292   0.10399909   0.08779512  -2.68437498 -12.41718633

Largest  eigenvalues:
 [1] 63950819 60559943 57214921 55841486 55799538 54107813 52962771 52257269
 [9] 52009351 51747433

Smallest eigenvalues:
 [1]  0.4627924  0.4515449  0.3483190  0.3441082  0.3022074  0.1902092
 [7]  0.1689880  0.1487121 -0.3972390 -1.0250360

Largest  eigenvalues:
 [1] 64986232 59629971 57078285 56515258 54264181 52742541 52502388 51462965
 [9] 51240974 50412621

Smallest eigenvalues:
 [1]  0.47440064  0.45541880  0.36783967  0.32543219  0.28070597  0.25383126
 [7]  0.03064683 -0.10842933 -0.21209974 -0.61047971

Largest  eigenvalues:
 [1] 64645633 60839636 58195016 56341965 55508687 54048645 53003425 52335633
 [9] 52271694 52153192

Smallest eigenvalues:
 [1]  0.52860711  0.50602432  0.44910439  0.38096836  0.36973862  0.36913605
 [7]  0.33458888  0.25560171  0.03730179 -0.17843664

Largest  eigenvalues:
 [1] 65333169 60250177 57689418 56398985 55541478 53517456 52659321 52163232
 [9] 51793067 51127497

Smallest eigenvalues:
 [1]  0.4684539  0.3580603  0.3500467  0.3371653  0.2599890  0.2316874
 [7]  0.1971039  0.1581134  0.1546257 -0.3412086

Largest  eigenvalues:
 [1] 63708269 61347639 57775485 56367958 55296870 53851974 52846802 52281484
 [9] 52256330 51908839

Smallest eigenvalues:
 [1]  0.4085848  0.3696719  0.3610226  0.3368879  0.3106543  0.3027610
 [7]  0.2210889  0.1492056 -1.0504551 -5.6213128

Largest  eigenvalues:
 [1] 66336823 60904467 57303363 57290213 55683677 53842934 53303311 52475593
 [9] 52271664 51532338

Smallest eigenvalues:
 [1]  0.4341795  0.4288170  0.3465456  0.3351632  0.2858962  0.2819554
 [7] -0.3915791 -1.4953083 -2.0059460 -3.1763198

Largest  eigenvalues:
 [1] 64445338 59740033 56749525 56383904 54603763 52822963 52156069 52119598
 [9] 51610916 51150374

Smallest eigenvalues:
 [1]  0.47414499  0.39191008  0.31645965  0.30515301  0.22465847  0.20404176
 [7]  0.15944242  0.15356296 -0.06557322 -0.57799704

Largest  eigenvalues:
 [1] 66287677 60150487 57975260 55944272 54914106 53113036 52403025 51771474
 [9] 51334794 51009736

Smallest eigenvalues:
 [1]  0.52262947  0.49456098  0.45228167  0.36379259  0.26541493  0.18972028
 [7]  0.17823375  0.16369692  0.06868716 -1.46927422

Largest  eigenvalues:
 [1] 65567238 61305572 58126318 56905750 55951857 54340055 53532821 52898953
 [9] 52433060 52141495

Smallest eigenvalues:
 [1]   0.359491317   0.316725401   0.303188397   0.087395327   0.084915891
 [6]   0.073125534  -0.009058002  -0.090305707  -3.404361370 -23.124767119

Largest  eigenvalues:
 [1] 63575839 59845969 57026909 55610680 54863587 53258768 52019940 51796018
 [9] 51581616 51018487

Smallest eigenvalues:
 [1]  0.58847563  0.58439112  0.48304140  0.43891327  0.34503924  0.32082815
 [7]  0.28543576  0.21930659  0.19753695 -0.01494624

Largest  eigenvalues:
 [1] 63410234 60651897 57238111 55887118 54964182 53962264 52007807 51828169
 [9] 51076926 50786357

Smallest eigenvalues:
 [1]  0.4829039  0.4411541  0.4402740  0.3638287  0.2803197  0.2758135
 [7] -0.2509864 -3.2133647 -4.5349836 -9.8932472

Largest  eigenvalues:
 [1] 65517617 60219811 57731374 56602001 54950426 53345087 52431123 52367019
 [9] 52007936 51595635

Smallest eigenvalues:
 [1]  0.49022287  0.44842297  0.42023439  0.41845079  0.33591054  0.26391905
 [7]  0.19665207 -0.06565401 -0.16904697 -0.64212192

Largest  eigenvalues:
 [1] 65936136 61016526 58335240 56706049 55716509 54046302 53107029 52657558
 [9] 52526708 52260459

Smallest eigenvalues:
 [1]  0.5091731  0.4988933  0.4635476  0.3837046  0.3553260  0.2483208
 [7]  0.1870440  0.1504206 -0.8252498 -6.4720725

Largest  eigenvalues:
 [1] 64682522 59691224 56578733 56293903 54501255 52768861 52348300 51584484
 [9] 51134778 50474530

Smallest eigenvalues:
 [1]  0.45716376  0.44675999  0.44032831  0.33661926  0.28228493  0.26023967
 [7]  0.22095369  0.21544754  0.09446898 -0.55000765

Largest  eigenvalues:
 [1] 62852535 59611108 56719973 54907857 54704344 53225484 51894505 51286076
 [9] 50867526 50479107

Smallest eigenvalues:
 [1]  0.5566516  0.5497998  0.5371614  0.3926779  0.3920331  0.3496225
 [7]  0.2891229  0.2354058  0.2290273 -0.1327787

Largest  eigenvalues:
 [1] 64026025 60334355 57531186 55892878 55403885 53637280 52173797 52113138
 [9] 52020071 51169166

Smallest eigenvalues:
 [1]   0.208202378   0.182164133   0.144571504   0.142474170   0.005658326
 [6]  -0.169415653  -0.271356775  -1.580269859 -13.101889962 -78.872866181

Largest  eigenvalues:
 [1] 66394273 60468445 57821383 56866718 55128835 53975427 52694053 52554097
 [9] 52415603 51878196

Smallest eigenvalues:
 [1]  0.47092887  0.39673917  0.37374886  0.30459197  0.30057850  0.20609619
 [7]  0.16883538  0.05347199 -0.18556661 -0.52515644

Largest  eigenvalues:
 [1] 66267447 60012662 57440091 56934727 54716480 53102366 52919398 52519317
 [9] 51716136 51642043

Smallest eigenvalues:
 [1]  0.4870925  0.4201529  0.3524366  0.2707847  0.2662001  0.2362070
 [7]  0.1981400  0.1886403 -0.2972681 -0.8451265

Largest  eigenvalues:
 [1] 64679471 60412348 57557884 56391465 55367023 53888970 52440969 52436978
 [9] 52241598 51370126

Smallest eigenvalues:
 [1]  0.47265321  0.43905638  0.40816087  0.37583259  0.35613690  0.30507054
 [7]  0.29656979  0.26183338  0.07229652 -8.55325326

Largest  eigenvalues:
 [1] 64839410 59716434 57199934 55814648 54969113 53564409 51983255 51906474
 [9] 51384200 50492619

Smallest eigenvalues:
 [1]  0.36979219  0.34686253  0.34555022  0.32810270  0.24652984  0.23777955
 [7]  0.21258142  0.18888686  0.09415171 -0.12239939

Largest  eigenvalues:
 [1] 64259980 60668607 57842826 56267074 55672748 54229906 52488012 52195034
 [9] 52095942 51540803

Smallest eigenvalues:
 [1]  0.39907536  0.31226478  0.30257437  0.26679892  0.24798533  0.17270903
 [7]  0.15577954  0.06888145  0.05246053 -4.82363239

Largest  eigenvalues:
 [1] 64351251 60520554 57336334 55747545 55538185 53856151 52942348 52023513
 [9] 51955174 51699811

Smallest eigenvalues:
 [1]   0.3474004   0.2910447   0.2809725   0.2579128   0.2362527   0.2082751
 [7]   0.1354125  -0.4076301  -3.9098781 -31.9134298

Largest  eigenvalues:
 [1] 62694985 60815276 57242799 55497258 55429043 53740710 52322965 52236456
 [9] 51405304 51218747

Smallest eigenvalues:
 [1]  0.5364960  0.4951196  0.3947891  0.3669663  0.2562212  0.2537648
 [7]  0.2444996  0.2042522 -0.6174763 -3.8959178

Largest  eigenvalues:
 [1] 62875462 60230210 57137033 55834864 54868885 54173293 52496332 52259350
 [9] 51130352 50899563

Smallest eigenvalues:
 [1]  0.4465246  0.4187393  0.4138390  0.3424988  0.3028660  0.2348833
 [7]  0.2290926  0.1843967 -0.4643544 -1.2229795

Largest  eigenvalues:
 [1] 64878431 60316363 57878499 56217490 55196172 53368590 52499838 52204281
 [9] 52132144 51655414

Smallest eigenvalues:
 [1]  0.5550184  0.4925687  0.4398451  0.3675941  0.3393733  0.3300166
 [7]  0.3124096  0.2532578  0.2167142 -1.4547489

Largest  eigenvalues:
 [1] 65295323 61190271 58376214 56778936 56205796 54762466 53112358 52765226
 [9] 52708031 52165363

Smallest eigenvalues:
 [1]  0.5487436  0.4834131  0.3658915  0.3560428  0.2742899  0.2410628
 [7]  0.2080247  0.1824926  0.1688730 -0.3472891

Largest  eigenvalues:
 [1] 65570937 60577458 57523745 56275345 55179465 53432642 52427320 52371246
 [9] 51966847 51391441

Smallest eigenvalues:
 [1]  0.36263043  0.26285390  0.21467178  0.20066332  0.17755906  0.11234721
 [7] -0.03433613 -0.24992273 -0.76688587 -1.93874694

Largest  eigenvalues:
 [1] 63100795 59980154 57178604 55229096 54794367 53171186 52243574 51402622
 [9] 51215979 50989546

Smallest eigenvalues:
 [1]  0.5854559  0.5338526  0.4780691  0.4113695  0.3800489  0.3351957
 [7]  0.3149091  0.2626591  0.1262375 -0.2925665

Largest  eigenvalues:
 [1] 65093749 60060161 57003507 56282110 54911051 53245152 52235738 51565875
 [9] 51484388 50738895

Smallest eigenvalues:
 [1]  0.54856036  0.44652671  0.42205664  0.40911038  0.39664975  0.35873767
 [7]  0.24180036  0.18233704 -0.01858205 -0.03243652

Largest  eigenvalues:
 [1] 61789060 59195945 56835602 54908764 54372150 53144543 51495767 51149699
 [9] 50454339 50143290

Smallest eigenvalues:
 [1]  0.5048170  0.4690351  0.3860628  0.3852930  0.3769440  0.3563368
 [7]  0.3276463  0.2590424  0.1667146 -0.3130165

Largest  eigenvalues:
 [1] 63581401 59735741 57253250 55046782 54981326 53467902 51899533 51604730
 [9] 51176779 51034629

Smallest eigenvalues:
 [1]  0.3991672  0.2842230  0.2575741  0.2406207  0.1655588  0.1486110
 [7] -0.3444484 -1.9012484 -2.3645298 -2.9585352

Largest  eigenvalues:
 [1] 65373108 60326961 58421759 55649203 55572464 54483705 52924234 52749572
 [9] 51907739 51611065

Smallest eigenvalues:
 [1]  0.4044360  0.3700122  0.3380100  0.2570864  0.2236595  0.2106244
 [7]  0.1774052  0.1771675 -0.1182595 -1.3200906

Largest  eigenvalues:
 [1] 63751087 59379090 57384541 55940798 54228980 52896185 51845470 51772902
 [9] 51440966 50758635

Smallest eigenvalues:
 [1]   0.4240648   0.4154436   0.3843697   0.3617769   0.3047146   0.3037085
 [7]   0.2413956  -0.2370802  -0.9400032 -16.8047873

Largest  eigenvalues:
 [1] 63141117 59976841 57069004 55410494 55046130 53513199 51849498 51615723
 [9] 51341837 50760183

Smallest eigenvalues:
 [1]  0.41079383  0.40004016  0.39186619  0.23227558  0.21161560  0.19731791
 [7]  0.16821605  0.04787791 -0.68951299 -1.15706176

Largest  eigenvalues:
 [1] 64113510 59758975 57134690 56030406 54769663 53263617 52140142 51878629
 [9] 51855517 50988740

Smallest eigenvalues:
 [1]  0.51208175  0.46359693  0.42486102  0.37572087  0.30933654  0.28308623
 [7]  0.27534646  0.25562913 -0.01522618 -0.13450978

Largest  eigenvalues:
 [1] 63243761 59677873 57194006 54835868 54688477 53195996 51913301 51409588
 [9] 50953990 50600816

Smallest eigenvalues:
 [1]  0.45935445  0.34154354  0.29565289  0.25858665  0.24081906  0.14932325
 [7]  0.08765192 -0.71586374 -0.78576505 -3.58276166

Largest  eigenvalues:
 [1] 61512218 59879142 57012750 56100549 54153126 54005372 52779347 51680797
 [9] 50796224 50727733

Smallest eigenvalues:
 [1]  0.4774591  0.4001589  0.3821787  0.3495943  0.3159623  0.2980202
 [7]  0.2680286  0.1940331 -0.1651045 -0.9206551

Largest  eigenvalues:
 [1] 62829746 59858801 57030816 55370418 54883636 53248419 51976502 51767486
 [9] 51215671 50834441

Smallest eigenvalues:
 [1]  0.5364089  0.4862082  0.4772586  0.4040991  0.3261372  0.2856991
 [7]  0.2835674  0.1768774  0.1304353 -0.3145844

Largest  eigenvalues:
 [1] 65017426 60620211 57428741 55756017 55643786 53825153 52595311 52134562
 [9] 51975601 51520368

Smallest eigenvalues:
 [1]   0.4434064   0.4395518   0.3525506   0.3152943   0.2793821   0.2435580
 [7]   0.2241346   0.1813491  -0.1195115 -15.8819635

Largest  eigenvalues:
 [1] 63780023 60756843 57376258 55969683 55884591 54167061 52593769 52061899
 [9] 51930395 51541088

Smallest eigenvalues:
 [1]  0.49775391  0.45683374  0.42963565  0.42254716  0.39353727  0.36640863
 [7]  0.26354221  0.23603533  0.03156872 -0.04335921

Largest  eigenvalues:
 [1] 61901980 60916646 57579560 55714668 55083593 53938743 52196613 52184141
 [9] 51310338 51048254

Smallest eigenvalues:
 [1]  0.56159057  0.53913405  0.51424397  0.44650607  0.35016410  0.27937198
 [7]  0.24378028  0.20893485  0.16579020 -0.06604083

Largest  eigenvalues:
 [1] 65844376 60113973 57449022 56172186 54977998 53108764 52469601 51776433
 [9] 51695232 50984391

Smallest eigenvalues:
 [1]  0.329482750  0.299406788  0.292092786  0.276973612  0.272808284
 [6]  0.270974185  0.115381683  0.009487049 -0.549922516 -0.705155022

Largest  eigenvalues:
 [1] 64685045 61441070 58361160 56656261 55906751 54067509 53827662 52889651
 [9] 52301327 52142906

Smallest eigenvalues:
 [1]  0.4926276  0.4252582  0.3247247  0.3203620  0.2782666  0.2696032
 [7]  0.2059279 -0.4013662 -1.6710334 -1.9346226

Largest  eigenvalues:
 [1] 67351440 60233791 57926855 57545911 55044970 53955029 53417343 52441801
 [9] 51689901 51393581

Smallest eigenvalues:
 [1]  0.5028066  0.4598284  0.3406696  0.3371947  0.2921826  0.2635888
 [7]  0.1489174 -0.2291181 -0.6490476 -2.8156941

Largest  eigenvalues:
 [1] 64957544 59830827 56993061 55519536 54713315 53056823 52019789 51701506
 [9] 51350618 51186215

Smallest eigenvalues:
 [1]  0.43220810  0.38636236  0.36793845  0.29676587  0.24093444  0.17698063
 [7]  0.17273032  0.08978660 -0.05412637 -0.74001572

Largest  eigenvalues:
 [1] 61429446 59978796 57185861 54760050 54529848 53254737 51503812 51435700
 [9] 50664543 50507936

Smallest eigenvalues:
 [1]  0.5244092  0.5058885  0.4621850  0.3854107  0.2503368  0.2023883
 [7]  0.1925894  0.1883249  0.1255680 -0.1032316

Largest  eigenvalues:
 [1] 66179908 60869187 58040440 57176096 55447147 53294012 53278424 52891039
 [9] 52145034 52021875

Smallest eigenvalues:
 [1]  0.5202558  0.4570686  0.4249764  0.4122457  0.4006000  0.2844237
 [7]  0.1264753  0.1146851 -0.6090154 -2.8584040

Largest  eigenvalues:
 [1] 65358649 60845581 57503041 57189387 55305721 53715620 52926826 52717604
 [9] 52390730 51473703

Smallest eigenvalues:
 [1]  0.40069336  0.36172398  0.29709438  0.24853261  0.23074548  0.13644957
 [7] -0.02623012 -0.03430969 -1.50780229 -4.77644863

Largest  eigenvalues:
 [1] 65383779 61081726 57456667 56280965 56067542 54173237 53113389 52592965
 [9] 52261687 51724421

Smallest eigenvalues:
 [1]  0.5783467  0.5492639  0.4903990  0.4173796  0.3279668  0.3085591
 [7]  0.2959652  0.2462573  0.1167170 -2.4047407

Largest  eigenvalues:
 [1] 64185674 60268420 57399950 56091047 55435454 53568602 52119494 52017087
 [9] 51834072 50856751

Smallest eigenvalues:
 [1]  0.404408027  0.361504118  0.322585431  0.316639368  0.256264481
 [6]  0.241559245  0.233504892  0.001168221 -0.218110778 -2.958904329

Largest  eigenvalues:
 [1] 63701866 59692499 57263466 55558321 55446519 53794299 51962390 51444093
 [9] 51404963 50602460

Smallest eigenvalues:
 [1]   0.14141059   0.13883528  -0.01223263  -0.06992098  -0.27988867
 [6]  -0.36051405  -1.96096052  -2.46839828 -11.83413634 -43.81338733

Largest  eigenvalues:
 [1] 62199161 58971650 56477483 54873447 54773226 53060590 52022000 51548419
 [9] 50768286 50530362

Smallest eigenvalues:
 [1]  0.5596169  0.5129533  0.4517147  0.4178378  0.4166618  0.3759475
 [7]  0.2478439  0.1605925  0.1566739 -0.8638321

Largest  eigenvalues:
 [1] 64035523 60093898 56724116 55475089 55351109 53642206 52267672 51508171
 [9] 51468208 50642928

Smallest eigenvalues:
 [1]  0.3672976  0.3582742  0.3268389  0.3168456  0.2481369  0.1948450
 [7]  0.1798662  0.1540865 -0.1478091 -1.9687731

Largest  eigenvalues:
 [1] 64993133 59232486 56750690 56435837 54647901 53084906 52473206 51657555
 [9] 50827152 50247334

Smallest eigenvalues:
 [1]  0.53147116  0.47976895  0.43886625  0.42846584  0.34837400  0.26593943
 [7]  0.23471560  0.11366452 -0.04505713 -0.44611046

Largest  eigenvalues:
 [1] 65526284 60435370 57556909 56102453 55558251 54012274 52720020 52218051
 [9] 52025995 51845651

Smallest eigenvalues:
 [1]  0.42034369  0.40364548  0.39459076  0.33490726  0.31175138  0.22955885
 [7]  0.19247885  0.05876411 -0.55990331 -1.69576473

Largest  eigenvalues:
 [1] 62959051 60401462 57502049 55426037 55080809 53725410 52027710 51837241
 [9] 51221604 50859656

Smallest eigenvalues:
 [1]  0.5025006  0.4720202  0.3527511  0.3397403  0.3050973  0.2037698
 [7]  0.1891805  0.1258058 -0.1187030 -0.2852127

Largest  eigenvalues:
 [1] 62515607 59677899 56844393 55429824 54515527 53506642 52132085 51852826
 [9] 51097314 50737816

Smallest eigenvalues:
 [1]  0.51926145  0.51170863  0.46626228  0.38989217  0.35517676  0.30743454
 [7]  0.28717816  0.25170314  0.20959253 -0.07195489

Largest  eigenvalues:
 [1] 64242436 60696544 57806979 56507526 55320795 53738012 52824229 52588714
 [9] 51989520 51672614

Smallest eigenvalues:
 [1]  0.4874746  0.4851699  0.4691206  0.4548387  0.3604664  0.2629032
 [7] -0.6340852 -2.3046159 -6.1862649 -7.0992374

Largest  eigenvalues:
 [1] 65753681 60174252 57398785 56975387 55001455 53806839 52848116 52223651
 [9] 52066150 51212054

Smallest eigenvalues:
 [1]  0.58012936  0.49962223  0.48867993  0.47137868  0.30818961  0.24196721
 [7]  0.11875628 -0.01764024 -0.43213145 -0.92839728

Largest  eigenvalues:
 [1] 65178972 60608807 57775887 56451767 55418327 53924886 52511814 52460861
 [9] 52074861 51417317

Smallest eigenvalues:
 [1]  0.5713031  0.4893699  0.4629765  0.4359207  0.2937939  0.2641157
 [7]  0.2264419  0.2149273 -0.3567650 -2.5545332

Largest  eigenvalues:
 [1] 64498337 60927996 57499315 55846139 55820113 54147413 52423565 52318910
 [9] 51948004 51389174

Smallest eigenvalues:
 [1]  0.47055351  0.42229862  0.36186616  0.30449530  0.28785649  0.19015364
 [7]  0.16544825  0.09250296 -1.63350141 -2.51834416

Largest  eigenvalues:
 [1] 63199872 60542384 56927855 55889197 55012968 53321381 52226294 51762524
 [9] 51589463 50796383

Smallest eigenvalues:
 [1]  0.45144524  0.41527873  0.39254774  0.34714667  0.29839453  0.28619885
 [7]  0.22725457 -0.01124519 -0.26446983 -4.62512366

Largest  eigenvalues:
 [1] 64994297 59885540 57501212 56111916 54768116 53144052 52247329 51908584
 [9] 51810107 51072469

Smallest eigenvalues:
 [1]  0.5221984  0.5153910  0.3986418  0.3637976  0.3511665  0.3133694
 [7]  0.3092224  0.1069729 -0.1353626 -0.2273444

Largest  eigenvalues:
 [1] 63632313 60301474 57504686 55646723 55232314 53699852 52222529 51971896
 [9] 51734877 51110215

Smallest eigenvalues:
 [1]  0.36893990  0.34833040  0.26851125  0.19541971  0.18012315  0.15154066
 [7]  0.01548687 -0.14529901 -1.44733600 -5.27980262

Largest  eigenvalues:
 [1] 64584752 59265620 56794742 54904093 54896497 53177404 52194779 51346174
 [9] 51268553 50655812

Smallest eigenvalues:
 [1]  0.5005562  0.4350601  0.3985985  0.3589825  0.3191489  0.3152433
 [7]  0.2819248  0.2816232 -1.1744147 -2.2487883

Largest  eigenvalues:
 [1] 63258390 60136150 57391915 55932966 54774178 53418205 52233535 51767703
 [9] 51708706 51262995

Smallest eigenvalues:
 [1]  0.4161857  0.3794335  0.2949921  0.2812370  0.2765253  0.2330728
 [7]  0.1867400 -0.1271999 -0.2500482 -1.1780693

Largest  eigenvalues:
 [1] 65012206 59858645 57710051 55985226 54691974 53519670 52272835 51753941
 [9] 51546467 50862011

Smallest eigenvalues:
 [1]  0.28340625  0.26473059  0.22640351  0.19818052  0.18209428  0.16626746
 [7]  0.13875135  0.06621314  0.02917200 -6.90873899

Largest  eigenvalues:
 [1] 62533692 60307250 57342346 55705124 55118293 53550309 52350443 52240598
 [9] 51511171 50876336

Smallest eigenvalues:
 [1]  0.34789506  0.33183102  0.32530547  0.29281073  0.28577904  0.24550149
 [7]  0.17013453  0.12269745  0.06637537 -1.14009785

Largest  eigenvalues:
 [1] 63673436 59531840 57031669 54877711 54758367 53278347 51649247 51184499
 [9] 51044313 50506501

Smallest eigenvalues:
 [1]  0.4584325  0.4333225  0.3582918  0.3074576  0.2577924  0.2047237
 [7]  0.1277437 -0.2867576 -1.5064289 -1.7980924

Largest  eigenvalues:
 [1] 65047246 59765000 56987611 56364494 54935287 53213247 52519439 52317855
 [9] 51811202 51326559

Smallest eigenvalues:
 [1]  0.42436130  0.33880340  0.32668277  0.32224075  0.25386499  0.13132488
 [7] -0.08021959 -0.11743139 -0.50124035 -2.50257072

Largest  eigenvalues:
 [1] 65956435 59844002 57127156 56680734 54633526 53119369 52722814 52249303
 [9] 51474506 51449975

Smallest eigenvalues:
 [1]  0.5408122  0.5328957  0.4685447  0.4518159  0.4113033  0.3076544
 [7]  0.2852938  0.2345276  0.1819165 -0.3397039

Largest  eigenvalues:
 [1] 63885006 59473290 56404851 55146894 54695714 52995278 51761836 51342906
 [9] 51188054 50433517

Smallest eigenvalues:
 [1]  0.466261262  0.437427203  0.425656048  0.362187336  0.317853143
 [6]  0.262597809  0.226635319  0.207970545 -0.007786358 -0.036772981

Largest  eigenvalues:
 [1] 63426416 59490417 56816766 54854058 54581901 53068476 51742847 51305115
 [9] 51131445 50706530

Smallest eigenvalues:
 [1]  0.2415813945  0.2273253978  0.1937465863  0.0949346837  0.0007970694
 [6] -0.2193448813 -0.2357611043 -0.4773698490 -3.0020953399 -3.6143458221

Largest  eigenvalues:
 [1] 65962942 59593381 56912351 56315480 54465763 53061088 52371886 51813708
 [9] 51414935 51009642

Smallest eigenvalues:
 [1]   0.4208521   0.4114712   0.4094289   0.3875344   0.3570711   0.2894118
 [7]   0.2382051  -0.1251349  -0.2998943 -10.1987027

Largest  eigenvalues:
 [1] 66525941 60483172 58522230 57011494 55203439 53257600 52947900 52283763
 [9] 51852717 51548519

Smallest eigenvalues:
 [1]  0.434444305  0.426163973  0.363162587  0.238188011  0.207862423
 [6]  0.177847395  0.152227120  0.147449057  0.059952267 -0.004589747

Largest  eigenvalues:
 [1] 64596809 60786319 58214509 55878681 55757262 54436362 52489528 52123289
 [9] 51981637 51254343

Smallest eigenvalues:
 [1]  0.40398985  0.28993059  0.28549567  0.24028940  0.13266274  0.09990907
 [7]  0.06953243 -0.06564481 -0.63784257 -1.53078405

Largest  eigenvalues:
 [1] 66224622 60461811 58040077 57317653 54917187 53433720 53173527 52862275
 [9] 51955190 51575189

Smallest eigenvalues:
 [1]  0.5591208  0.5545035  0.4925871  0.4320349  0.4013075  0.3762457
 [7]  0.3267191  0.2626546  0.2324088 -0.2916859

Largest  eigenvalues:
 [1] 63720377 60116309 56886227 55638981 55201961 53382512 51634090 51620390
 [9] 51556789 50679307

Smallest eigenvalues:
 [1]   0.38386540   0.37805452   0.34003551   0.30947581   0.29734050
 [6]   0.28207337   0.18907370   0.04500703  -2.65313247 -14.95351402

Largest  eigenvalues:
 [1] 63704824 60337250 57466047 56339276 55076040 53401728 52578461 52120606
 [9] 51882475 51396763

Smallest eigenvalues:
 [1]  0.4322080  0.3281810  0.3183111  0.3109831  0.2714275  0.2617141
 [7]  0.1612092  0.1309599 -0.2709503 -0.6854954

Largest  eigenvalues:
 [1] 66329832 60112264 57838001 57157511 54927072 53635504 53252536 51998843
 [9] 51804282 51054854

Smallest eigenvalues:
 [1]  0.35093574  0.30243586  0.28726189  0.25670133  0.15429107  0.14498640
 [7]  0.09098483 -0.63385053 -1.29929390 -2.17960787

Largest  eigenvalues:
 [1] 65016029 60177187 57095141 56634755 54961632 53364063 52603558 52547768
 [9] 52031266 51598556

Smallest eigenvalues:
 [1]  0.49988845  0.47529707  0.46638092  0.27996576  0.23874053  0.22102476
 [7] -0.01512170 -0.05025554 -0.44761128 -6.03208135

Largest  eigenvalues:
 [1] 65890820 59874780 57192564 56264223 54589980 53014725 52485182 51567248
 [9] 51520916 50563826

Smallest eigenvalues:
 [1]  0.46332744  0.38686915  0.38112818  0.32362992  0.24769322  0.24263068
 [7]  0.06749610  0.06551303 -0.07890308 -0.13695690

Largest  eigenvalues:
 [1] 65364059 60360038 57765094 56575277 54829272 53495650 52703738 52224807
 [9] 51675941 51418518

Smallest eigenvalues:
 [1]   0.5305591   0.5075246   0.5062072   0.4537682   0.3536183   0.3294674
 [7]   0.1676961  -0.2420098  -0.2697666 -14.8295587

Largest  eigenvalues:
 [1] 64271153 59318899 56661006 55621899 54412221 52350677 51672772 51175722
 [9] 51151279 50334644

Smallest eigenvalues:
 [1]  0.5743931  0.5493130  0.4858762  0.3989672  0.3351589  0.3212625
 [7]  0.1091344 -0.1554295 -0.3136636 -1.4933195

Largest  eigenvalues:
 [1] 65554236 59878330 56893590 56499604 54610444 52608177 52313604 51531469
 [9] 51469158 50703526

Smallest eigenvalues:
 [1]  0.4495952  0.4399953  0.3982052  0.2379758  0.2186152  0.2003421
 [7]  0.1730716 -0.2911618 -0.9133189 -1.9214797

Largest  eigenvalues:
 [1] 66399867 60468573 57442417 57251624 55058784 53334485 53188891 52883126
 [9] 51909840 51866537

Smallest eigenvalues:
 [1]  0.57176123  0.48574687  0.45428844  0.44243157  0.34061053  0.24904783
 [7]  0.24869553  0.00457662 -0.04234539 -0.54184527

Largest  eigenvalues:
 [1] 64195376 59920448 56952940 55197531 54745090 53153994 51827438 51711555
 [9] 51345781 51106600

Smallest eigenvalues:
 [1]  0.4890101  0.4517800  0.3682552  0.2948088  0.2907152  0.1775843
 [7]  0.1414866 -0.1117288 -0.1457795 -0.3714791

Largest  eigenvalues:
 [1] 64154087 59832977 57256539 55768918 54677701 53306797 52063670 51851831
 [9] 51729582 50827569

Smallest eigenvalues:
 [1]  0.4776109  0.4771060  0.4559435  0.4341539  0.3583790  0.2678629
 [7]  0.2404454  0.1621592 -0.8983148 -3.1907707

Largest  eigenvalues:
 [1] 64683767 60382793 56924640 56101382 55465793 53699398 51965701 51836344
 [9] 51777165 50937773

Smallest eigenvalues:
 [1]  0.5306352  0.5296879  0.4059932  0.3156602  0.2887626  0.2886394
 [7]  0.1939669  0.1453778  0.0907439 -0.4474634

Largest  eigenvalues:
 [1] 66219979 60822738 58241203 56418207 55323593 53828261 52644160 52339004
 [9] 51967982 51508198

Smallest eigenvalues:
 [1]  0.5450274  0.5271497  0.4839840  0.4417641  0.3843889  0.3784636
 [7]  0.3370521  0.1922719 -0.6498761 -1.5077960

Largest  eigenvalues:
 [1] 65381905 60151309 57165539 56532344 55271170 53777933 52439671 52199484
 [9] 52016625 51332287

Smallest eigenvalues:
 [1]  0.4491205  0.3961330  0.3606945  0.3201626  0.2609917  0.2525351
 [7]  0.2443581  0.2352861  0.1882568 -0.7495873

Largest  eigenvalues:
 [1] 64515620 59885305 56611753 55923642 54765470 53171315 51971075 51924063
 [9] 51505105 50861641

Smallest eigenvalues:
 [1]  0.53308618  0.51744240  0.47585514  0.44785083  0.27852202  0.26670976
 [7]  0.01367621 -0.01091271 -0.05497936 -2.89193457

Largest  eigenvalues:
 [1] 65559979 60824817 57468016 55944090 55426795 53507889 52062479 51953165
 [9] 51683793 51213346

Smallest eigenvalues:
 [1]   0.4309154   0.4216400   0.3656186   0.3599604   0.2927533   0.1678212
 [7]  -0.2632419  -0.7448668  -5.6835426 -13.8155333

Largest  eigenvalues:
 [1] 66631900 60485496 58202582 57637510 54838726 53680894 53559720 52182750
 [9] 51808686 51304561

Smallest eigenvalues:
 [1]   0.4398044   0.4323594   0.4234483   0.4209823   0.3904476   0.3623953
 [7]   0.3205402   0.2543731   0.2331397 -26.3787623

Largest  eigenvalues:
 [1] 64380217 59436844 56951791 56370705 54485346 52395617 52324390 52072265
 [9] 51112143 50749537

Smallest eigenvalues:
 [1]  0.4769435  0.4730963  0.4114147  0.4008876  0.3778841  0.3272200
 [7]  0.3162803  0.2118835  0.1100390 -1.8263022

Largest  eigenvalues:
 [1] 64237505 60185987 57341417 55507893 55476112 53835862 51955261 51623677
 [9] 51390341 50493087

Smallest eigenvalues:
 [1]  0.39625962  0.38157149  0.35342311  0.32583066  0.27074997  0.20847047
 [7] -0.02167151 -0.17127891 -1.64305769 -2.80552804

Largest  eigenvalues:
 [1] 65800277 60402343 57493645 56499415 55430630 53998070 52533358 52042311
 [9] 51899116 50678653

Smallest eigenvalues:
 [1]  0.4832357  0.4332341  0.3803877  0.3701274  0.2927207  0.2530939
 [7]  0.2465986  0.1726147  0.1341766 -0.4302989

Largest  eigenvalues:
 [1] 64348332 60346133 57329240 56131624 55304682 53606162 52421312 52094844
 [9] 51891369 51391340

Smallest eigenvalues:
 [1]   0.3689468   0.3574100   0.2452902   0.2289294   0.2216702   0.1257119
 [7]  -0.2730172  -0.6618811 -11.2429554 -16.1895911

Largest  eigenvalues:
 [1] 65383593 59876893 57708685 55999810 55068015 53790423 52592117 52070824
 [9] 52061073 51712467

Smallest eigenvalues:
 [1]  0.5406926  0.4697975  0.4517916  0.3750419  0.3056596  0.2682609
 [7]  0.2283717  0.0210087 -0.1077770 -0.7328168

Largest  eigenvalues:
 [1] 65498816 60246536 57965849 56772044 54864376 53246998 52784297 52048504
 [9] 51842346 51274974

Smallest eigenvalues:
 [1]  0.54072058  0.52944273  0.43453421  0.39734882  0.33277288  0.16204473
 [7]  0.15650868  0.07111315 -0.05915046 -6.19028250

Largest  eigenvalues:
 [1] 64265374 59415228 56794181 55292918 54604631 53005091 51530621 51449540
 [9] 51352219 50541916

Smallest eigenvalues:
 [1]  0.58651710  0.50571635  0.42750083  0.40600214  0.34097664  0.21093217
 [7]  0.16199785  0.07832537  0.05664466 -0.59843557

Largest  eigenvalues:
 [1] 63659433 60535382 57840866 55187611 55045144 53812851 51995940 51942472
 [9] 51226687 51010547

Smallest eigenvalues:
 [1]  0.49021341  0.42461715  0.38762597  0.38303786  0.33617703  0.29306333
 [7]  0.20388292  0.09266713 -0.08945048 -1.83237952

Largest  eigenvalues:
 [1] 65186530 60356009 58081255 55798651 55443708 53714582 52488709 52134078
 [9] 52006769 51546137

Smallest eigenvalues:
 [1]  0.36056382  0.34021378  0.29258483  0.28240462  0.24689612  0.17544780
 [7]  0.09905085  0.08256006 -1.30397905 -1.98239575

Largest  eigenvalues:
 [1] 66244544 60615705 58023050 56666242 55053661 53661261 52728561 52672522
 [9] 51980704 51824708

Smallest eigenvalues:
 [1]  0.4778597  0.4435899  0.4068742  0.4062279  0.3787896  0.3586641
 [7]  0.3158504  0.1870563  0.1222329 -0.1793295

Largest  eigenvalues:
 [1] 61909813 59834985 56839004 54916578 54615913 53405222 51970260 51209453
 [9] 50670842 50430270

Smallest eigenvalues:
 [1]  0.45195193  0.41115985  0.33329924  0.31201618  0.31015451  0.19867034
 [7]  0.18886407  0.08014479 -2.82524194 -3.31910731

Largest  eigenvalues:
 [1] 66621614 61073822 57943279 57338792 56115200 54422012 53369645 53278776
 [9] 52460712 52065854

Smallest eigenvalues:
 [1]  0.4660936  0.3685865  0.3603954  0.3578815  0.3484880  0.3378645
 [7]  0.3246350  0.2219678  0.1820377 -0.4078484

Largest  eigenvalues:
 [1] 64726710 60973669 57886930 56046089 55943532 54226049 52512248 52166820
 [9] 52057019 51553353

Smallest eigenvalues:
 [1]  0.3764079  0.3480869  0.3441127  0.3310985  0.2568513  0.2216378
 [7]  0.1127019 -0.2594567 -0.8621922 -1.4643204

Largest  eigenvalues:
 [1] 65549750 59600336 57341334 56851883 54670519 53390008 52790668 51931754
 [9] 51537623 51054069

Smallest eigenvalues:
 [1]  0.5060991  0.4870456  0.4610628  0.4553131  0.3943436  0.3348051
 [7]  0.2695934  0.2224787  0.1437522 -0.8872853

Largest  eigenvalues:
 [1] 63861132 60694511 57968395 56085826 55761381 54465041 52764048 52714974
 [9] 51945764 51642869

Smallest eigenvalues:
 [1]   0.4263046   0.4003046   0.3723493   0.3383564   0.2936327   0.2406578
 [7]   0.1796888   0.1486866  -4.2383471 -19.2118721

Largest  eigenvalues:
 [1] 64289374 60376723 57775001 55686070 55593431 54219178 52596074 52346362
 [9] 51676903 51171061

Smallest eigenvalues:
 [1]   0.5548711   0.4931591   0.4575653   0.4320617   0.3139352   0.2886235
 [7]   0.2763743   0.2569307   0.1211830 -19.1282041

Largest  eigenvalues:
 [1] 63072247 60119423 57001363 55424894 54712440 53675173 51838142 51738903
 [9] 50978677 50878156

Smallest eigenvalues:
 [1]  0.4846561  0.4607000  0.3844532  0.3098568  0.2715368  0.2377455
 [7]  0.1077077 -0.1850138 -0.8344726 -1.4884489

Largest  eigenvalues:
 [1] 65243394 61339602 57731511 56649661 56354961 54624259 53492563 52629288
 [9] 52334143 51883163

Smallest eigenvalues:
 [1]  0.41566287  0.40642435  0.32463694  0.30233169  0.27980582  0.24816331
 [7]  0.21782159  0.19045934  0.06856897 -2.13150705

Largest  eigenvalues:
 [1] 63873119 59830778 57199124 55455712 54820795 53415017 51826371 51591862
 [9] 51546287 50813437

Smallest eigenvalues:
 [1]  0.45826277  0.37661712  0.37518788  0.26561324  0.19295784  0.16999554
 [7]  0.12859338 -0.04130816 -0.79620896 -3.69373523

Largest  eigenvalues:
 [1] 65937546 59865360 57822638 56167997 55018247 53852151 52539872 52355663
 [9] 52060609 51499046

Smallest eigenvalues:
 [1]  0.4139886  0.3641170  0.3464064  0.3293694  0.3244529  0.3093846
 [7]  0.1291062  0.0249714 -5.6929043 -9.3069458

Largest  eigenvalues:
 [1] 64008928 60408479 57746086 55719560 55324554 54071320 51911299 51876264
 [9] 51423796 50885048

Smallest eigenvalues:
 [1]  0.6403346  0.5855630  0.5592453  0.3966013  0.3757541  0.3739998
 [7]  0.3017524  0.2542082 -0.2473475 -0.3472239

Largest  eigenvalues:
 [1] 65821871 60477506 57718384 56972401 54911748 52960939 52905841 52494687
 [9] 51779747 51596833

Smallest eigenvalues:
 [1]  0.5795766  0.3888811  0.3595193  0.3188216  0.2690237  0.2510893
 [7]  0.2201783  0.0801908 -0.4393881 -0.4694700

Largest  eigenvalues:
 [1] 65565381 60801012 57737444 56707756 55540550 53802333 52838172 52661072
 [9] 52008593 51465674

Smallest eigenvalues:
 [1]  0.38472066  0.35331810  0.32975636  0.31088146  0.25222224  0.19079225
 [7]  0.06460247 -0.25671302 -0.44770621 -1.40856262

Largest  eigenvalues:
 [1] 65212187 60296345 57754453 56430604 55160844 53529062 53275694 52625681
 [9] 51916021 51661593

Smallest eigenvalues:
 [1]   0.42237180   0.42032528   0.31233382   0.16524639   0.05787527
 [6]   0.01202229  -0.63636918  -1.68376650 -14.93204405 -16.16891740

Largest  eigenvalues:
 [1] 64552038 60472445 57342727 55983733 55185087 53460466 51956421 51881523
 [9] 51853834 50961401

Smallest eigenvalues:
 [1]  0.4286482  0.3473948  0.3297445  0.3159395  0.2949013  0.2788363
 [7]  0.2747424  0.2642496 -0.1466519 -1.1626724

Largest  eigenvalues:
 [1] 65700000 60796125 58178536 56760625 55445271 53968170 52714220 52367880
 [9] 52325203 51485866

Smallest eigenvalues:
 [1]  0.3286857  0.3194254  0.3132222  0.2723912  0.2676347  0.2431626
 [7]  0.2395744  0.1641341  0.0429887 -2.4088361

Largest  eigenvalues:
 [1] 65068798 60052382 57560834 56030043 54736076 53404028 52147713 51920559
 [9] 51624305 51253356

Smallest eigenvalues:
 [1]  0.6614362  0.6403125  0.5126743  0.4071050  0.3952139  0.3674139
 [7]  0.3460903  0.2670907  0.2648928 -0.7606246

Largest  eigenvalues:
 [1] 64600665 59900758 57115765 55762293 55089866 53649784 52203205 51892990
 [9] 51692900 50862597

Smallest eigenvalues:
 [1]  0.34926447  0.30013149  0.29411579  0.18386155  0.17518293  0.03194533
 [7] -0.11371876 -0.66660138 -2.20708859 -2.40010136

Largest  eigenvalues:
 [1] 65867518 60715944 58399371 56423239 55533358 53963358 52633517 52469002
 [9] 52386662 51856974

Smallest eigenvalues:
 [1]  0.4062109  0.3548507  0.2620249  0.2274064  0.1787668  0.1624238
 [7]  0.1595502  0.1217733 -0.0695975 -0.3605582

Largest  eigenvalues:
 [1] 63416808 61049453 56959543 55899649 55281965 54022118 51999001 51856170
 [9] 51392778 50637348

Smallest eigenvalues:
 [1]  0.4767220  0.4514406  0.4259908  0.4115469  0.2173005  0.1676919
 [7] -0.5425180 -1.6655514 -7.1278341 -9.9574590

Largest  eigenvalues:
 [1] 65497881 59884294 57176821 56820661 54909157 52902306 52701398 52483434
 [9] 51888812 51542175

Smallest eigenvalues:
 [1]   0.4060931   0.3150107   0.2145123   0.2082711   0.1386461   0.1279345
 [7]  -0.1606087  -1.8452163  -2.5555222 -10.6843925

Largest  eigenvalues:
 [1] 62046911 59537646 56211139 54871859 54865287 53119149 52012013 52006173
 [9] 50932514 50735064

Smallest eigenvalues:
 [1]  0.198303712  0.155067222  0.097439951  0.027048659  0.011378508
 [6]  0.005265852 -0.281215271 -0.493394858 -0.884524960 -1.862326452

Largest  eigenvalues:
 [1] 65351690 61514551 58327310 57309372 55428947 53737179 53442117 52740637
 [9] 52343485 51506782

Smallest eigenvalues:
 [1]  0.46450843  0.46054168  0.45284442  0.41450965  0.37355043  0.27335440
 [7]  0.20753410  0.19570522  0.16160896 -0.01449703

Largest  eigenvalues:
 [1] 62976642 59457855 56950107 54880378 54772066 53294796 51970638 51260449
 [9] 50905360 50530197

Smallest eigenvalues:
 [1]  0.55305861  0.54941815  0.54413921  0.50327213  0.44790488  0.44528093
 [7]  0.38393194  0.22429424  0.07960443 -0.08169211

Largest  eigenvalues:
 [1] 63483000 60556650 57658353 55429371 55381283 53886898 52126457 51854446
 [9] 51436065 50882670

Smallest eigenvalues:
 [1]   0.44223909   0.44120642   0.38524675   0.37500863   0.31265581
 [6]   0.25437073   0.06182566   0.05031048  -0.28850931 -11.67986817

Largest  eigenvalues:
 [1] 65248968 60746361 57638220 57029907 55038544 53253835 53069990 52039874
 [9] 51944501 51181638

Smallest eigenvalues:
 [1]  0.4360076  0.4202398  0.3889183  0.3880379  0.3236710  0.3046222
 [7]  0.2550710 -0.1149168 -0.5660980 -1.5233874

Largest  eigenvalues:
 [1] 64147105 60019420 57599055 55797462 54904387 53625591 51848097 51825624
 [9] 51767888 50890702

Smallest eigenvalues:
 [1]  0.5085601  0.5059506  0.4490781  0.4049120  0.3501748  0.2672402
 [7]  0.2226407  0.2133033  0.1708226 -1.3584313

Largest  eigenvalues:
 [1] 63702979 60239126 57092081 55698385 55443170 53895907 52250143 51820241
 [9] 51307070 50933972

Smallest eigenvalues:
 [1]  0.6933409  0.5524056  0.5121185  0.3767376  0.3618350  0.3338048
 [7]  0.3005060  0.2620378  0.1317146 -0.1480377

Largest  eigenvalues:
 [1] 63892461 60325373 57481052 55669956 55559986 53822663 52686715 51871872
 [9] 51791487 51347378

Smallest eigenvalues:
 [1]   0.17902819   0.13735683   0.13413892   0.09712550   0.08150493
 [6]  -0.06849755  -0.11427658  -0.41936993  -2.49260382 -11.27649523

Largest  eigenvalues:
 [1] 63661147 59378065 56441556 55595307 54846100 53145422 51822430 51550666
 [9] 50893874 50263697

Smallest eigenvalues:
 [1]  0.486330705  0.401310625  0.361569251  0.291178136  0.288211599
 [6]  0.274139766  0.192191030 -0.007872327 -0.531349612 -2.865874205

Largest  eigenvalues:
 [1] 64602378 60810156 57849329 56003413 55418830 53819263 52851527 52225698
 [9] 52159588 51942990

Smallest eigenvalues:
 [1]   0.4297659   0.2969011   0.2879350   0.2405863   0.2353714   0.2013860
 [7]   0.1412234   0.1290179  -1.4790095 -15.5185224

Largest  eigenvalues:
 [1] 64664764 59624506 56944092 56048611 54706838 53098375 52299283 52050540
 [9] 51654430 51088358

Smallest eigenvalues:
 [1]   0.4690986   0.4671841   0.4160146   0.3865764   0.3245286   0.3200399
 [7]   0.2716805  -0.6287659  -7.1402322 -28.1024389

Largest  eigenvalues:
 [1] 64507080 60615817 57274571 56322253 55661814 54022942 52281343 52145345
 [9] 51995816 51115181

Smallest eigenvalues:
 [1]  0.42515764  0.38707386  0.38168610  0.25775125  0.22365832  0.19184253
 [7]  0.18927772  0.11209596  0.02461388 -0.88692641

Largest  eigenvalues:
 [1] 65463396 61192026 58655962 56557350 55656957 54238820 52758294 52632723
 [9] 52468398 51848997

Smallest eigenvalues:
 [1]  0.4807497  0.3589228  0.3012715  0.2997176  0.2974495  0.2919229
 [7]  0.2827454  0.2601469  0.1770138 -0.6608962

Largest  eigenvalues:
 [1] 64329002 59862198 56879615 55686579 54787696 53127926 51915843 51826370
 [9] 51345560 51025563

Smallest eigenvalues:
 [1]  0.4383523  0.4287468  0.4243869  0.3264658  0.3031195  0.2817753
 [7]  0.2279140  0.2142666  0.1657544 -1.1273006

Largest  eigenvalues:
 [1] 65062571 60488852 57441608 56610897 54915390 53613978 52545262 52471781
 [9] 51842764 51709671

Smallest eigenvalues:
 [1]  0.3440562  0.2972671  0.2789140  0.2334340  0.2285750 -0.1489077
 [7] -0.6235325 -0.6600562 -1.6493303 -6.1141973

Largest  eigenvalues:
 [1] 64188076 59297122 57089277 55529979 54328238 53232339 51905846 51695037
 [9] 51520910 51004256

Smallest eigenvalues:
 [1]  0.3679006  0.3589779  0.3323990  0.3097555  0.2737755  0.2658786
 [7]  0.2091142  0.1310916 -0.4877401 -4.5705615

Largest  eigenvalues:
 [1] 62030613 59288621 56405619 54602514 54389954 53003010 51733344 51277357
 [9] 50599073 50472286

Smallest eigenvalues:
 [1]  0.3711072  0.3515920  0.3241428  0.3214037  0.2901418  0.1984046
 [7]  0.1846894  0.1846851  0.1410481 -4.0522866

Largest  eigenvalues:
 [1] 64872565 60884767 57819973 56136849 55728928 54385399 52731393 52663380
 [9] 52077315 51889963

Smallest eigenvalues:
 [1]  0.5427293  0.4457126  0.3975445  0.3885092  0.3600539  0.3346986
 [7]  0.3194983  0.1537804 -0.1775802 -9.3676397

Largest  eigenvalues:
 [1] 64004823 60083941 57351803 55459867 55451526 53972452 52340519 52187071
 [9] 51565397 51214728

Smallest eigenvalues:
 [1]  0.5659330  0.5125104  0.4268804  0.4120106  0.3154069  0.2870757
 [7]  0.2809774  0.2719967  0.1644634 -0.9117688

Largest  eigenvalues:
 [1] 62386470 59924937 56853106 55060536 54763992 53368543 51747769 51650931
 [9] 50723234 50552338

Smallest eigenvalues:
 [1]  0.5214853  0.5078764  0.4104156  0.3182400  0.3139806  0.2605687
 [7]  0.2545131  0.1311899  0.1181188 -0.1641932

Largest  eigenvalues:
 [1] 64706046 60883901 57989507 56019024 55774126 54277521 52630187 52302357
 [9] 52158812 51398535

Smallest eigenvalues:
 [1]  0.50662068  0.50098790  0.43533707  0.38707777  0.34083586  0.31003635
 [7]  0.07233502  0.05012036 -0.02410819 -7.14065752

Largest  eigenvalues:
 [1] 63928280 59891202 57214322 55518332 55117478 53627896 52228955 51963762
 [9] 51541175 51045167

Smallest eigenvalues:
 [1]  0.2989950  0.2550337  0.1502615  0.1291306  0.1279780  0.1256411
 [7] -0.6146667 -0.8459516 -1.4656638 -3.2379288

Largest  eigenvalues:
 [1] 62754731 60102345 57163953 55517682 55162538 53372643 52487571 52304303
 [9] 51362555 51140771

Smallest eigenvalues:
 [1]   0.3485707   0.3380235   0.2695217   0.2148699   0.1657066   0.1174540
 [7]   0.1068433  -0.7518550  -5.0166651 -30.9693160

Largest  eigenvalues:
 [1] 65552034 60167825 57144656 56726714 55247771 53688975 52631441 52420851
 [9] 52058507 51649182

Smallest eigenvalues:
 [1]  0.54103680  0.52987206  0.45859309  0.31873353  0.26511036  0.23010307
 [7]  0.22161534  0.06543372 -0.02668467 -0.05773266

Largest  eigenvalues:
 [1] 63012792 60856183 57701532 56327576 54945243 54463426 52866543 52569567
 [9] 51629791 51126495

Smallest eigenvalues:
 [1]  0.51394867  0.48694573  0.34642951  0.33550289  0.32814874  0.20139485
 [7]  0.17144900  0.10751981 -0.02051304 -1.09090557

Largest  eigenvalues:
 [1] 63066018 61100929 57903420 56527610 55186528 54695862 52933778 52845990
 [9] 51932618 51268881

Smallest eigenvalues:
 [1]  0.35682451  0.24193373  0.22294541  0.21559344  0.20550307  0.19011960
 [7]  0.16205078  0.04673723 -1.89516848 -6.01773199

Largest  eigenvalues:
 [1] 65252231 59877344 57402895 56239435 54697675 53400471 52332243 52039031
 [9] 51766494 51260483

Smallest eigenvalues:
 [1]  0.47023212  0.43494665  0.40907428  0.37657835  0.37523447  0.29405689
 [7]  0.15445700  0.14943049 -0.03897097 -0.06423467

Largest  eigenvalues:
 [1] 64236936 60818448 58145114 56233424 55314495 53790260 52066118 52001542
 [9] 51899200 50999333

Smallest eigenvalues:
 [1]   0.32756505   0.32626878   0.20643357   0.20242644   0.01903709
 [6]  -1.39830508  -2.68564863  -9.47163581 -10.36819970 -11.68292471

Largest  eigenvalues:
 [1] 65072573 59910117 57647424 56544694 55210904 53983881 53003440 52386733
 [9] 52330172 51956962

Smallest eigenvalues:
 [1]   0.3096654   0.3090025   0.2804232   0.2802372   0.2728030   0.2104141
 [7]   0.1670914  -1.3165414  -2.2910843 -16.9555180

Largest  eigenvalues:
 [1] 64638089 60318555 57158846 56351941 54788890 53212547 52482490 52336762
 [9] 51833797 51675028

Smallest eigenvalues:
 [1]  0.5990672  0.5753152  0.5088953  0.4419816  0.4380498  0.4013660
 [7]  0.2768234  0.2386689  0.1065587 -0.2715800

Largest  eigenvalues:
 [1] 65643142 59796376 56791181 56350979 54435819 52680183 52366000 51451129
 [9] 51186549 50700039

Smallest eigenvalues:
 [1]  0.36895721  0.34396163  0.31410840  0.28298139  0.25909227  0.21975918
 [7]  0.05981791  0.01201510 -0.28140585 -0.66953327

Largest  eigenvalues:
 [1] 64797505 59868026 57490639 55445021 55359860 53871038 51769984 51652509
 [9] 51544514 50789831

Smallest eigenvalues:
 [1]  0.42470322  0.41055890  0.27497065  0.21800859  0.21152169  0.09437311
 [7]  0.03334797 -0.35497369 -0.82023264 -2.80679120

Largest  eigenvalues:
 [1] 64349347 60225770 57365724 55938268 55768186 54190848 52436484 52363377
 [9] 51865357 51769467

Smallest eigenvalues:
 [1]   0.5237585   0.4634357   0.4386310   0.4374384   0.2856463   0.2246010
 [7]   0.2228062   0.1838654   0.1734203 -11.3668351

Largest  eigenvalues:
 [1] 63439325 60194733 57670206 55434559 55110543 53772095 52639540 51815082
 [9] 51270688 51018156

Smallest eigenvalues:
 [1]  0.4913837  0.3941252  0.3486019  0.2890221  0.2782221  0.2726352
 [7]  0.2538432  0.2389814 -1.6265157 -4.4181662

Largest  eigenvalues:
 [1] 65820029 59765195 57302032 56801695 54677183 53159629 52693893 52191980
 [9] 51660452 51195984

Smallest eigenvalues:
 [1]   0.50489358   0.50365432   0.49193032   0.43581565   0.34947623
 [6]   0.22595731   0.20026470   0.14911770   0.03814112 -15.73330755

Largest  eigenvalues:
 [1] 64389014 60073505 56823247 56037478 54993227 53160060 52026139 51968122
 [9] 51738982 50929732

Smallest eigenvalues:
 [1]  0.5211476  0.4309044  0.4262893  0.3359452  0.2760792  0.2639118
 [7]  0.2572332  0.1870684 -0.1463880 -0.3596316

Largest  eigenvalues:
 [1] 64646156 60256438 57585373 55503915 55292578 53857069 52540883 52187185
 [9] 51627267 51404687

Smallest eigenvalues:
 [1]  0.498045951  0.446217558  0.372592248  0.333866438  0.284588928
 [6]  0.270684177  0.085222644 -0.008961274 -1.378552731 -8.874650204

Largest  eigenvalues:
 [1] 64527615 59793747 56889091 56142488 55021822 53439635 52223899 52169400
 [9] 51674675 51107127

Smallest eigenvalues:
 [1]  0.48233708  0.36992749  0.36207737  0.35415485  0.23478621  0.23062738
 [7]  0.18878878 -0.05536206 -0.39166060 -1.40072389

Largest  eigenvalues:
 [1] 63519575 59640641 57367400 55344104 54802799 53592206 52265371 51892833
 [9] 51506713 51094671

Smallest eigenvalues:
 [1]  0.50979273  0.44799375  0.39664625  0.37864999  0.34871614  0.33743973
 [7]  0.33171887  0.31597474  0.31462146 -0.06652291

Largest  eigenvalues:
 [1] 62888454 59727528 57120586 55635237 54921626 53261246 51669744 51569105
 [9] 51490267 50478484

Smallest eigenvalues:
 [1]  0.4910824  0.3972007  0.3154717  0.2861554  0.2733556  0.2211642
 [7]  0.1811651  0.1288606 -0.3257948 -0.7971756

Largest  eigenvalues:
 [1] 64110555 60512999 57369419 55975025 55724813 54004942 52735302 52373465
 [9] 52134294 51544277

Smallest eigenvalues:
 [1]  4.943753e-01  4.644037e-01  4.099888e-01  3.556866e-01  3.222602e-01
 [6]  5.637430e-02  8.488341e-04 -2.689939e+00 -4.092281e+00 -1.093544e+01

Largest  eigenvalues:
 [1] 63845342 60123164 56903036 55819898 55171739 53496958 51827463 51651492
 [9] 51632371 50635157

Smallest eigenvalues:
 [1]  0.511902826  0.391811157  0.355104186  0.338616642  0.224828174
 [6]  0.195832998  0.147541926  0.008617541 -0.435038316 -1.274842798

Largest  eigenvalues:
 [1] 63703858 59492645 56677602 55419044 54761169 52948938 52523007 51448248
 [9] 51244392 50849026

Smallest eigenvalues:
 [1]   0.4037483   0.3448537   0.2283588   0.1234852   0.0243138  -1.0464683
 [7]  -1.0969872  -1.4954078 -16.9805327 -26.6206378

Largest  eigenvalues:
 [1] 65925359 59772096 57408318 56116769 54804511 53272863 52296392 52008850
 [9] 51908258 50826511

Smallest eigenvalues:
 [1]  0.36182890  0.30900435  0.29322075  0.21342664  0.18976960  0.13990826
 [7]  0.05191947 -1.90202254 -6.21153044 -8.57171392

Largest  eigenvalues:
 [1] 64789453 59837587 57122325 55972095 55264381 53634971 52016771 51733060
 [9] 51247360 50187423

Smallest eigenvalues:
 [1]  0.44947592  0.43765086  0.41989136  0.33485956  0.26842534  0.25984820
 [7]  0.17658225  0.09902333 -0.06692555 -2.98197615

Largest  eigenvalues:
 [1] 62907013 59173045 56711266 54626259 54594023 52988384 51385151 51112734
 [9] 50794823 50437308

Smallest eigenvalues:
 [1]  0.49043409  0.47585817  0.40458216  0.39927649  0.36304888  0.26643871
 [7]  0.13765931  0.06804248  0.03264467 -2.39048668

Largest  eigenvalues:
 [1] 62273270 59499321 56320411 54835306 54669833 53004833 52010331 51359682
 [9] 50797037 50629046

Smallest eigenvalues:
 [1]  0.5232948  0.4804485  0.4329797  0.4202325  0.4164453  0.3675846
 [7]  0.2900074  0.2028474 -0.1084662 -1.6457422

Largest  eigenvalues:
 [1] 65565493 59745979 56976391 56855160 54734853 52892560 52861791 51664491
 [9] 51268744 50620728

Smallest eigenvalues:
 [1]  0.5178064  0.4179244  0.4030907  0.3577429  0.3257148  0.2918364
 [7]  0.2267856 -0.1917349 -1.4290024 -1.5326092

Largest  eigenvalues:
 [1] 65620870 60074169 57526222 56810956 54667560 52865144 52649759 52050366
 [9] 51629791 51181589

Smallest eigenvalues:
 [1]  0.39260410  0.34953644  0.31170280  0.26112896  0.12487434  0.09307156
 [7]  0.02481046  0.01645569 -4.74246393 -5.85633424

Largest  eigenvalues:
 [1] 65139334 61321232 57618347 57066327 56074727 54095637 53681841 52637686
 [9] 52592386 52083911

Smallest eigenvalues:
 [1]  0.36571956  0.33700234  0.33322130  0.32827244  0.29718526  0.26899324
 [7]  0.20399366  0.17770055  0.09028794 -0.96468343

Largest  eigenvalues:
 [1] 66152809 59670620 57008219 56690274 54315354 52836945 52820326 51995762
 [9] 51231714 51187809

Smallest eigenvalues:
 [1]  0.4344119  0.3866784  0.3545301  0.3312515  0.2167982  0.2162476
 [7]  0.1794588  0.1360532 -1.0033746 -2.4314693

Largest  eigenvalues:
 [1] 64344965 59233572 56672244 55420241 54575984 52968008 51756274 51371445
 [9] 51050317 50390125

Smallest eigenvalues:
 [1]  0.58735794  0.58439897  0.55705517  0.45004977  0.40355399  0.37806130
 [7]  0.36149598  0.16865441 -0.03656117 -0.25703712

Largest  eigenvalues:
 [1] 63909803 59468496 56639740 55616033 54331479 52774705 51637263 51438670
 [9] 50903888 50032762

Smallest eigenvalues:
 [1]   0.3317985   0.2829668   0.2701496   0.2534508   0.2304108   0.1637035
 [7]  -0.1366548  -0.1699129  -3.1024367 -22.0833133

Largest  eigenvalues:
 [1] 65562918 60745086 58354216 56859163 55306949 54106764 52796623 52465027
 [9] 52232344 51368995

Smallest eigenvalues:
 [1]  0.45199364  0.45142586  0.37355628  0.35873771  0.30615962  0.28058194
 [7]  0.17715282  0.03441338 -0.28165633 -1.77421589

Largest  eigenvalues:
 [1] 62970373 60255539 57449498 55719557 55318768 54119362 52295189 52219458
 [9] 51329566 51125936

Smallest eigenvalues:
 [1]   0.37214233   0.33843039   0.28558953   0.22058754   0.01874993
 [6]  -0.13182764  -0.87666441  -1.92890787  -4.17955045 -31.49485577

Largest  eigenvalues:
 [1] 65151931 59723014 56858919 55364936 54604880 53053399 51846055 51474343
 [9] 51338154 50991641

Smallest eigenvalues:
 [1]  0.4095651  0.4023405  0.3976419  0.3295473  0.3027252  0.2535563
 [7]  0.1851376  0.1461018 -0.3584446 -0.5377062

Largest  eigenvalues:
 [1] 63941470 59899283 57231504 55652351 55206554 53410827 52580042 51586551
 [9] 51520506 51297029

Smallest eigenvalues:
 [1]  0.52770824  0.51318534  0.45686886  0.42542908  0.41305383  0.27805446
 [7]  0.26843279  0.26483839 -0.03980633 -0.23471707

Largest  eigenvalues:
 [1] 64511101 59750617 56674057 55365101 54665551 53142965 51614166 51450739
 [9] 51143714 50393605

Smallest eigenvalues:
 [1]  0.3094944  0.2909495  0.2782641  0.2573035  0.1300734 -0.6695198
 [7] -1.1145329 -2.0404946 -2.6458127 -2.6554158

Largest  eigenvalues:
 [1] 65235231 60452407 57834573 55612622 55249439 53700569 52283082 51770623
 [9] 51620031 51568499

Smallest eigenvalues:
 [1]  0.4800631  0.4585918  0.4483562  0.4119571  0.4049369  0.4048675
 [7]  0.3801985  0.2341481  0.1921845 -0.3389320

Largest  eigenvalues:
 [1] 64247433 60081791 57486908 55861861 55324579 53753431 52067930 51927612
 [9] 51708346 50968941

Smallest eigenvalues:
 [1]  0.45799798  0.37013537  0.35011968  0.31336693  0.31006175  0.24372401
 [7]  0.21297489  0.17176743 -0.02461585 -0.69865875

Largest  eigenvalues:
 [1] 63382578 60457092 56989019 55556444 55193983 53505991 52586150 51604084
 [9] 51549199 51370289

Smallest eigenvalues:
 [1]  0.4293221  0.4054114  0.2970813  0.2816352  0.1962420  0.1787878
 [7]  0.1646537  0.1629980 -1.3821071 -1.8896098

Largest  eigenvalues:
 [1] 63806469 60123208 57006236 55430143 55298102 53756710 52329487 52170220
 [9] 51545726 51244078

Smallest eigenvalues:
 [1]  0.52543925  0.47528417  0.42826691  0.37678783  0.37473071  0.35180748
 [7]  0.30405575  0.27209099 -0.00451787 -0.64916346

Largest  eigenvalues:
 [1] 65665319 60422227 57684417 56436265 55038987 53622329 52590517 51940032
 [9] 51739034 51128415

Smallest eigenvalues:
 [1]  0.6050815  0.4540769  0.4159589  0.3916320  0.3191691  0.2875455
 [7]  0.2775322  0.2313483  0.2265472 -1.2249425

Largest  eigenvalues:
 [1] 66147800 60495421 57914147 56554371 55294724 53945929 52667259 52468596
 [9] 51939389 51508193

Smallest eigenvalues:
 [1]  0.44092375  0.37704863  0.37614067  0.36630488  0.17029349  0.14374279
 [7]  0.04201448 -0.48832531 -1.55736974 -2.47170599

Largest  eigenvalues:
 [1] 65190724 60841645 58140224 56574760 55338689 54051223 52483682 52342578
 [9] 52119098 51210054

Smallest eigenvalues:
 [1]   0.39501378   0.39034721   0.38672347   0.29609991   0.09380120
 [6]   0.07522996  -0.64518221  -1.94474786  -2.15186961 -15.22652123

Largest  eigenvalues:
 [1] 64974230 59631272 56635984 56458013 54459930 52999864 52273082 51789803
 [9] 51509588 50533324

Smallest eigenvalues:
 [1]  0.55100071  0.47030707  0.44955272  0.42784270  0.22999470  0.17706786
 [7]  0.15442987 -0.04238832 -0.88612253 -1.97862781

Largest  eigenvalues:
 [1] 63874236 60261060 57057849 55415575 55347800 53806837 52348497 52060619
 [9] 51507414 51329895

Smallest eigenvalues:
 [1]  0.32664073  0.31620186  0.29239656  0.18099823  0.14323823  0.12115699
 [7]  0.11847783  0.09850989 -0.48055052 -9.08741087

Largest  eigenvalues:
 [1] 62097229 60397236 57484512 56003076 55079187 54228388 52702656 52403581
 [9] 51568554 51068446

Smallest eigenvalues:
 [1]  0.52870699  0.49924345  0.42511647  0.39849348  0.25205413  0.21436063
 [7]  0.09580388  0.03257360 -1.23034655 -1.96314667

Largest  eigenvalues:
 [1] 64204835 60719614 57094034 55739680 55662182 54038637 52393168 52227470
 [9] 51586799 51131383

Smallest eigenvalues:
 [1]  0.4253974  0.4218092  0.3156482  0.2842590  0.2811186  0.2441448
 [7]  0.2099048  0.1925365 -1.0390803 -1.2280968

Largest  eigenvalues:
 [1] 65987487 60139376 57589420 57291364 54922370 53515124 53263022 52132776
 [9] 52056488 51204587

Smallest eigenvalues:
 [1]  0.5286978  0.4811105  0.4627575  0.4175315  0.3879989  0.3701321
 [7]  0.2383504  0.1616359 -0.0625703 -0.8114657

Largest  eigenvalues:
 [1] 63531253 60363673 57025081 55377033 54997084 53297403 52068976 51597092
 [9] 51417828 51178776

Smallest eigenvalues:
 [1]  0.5173593  0.4241830  0.4168549  0.4036091  0.3727598  0.3368390
 [7]  0.3363504  0.2868963  0.2113646 -0.6128432

Largest  eigenvalues:
 [1] 65333403 60580212 58013965 56430980 55296437 53911289 52518356 52282295
 [9] 52217627 51534071

Smallest eigenvalues:
 [1]  0.5516432  0.4793307  0.4626052  0.3586353  0.3109301  0.1953726
 [7] -0.2754357 -0.3103752 -0.3835025 -1.7941468

Largest  eigenvalues:
 [1] 64845273 60031034 57401692 56147614 54753417 53270533 52212877 52146042
 [9] 51917847 51424277

Smallest eigenvalues:
 [1]  0.5127143  0.4282646  0.3082915  0.3004294  0.2768270  0.2753660
 [7]  0.2750297  0.2100153  0.1925527 -0.3526256

Largest  eigenvalues:
 [1] 63647176 59571371 57182015 55876939 54297241 52863618 51861190 51560535
 [9] 51149371 50496776

Smallest eigenvalues:
 [1]  0.5926437  0.5227920  0.4321543  0.4059330  0.3634937  0.3253431
 [7]  0.2439899  0.1578668  0.1077979 -1.6558530

Largest  eigenvalues:
 [1] 63713602 59849890 57082136 55542713 54818015 53309189 51677624 51579808
 [9] 51523474 50723955

Smallest eigenvalues:
 [1]  0.51159759  0.51023638  0.46651832  0.35157554  0.33044883  0.25126617
 [7]  0.20925133 -0.01139049 -0.24336957 -2.40125854

Largest  eigenvalues:
 [1] 65452650 59537760 57179640 56419018 54535451 52724970 52483652 51911319
 [9] 51349658 51039505

Smallest eigenvalues:
 [1]  0.5468221  0.5206742  0.5017553  0.4939106  0.4584472  0.4165003
 [7]  0.2748860  0.2451470  0.1930362 -1.2702561

Largest  eigenvalues:
 [1] 64429339 60145463 57168661 56209265 54565969 53104887 52078193 51804935
 [9] 51419981 50876500

Smallest eigenvalues:
 [1]  0.5268249  0.4517559  0.4136712  0.3245934  0.2966428  0.2628115
 [7]  0.2274559  0.2102162  0.1068605 -0.4655085

Largest  eigenvalues:
 [1] 63456236 60575416 57333946 55639196 55037543 53498121 52075872 52049983
 [9] 51773999 51369596

Smallest eigenvalues:
 [1]   0.27430203   0.26186675   0.24327558   0.17264445   0.04632937
 [6]  -0.12428402  -0.24562340  -0.53274021  -7.43571511 -24.47684151

Largest  eigenvalues:
 [1] 64542538 59654738 57419203 57052963 54510624 53013153 52660754 52619683
 [9] 51874946 51154474

Smallest eigenvalues:
 [1]  0.38551201  0.36709385  0.30890115  0.29238059  0.24566885  0.21693885
 [7]  0.19537717 -0.08615009 -0.69799262 -0.95670799

Largest  eigenvalues:
 [1] 66574474 61656428 58858014 57754230 55760225 54157496 53685093 53018637
 [9] 52598739 52290158

Smallest eigenvalues:
 [1]  0.38330265  0.33983169  0.31088425  0.29385943  0.21864243  0.20352898
 [7]  0.09052186 -0.13745425 -0.24621362 -1.95626287

Largest  eigenvalues:
 [1] 64887439 60174941 57556176 56049647 54452651 53387063 52142076 51973781
 [9] 51739898 51463037

Smallest eigenvalues:
 [1]  0.56027791  0.52995718  0.45405906  0.40876858  0.40172535  0.31803179
 [7]  0.30463395  0.25097989  0.19497654 -0.02943948

Largest  eigenvalues:
 [1] 62855840 59622719 56940411 55264515 55001858 53364579 51869545 51544546
 [9] 51115441 50697550

Smallest eigenvalues:
 [1]  0.4414426  0.4250377  0.3865849  0.3048058  0.2862079  0.2246387
 [7]  0.2211863 -0.3229429 -1.7776075 -3.7721216

Largest  eigenvalues:
 [1] 65329647 60249736 57889025 56201399 54975888 53399942 52118259 52066470
 [9] 51588964 51264106

Smallest eigenvalues:
 [1]  0.4840260  0.4094132  0.3396146  0.2616245  0.2448007  0.2012485
 [7] -0.1039864 -1.2452201 -1.5216364 -3.1470824

Largest  eigenvalues:
 [1] 65994082 60766595 58007289 56520872 55580839 54030819 52833709 52737658
 [9] 52516318 51876698

Smallest eigenvalues:
 [1]  0.5515044  0.5327682  0.4172179  0.3731582  0.3111289  0.3097984
 [7]  0.2922014  0.2581040  0.2566385 -1.1498372

Largest  eigenvalues:
 [1] 65944974 60412596 57685059 56890772 55266755 53932457 52952915 52196180
 [9] 52159915 51302298

Smallest eigenvalues:
 [1]  0.41814456  0.39314189  0.34541985  0.26939281  0.23489792  0.20951774
 [7]  0.17057690  0.01315328 -0.29688561 -0.37089323

Largest  eigenvalues:
 [1] 62773651 59294909 57020914 54835388 54101565 53274560 51614297 51158836
 [9] 50579001 50372914

Smallest eigenvalues:
 [1]  0.39621089  0.35446720  0.32385079  0.29143220  0.26155909  0.21787816
 [7] -0.07438769 -0.18326823 -0.78118679 -1.81490836

Largest  eigenvalues:
 [1] 64990477 60353503 57716952 55375271 54851460 53480116 52156701 51556627
 [9] 51370760 51274415

Smallest eigenvalues:
 [1]  0.5556954  0.5419353  0.4194125  0.3984480  0.3524597  0.3399399
 [7]  0.2993663  0.2752001  0.1469461 -0.4885378

Largest  eigenvalues:
 [1] 65553019 59908222 57279562 56375462 54758511 53357263 52483808 51897466
 [9] 51872609 51074221

Smallest eigenvalues:
 [1]  0.5072311  0.5011225  0.4381494  0.3204689  0.3144934  0.1876537
 [7]  0.1588890 -0.1159627 -0.1477688 -2.6359257

Largest  eigenvalues:
 [1] 62271960 59411371 55978215 54735408 54223269 52760371 51496625 50779556
 [9] 50285884 49984810

Smallest eigenvalues:
 [1]  0.4540579016  0.4310665511  0.3277427272  0.2825839286 -0.0002956543
 [6] -0.5075927693 -0.6863605835 -1.0263465535 -1.1192722922 -8.0652487815

Largest  eigenvalues:
 [1] 64055192 59889378 57234696 55732339 55476351 53903096 52576875 52021694
 [9] 51682074 51537125

Smallest eigenvalues:
 [1]  0.48493020  0.47788870  0.45982691  0.40050190  0.29110657  0.25780536
 [7]  0.13460961 -0.06933544 -0.25325773 -2.42433678

Largest  eigenvalues:
 [1] 64302617 59861610 56428838 55156477 54799235 52912201 51550916 51217698
 [9] 51155130 50658275

Smallest eigenvalues:
 [1]   0.05244473   0.01147945  -0.08758079  -0.09317591  -0.11736709
 [6]  -0.81174103  -3.94934272 -14.73925193 -18.21714085 -25.77473237

Largest  eigenvalues:
 [1] 63020097 59168880 56149827 54902395 54418028 52888214 52040182 51501380
 [9] 50879959 50568464

Smallest eigenvalues:
 [1]  0.61633834  0.57728836  0.51973719  0.44701169  0.38636337  0.31265732
 [7]  0.31012775  0.27994223 -0.02494265 -0.26963271

Largest  eigenvalues:
 [1] 64439396 60471002 57201895 56385935 55087244 53241989 52670164 52385631
 [9] 51784672 51526406

Smallest eigenvalues:
 [1]  0.46706762  0.41605830  0.39442802  0.35862910  0.33549837  0.29207152
 [7]  0.09859399 -0.10332923 -0.28941812 -0.70817400

Largest  eigenvalues:
 [1] 63375971 60243014 57425385 55898428 55052299 53264420 52036736 51971406
 [9] 51857585 50962234

Smallest eigenvalues:
 [1]   0.47980785   0.44710076   0.44657018   0.39527325   0.36174831
 [6]   0.20674897   0.18598973   0.13748697   0.03140506 -10.08939872

Largest  eigenvalues:
 [1] 62931633 60848425 57151671 55835808 55264252 53958788 52262966 51886904
 [9] 51302185 51007436

Smallest eigenvalues:
 [1]  0.383898325  0.376777826  0.365144325  0.300214407  0.275211468
 [6]  0.215242439  0.213603201 -0.009588923 -1.265726516 -1.803717930

Largest  eigenvalues:
 [1] 65042280 60016698 57715039 56721182 54889431 53638990 52532446 52331708
 [9] 51888005 51552777

Smallest eigenvalues:
 [1]   0.36867587   0.36506960   0.34734056   0.34235227   0.26131910
 [6]   0.23512634   0.23244818  -0.09985559  -1.31761321 -39.12820069

Largest  eigenvalues:
 [1] 64259633 60524063 57413247 56051294 55332096 53815639 52452895 52399566
 [9] 51988948 51406286

Smallest eigenvalues:
 [1]  0.30669706  0.18206619  0.13001425  0.06654499  0.06311839 -0.49289964
 [7] -0.89830542 -2.18911448 -3.23607252 -4.00674612

Largest  eigenvalues:
 [1] 65789223 59309050 56508649 56025280 54138677 52673872 52099719 51643971
 [9] 51347791 50796745

Smallest eigenvalues:
 [1]  0.4487168  0.4400651  0.4365738  0.3434058  0.3397972  0.2950390
 [7]  0.2297574  0.1445853 -0.9420785 -9.4822939

Largest  eigenvalues:
 [1] 64747170 60779273 57840377 55927244 55785957 54215574 53061880 52136729
 [9] 51979816 51748446

Smallest eigenvalues:
 [1]  0.45622207  0.42307033  0.37501464  0.34258708  0.29661265  0.24997378
 [7]  0.17721858  0.13745818 -0.04494189 -0.40437979

Largest  eigenvalues:
 [1] 64987615 60773986 58098685 56235799 55601425 53830389 52815305 52205880
 [9] 52107678 51733891

Smallest eigenvalues:
 [1]  0.5434395  0.5239444  0.4883744  0.3643272  0.3398252  0.2901428
 [7]  0.2515719  0.2110094  0.1774434 -0.2383405

Largest  eigenvalues:
 [1] 61659011 59790069 56949753 55144223 54301434 53291700 52276265 51319946
 [9] 50968891 50430067

Smallest eigenvalues:
 [1]   0.22953610   0.19748145   0.18878846   0.15493491   0.12423313
 [6]   0.09859973  -0.03579610  -1.73033894  -2.86712317 -15.97736133

Largest  eigenvalues:
 [1] 66311871 60185495 57615424 57421343 55051094 53787984 53061173 52240735
 [9] 52077910 51520646

Smallest eigenvalues:
 [1]  0.4893959  0.4633498  0.4134872  0.3476526  0.3026531  0.2836557
 [7]  0.2625640  0.1580110  0.1114099 -0.9127022

Largest  eigenvalues:
 [1] 64267698 61024114 57932219 56347031 56265742 54542587 52976559 52504179
 [9] 52318400 51717176

Smallest eigenvalues:
 [1]   0.36876946   0.36660799   0.27994515   0.27293021   0.21620436
 [6]   0.17670845   0.13189257   0.08950989  -1.34918703 -22.48984732

Largest  eigenvalues:
 [1] 64147320 59647604 56858858 55086985 54872494 53351468 51719081 51485611
 [9] 51145580 50956039

Smallest eigenvalues:
 [1]  0.55597881  0.50011038  0.44034585  0.41639828  0.25749607  0.25156686
 [7]  0.24949020  0.22544044  0.11176994 -0.02952555

Largest  eigenvalues:
 [1] 64136848 60369642 57837191 55706692 54899367 54180583 52861791 51906424
 [9] 51649890 51179798

Smallest eigenvalues:
 [1]  0.52624047  0.48316042  0.45713392  0.41224744  0.34693880  0.25484233
 [7]  0.18280351  0.17924019  0.05478638 -0.02695582

Largest  eigenvalues:
 [1] 65165304 59979734 57837644 55881372 54924788 53357714 52157225 52148538
 [9] 51891329 51305529

Smallest eigenvalues:
 [1]  0.52255831  0.46641143  0.39745544  0.36297084  0.29715088  0.17275600
 [7]  0.16883544  0.02204042 -0.10780769 -1.25536952

Largest  eigenvalues:
 [1] 63270216 60632117 57063569 55742424 55579661 53484212 52366672 51824517
 [9] 51361399 50862664

Smallest eigenvalues:
 [1]   0.35326989   0.30794250   0.24389959   0.22674539   0.15009024
 [6]   0.11914683   0.03556131  -0.52730149  -4.85948714 -24.05417678

Largest  eigenvalues:
 [1] 64101748 59888006 57144308 55310849 55278939 53308216 52475716 51832087
 [9] 51597346 51513396

Smallest eigenvalues:
 [1]  0.48694943  0.48290118  0.45219524  0.42489809  0.30586551  0.20240792
 [7]  0.19600969  0.16692336  0.07440068 -0.54406467

Largest  eigenvalues:
 [1] 64636419 60172021 56964311 55819633 55098549 53467999 52394112 51897803
 [9] 51701765 51108802

Smallest eigenvalues:
 [1]  0.50415756  0.47391765  0.36608868  0.32366657  0.31798859  0.26188897
 [7]  0.20026326 -0.06817588 -1.41899616 -2.16789904

Largest  eigenvalues:
 [1] 63702727 60091511 57600699 56022933 55301747 54372158 52787674 52031265
 [9] 51435423 51103610

Smallest eigenvalues:
 [1]  0.54851205  0.50106283  0.41192100  0.40394495  0.37838009  0.37276818
 [7]  0.33625466  0.29592259  0.27756369 -0.03711557

Largest  eigenvalues:
 [1] 64820616 60247076 57140986 56105106 55398404 53454936 52582613 52238798
 [9] 51641006 51464116

Smallest eigenvalues:
 [1]  0.5833595  0.4488149  0.4001408  0.3703876  0.3006038  0.2817226
 [7]  0.2701746  0.2034730 -0.1537544 -0.3188478

Largest  eigenvalues:
 [1] 62209166 59481037 57065929 55129037 54528572 53381072 51750165 51382137
 [9] 50620135 50471273

Smallest eigenvalues:
 [1]  0.45350775  0.36410385  0.29198560  0.28835189  0.23472534  0.22611414
 [7]  0.14337925  0.06857251 -0.53092901 -0.88713100

Largest  eigenvalues:
 [1] 64604005 60314805 57618620 55481360 55339076 53830271 52374846 52135757
 [9] 51703320 51326505

Smallest eigenvalues:
 [1]  0.56381361  0.51331384  0.47362914  0.44724254  0.35469392  0.24324481
 [7] -0.08084322 -0.13984993 -0.57924724 -1.30626116

Largest  eigenvalues:
 [1] 63551399 59597631 56482930 55274790 54309343 52655397 51433084 51289137
 [9] 51247174 50426864

Smallest eigenvalues:
 [1]  0.51632690  0.47304526  0.41726490  0.37837206  0.37036446  0.34850952
 [7]  0.31367232  0.23430750  0.06151551 -0.11362747

Largest  eigenvalues:
 [1] 62593545 59086250 56207656 54967606 54334202 52640591 51525232 51258116
 [9] 50942187 50439364

Smallest eigenvalues:
 [1]   0.4301214   0.3915651   0.2330392   0.2166153   0.1520424   0.1116029
 [7]   0.1065242  -1.1516490 -10.9656849 -14.0333327

Largest  eigenvalues:
 [1] 62680260 60744588 56895459 55816573 55296863 54173593 52474333 52408347
 [9] 51250665 51175614

Smallest eigenvalues:
 [1]  0.4885155  0.4749414  0.4643886  0.4094536  0.3792688  0.3678651
 [7]  0.3199618  0.3008881  0.2692542 -2.6180365

Largest  eigenvalues:
 [1] 64591762 59798747 57114844 56735733 54540568 53156395 52565746 51715713
 [9] 51616294 50861736

Smallest eigenvalues:
 [1]  0.4922706  0.4168315  0.3659510  0.3141811  0.2814506  0.2631293
 [7]  0.2271075  0.1717822 -2.8144733 -4.2711065

Largest  eigenvalues:
 [1] 65076343 60151562 57545828 55692804 55290595 53858003 52373980 51749940
 [9] 51730283 51562485

Smallest eigenvalues:
 [1]  0.41423009  0.40797371  0.40429173  0.27367731  0.25817378  0.23670355
 [7]  0.20788047  0.02670546 -0.16663186 -0.89294617

Largest  eigenvalues:
 [1] 65540211 60066933 57548371 56149164 55211026 53795514 52296852 52226940
 [9] 52129404 51247392

Smallest eigenvalues:
 [1]  0.3954087  0.3204928  0.3169391  0.3026497  0.2731129  0.2722381
 [7]  0.2424215  0.2183580  0.2158269 -2.2519128

Largest  eigenvalues:
 [1] 64888489 60513250 57309873 56462839 55041998 53550771 52519860 52167031
 [9] 51940595 51061923

Smallest eigenvalues:
 [1]  0.53671602  0.51763776  0.44863186  0.34084719  0.28206260  0.27268519
 [7]  0.23721966  0.14159899  0.07225824 -0.22693872

Largest  eigenvalues:
 [1] 63581936 60494901 58151493 55860274 55101232 54589208 52769930 52338351
 [9] 51547990 51362970

Smallest eigenvalues:
 [1]  0.52501304  0.49803192  0.45372017  0.32331354  0.32000200  0.30433109
 [7]  0.09690191 -0.17463927 -0.31365473 -4.16352422

Largest  eigenvalues:
 [1] 65282955 60869471 57823509 55799485 55774965 54282961 52182670 52145989
 [9] 51986505 51396203

Smallest eigenvalues:
 [1]  0.41450056  0.40700190  0.37991430  0.27652375  0.14512729  0.04712675
 [7]  0.03715285  0.02444949 -0.29606994 -1.05614948

Largest  eigenvalues:
 [1] 64100890 59472564 56526493 55292362 54594372 53066232 51700571 51456839
 [9] 51384307 50598979

Smallest eigenvalues:
 [1]  0.4466548  0.4212523  0.3634084  0.3449585  0.2236894  0.2120392
 [7]  0.1981229  0.1819816 -0.3570136 -0.7909789

Largest  eigenvalues:
 [1] 64705746 60221863 57031411 55683456 55604017 53920192 52232050 52178107
 [9] 51679196 51255432

Smallest eigenvalues:
 [1]  0.43215835  0.39903997  0.31312094  0.20121132  0.18272829  0.15362316
 [7] -0.05137536 -0.29879330 -0.33981888 -1.04978910

Largest  eigenvalues:
 [1] 63479401 60165044 57119621 55465674 54873310 53396961 52339479 51727713
 [9] 51661483 51424494

Smallest eigenvalues:
 [1]  0.3383743  0.3253573  0.3022169  0.2933104  0.2615272  0.2109413
 [7]  0.2088187 -0.3266090 -1.8309206 -3.8078591

Largest  eigenvalues:
 [1] 65293378 60632251 57819269 56839513 55019116 53088501 52620818 52498445
 [9] 51843331 51403317

Smallest eigenvalues:
 [1]  0.5204391  0.5046829  0.4329070  0.3829721  0.3484199  0.3258325
 [7]  0.2419167  0.2044632  0.1212280 -0.1912412

Largest  eigenvalues:
 [1] 65164295 60378136 57656977 56022274 55474334 53812720 52296574 52270925
 [9] 52234881 51216244

Smallest eigenvalues:
 [1]  0.5333894  0.4869640  0.4775101  0.4585743  0.3064971  0.2922270
 [7]  0.2795078  0.2207584  0.1397938 -3.0483263

Largest  eigenvalues:
 [1] 65553675 60294348 57285893 57127400 55424384 53733052 53015457 52811973
 [9] 52074460 51557435

Smallest eigenvalues:
 [1]  0.47864687  0.41613528  0.37893291  0.36861429  0.33733748  0.31211842
 [7]  0.23396834  0.09058538 -0.00906576 -1.80968394

Largest  eigenvalues:
 [1] 63954265 59374372 56809316 55590799 54726130 53173100 51718021 51664485
 [9] 51310437 50399880

Smallest eigenvalues:
 [1]  0.45310925  0.33654891  0.30349949  0.25381391  0.24817438  0.23131659
 [7]  0.10211583  0.05524651 -0.17795393 -4.72547798

Largest  eigenvalues:
 [1] 62805494 59750444 56916141 55128171 54951538 53243741 51868750 51513934
 [9] 51033933 50566058

Smallest eigenvalues:
 [1]  0.3972587  0.3202435  0.3090080  0.2104679  0.1592468  0.1198572
 [7] -0.3846592 -1.4215613 -3.3367006 -8.4682147

Largest  eigenvalues:
 [1] 65743858 60283940 57758542 56230526 55223652 53800541 52639613 52426424
 [9] 52222864 51354042

Smallest eigenvalues:
 [1]  0.52258009  0.41781290  0.40511864  0.40425046  0.39020029  0.30903487
 [7]  0.26640414  0.23421111  0.02104919 -0.65343221

Largest  eigenvalues:
 [1] 63718046 59792084 56982917 55695338 54595026 53066466 51959387 51824049
 [9] 51633883 50915598

Smallest eigenvalues:
 [1]  0.5724934  0.5482017  0.3785101  0.3720853  0.3233181  0.3102313
 [7]  0.2829779  0.2777779  0.2234471 -1.7910019

Largest  eigenvalues:
 [1] 65709402 60901956 57912672 56900245 55401431 53949375 52827558 52431175
 [9] 51995446 51443226

Smallest eigenvalues:
 [1]  0.38454898  0.38298573  0.33463964  0.28159869  0.23504111 -0.05824037
 [7] -0.23550332 -0.52195435 -4.08058108 -6.28385702

Largest  eigenvalues:
 [1] 65744834 60729694 57684510 56785826 55400842 54017221 52739971 52209527
 [9] 51899878 51527616

Smallest eigenvalues:
 [1]  0.52624610  0.47731871  0.46561698  0.38174030  0.34652898  0.33682022
 [7]  0.31969031  0.31716565  0.26711378 -0.04875817

Largest  eigenvalues:
 [1] 63437678 60028142 57203485 55733735 54936103 53467301 51800957 51772752
 [9] 51712463 50789674

Smallest eigenvalues:
 [1]  0.3927441  0.3770245  0.3301044  0.3270530  0.2264842  0.2096890
 [7]  0.1907412  0.1325536 -0.7517308 -0.9367566

Largest  eigenvalues:
 [1] 65264781 59720896 57133935 56159589 54948044 53444519 52273242 52133447
 [9] 51396596 50524994

Smallest eigenvalues:
 [1]   0.18366850   0.14723774   0.05224793  -0.05280047  -0.76159670
 [6]  -3.24075590  -3.74096086  -6.47079522 -10.62836355 -10.79773562

Largest  eigenvalues:
 [1] 62985059 59277661 56739752 54912864 54598707 53043782 51866513 51333484
 [9] 50912342 50469386

Smallest eigenvalues:
 [1]   0.3949822   0.3568214   0.3435166   0.3319766   0.3038300   0.1930858
 [7]   0.1068591  -0.3541584  -0.4123566 -19.1044936

Largest  eigenvalues:
 [1] 65633265 60350118 56947177 56688288 55017829 53275758 52686983 52181234
 [9] 51985663 51560981

Smallest eigenvalues:
 [1]  0.5798457  0.4574402  0.3907756  0.3490754  0.3072805  0.3050042
 [7]  0.2684418  0.2166533  0.1736339 -1.1111754

Largest  eigenvalues:
 [1] 64916082 60049120 57596556 55817355 54746942 53472608 51981497 51866323
 [9] 51857661 51169494

Smallest eigenvalues:
 [1]  0.3868718  0.3667433  0.3375549  0.3123727  0.2013986  0.1668878
 [7]  0.1354314 -0.1297068 -0.7951714 -7.9008512

Largest  eigenvalues:
 [1] 64950407 59600447 56995097 55767914 54654235 53286705 51903472 51795154
 [9] 51733033 51032028

Smallest eigenvalues:
 [1]  0.3905614  0.3583204  0.3238455  0.2257750  0.2072003  0.1856659
 [7]  0.1746135 -0.0379976 -1.2735689 -2.0499019

Largest  eigenvalues:
 [1] 62814378 60072902 56759466 55632161 55336689 53827009 52162906 52084403
 [9] 51211447 50942002

Smallest eigenvalues:
 [1]  0.4174676  0.4036819  0.3979266  0.3799572  0.3780303  0.3133215
 [7]  0.2637527  0.2188645  0.1828826 -1.4909045

Largest  eigenvalues:
 [1] 65632006 60028786 57395232 56324373 55009085 53657204 52384662 52198105
 [9] 52001570 51240226

Smallest eigenvalues:
 [1]  0.5055472  0.4488932  0.4247336  0.4224994  0.3730829  0.2293993
 [7]  0.2057087  0.1551695  0.1187892 -0.6950585

Largest  eigenvalues:
 [1] 63714349 60338878 56654189 55408319 55192868 53521757 52304978 51658230
 [9] 51364444 51197831

Smallest eigenvalues:
 [1]  0.56355750  0.50469395  0.42543564  0.42367403  0.42187728  0.40356172
 [7]  0.19391563  0.16171233  0.09900345 -0.02989223

Largest  eigenvalues:
 [1] 63629082 60848618 57991038 55469468 55366127 53943275 52064775 51977202
 [9] 51462830 51045018

Smallest eigenvalues:
 [1]  0.4999547  0.4242853  0.4070582  0.4011577  0.3378600  0.2541987
 [7]  0.2360872  0.1779882  0.1633674 -1.3838193

Largest  eigenvalues:
 [1] 64886841 60717635 58056520 56606923 55440684 53960038 52544578 52397829
 [9] 51966702 51254325

Smallest eigenvalues:
 [1]   0.0195167  -0.0521489  -0.1039803  -1.0326219  -1.0885018  -1.3258018
 [7]  -1.8535346  -4.9984163 -29.5039805 -95.1446875

Largest  eigenvalues:
 [1] 64815048 60786927 57652890 57105412 55797379 53913438 53279986 52901442
 [9] 52161899 52139591

Smallest eigenvalues:
 [1]   0.40121044   0.32139279   0.26891911   0.24002220   0.16900970
 [6]   0.10233386  -0.02403391  -5.48446574  -5.53955665 -22.86751397

Largest  eigenvalues:
 [1] 64445348 60488436 56794722 55851457 55212474 53391065 52349730 51833073
 [9] 51265376 51239324

Smallest eigenvalues:
 [1]  0.44631156  0.43880811  0.42475382  0.36816294  0.34666918  0.28838825
 [7]  0.18060447  0.09358551 -0.25291456 -0.43651977

Largest  eigenvalues:
 [1] 64190545 60120469 57091801 55817894 54982105 53082812 51877330 51785098
 [9] 51648556 50790621

Smallest eigenvalues:
 [1]  0.5726905  0.5528845  0.4603301  0.4097984  0.3961458  0.3390871
 [7]  0.3076692  0.2914478  0.2877053 -0.9898604

Largest  eigenvalues:
 [1] 64728489 60500390 57851835 55824191 55780306 54271312 52466438 52431263
 [9] 51890742 51575871

Smallest eigenvalues:
 [1]  0.3680929  0.3578169  0.3336184  0.3235404  0.2861786  0.2490393
 [7]  0.2459757  0.2417218 -0.6295317 -1.3839640

Largest  eigenvalues:
 [1] 63313376 60182047 57106055 55780369 55474600 53607215 51761671 51676248
 [9] 51595507 50711870

Smallest eigenvalues:
 [1]   0.41658068   0.32506938   0.29691236   0.27005510   0.24228045
 [6]   0.22626037   0.14949912   0.03770387  -1.70114147 -25.39538527

Largest  eigenvalues:
 [1] 66600471 60446575 57781217 57096461 54819047 53430499 53141025 52090897
 [9] 51860703 51400576

Smallest eigenvalues:
 [1]  0.5189127  0.4620726  0.4247554  0.3576267  0.3325198  0.3246832
 [7]  0.2247279  0.2229573  0.2157122 -6.5047637

Largest  eigenvalues:
 [1] 63699845 60173421 57549723 55515491 54789339 53356881 51725045 51711814
 [9] 51653637 50863668

Smallest eigenvalues:
 [1]  0.4178070  0.3367404  0.2688692  0.2590147  0.2465043  0.2311974
 [7]  0.1790864  0.1733880  0.1417462 -2.9555011

Largest  eigenvalues:
 [1] 64387703 60457158 57625016 55943517 55385492 53834958 52500240 51981369
 [9] 51766629 51319134

Smallest eigenvalues:
 [1]  0.49517612  0.46702636  0.46030812  0.37365384  0.30437872  0.29419147
 [7]  0.26634238  0.05348424 -0.38240033 -1.85343475

Largest  eigenvalues:
 [1] 62616589 59859601 56893574 55508497 54562205 53666692 51796436 51758655
 [9] 50656753 50399735

Smallest eigenvalues:
 [1]  0.6107704  0.5959310  0.4363606  0.4015563  0.3927078  0.3471172
 [7]  0.3389834  0.3003118  0.2217068 -0.2236928

Largest  eigenvalues:
 [1] 62572553 60086455 57003074 55463515 54741237 53739994 52179965 51830448
 [9] 50918452 50689874

Smallest eigenvalues:
 [1]  0.3734243  0.3604829  0.2591976  0.2566262  0.1745959  0.1195805
 [7] -0.2452559 -0.9685733 -2.4843297 -7.2228896

Largest  eigenvalues:
 [1] 63830089 59475970 57042462 55474309 54823687 52887047 52408986 51697748
 [9] 51496299 51193689

Smallest eigenvalues:
 [1]  0.4652176  0.4518893  0.3349425  0.3078752  0.2909437  0.2238323
 [7]  0.1772416  0.1571681 -0.1935769 -1.5736215

Largest  eigenvalues:
 [1] 64241914 60437850 57702649 55846659 55578117 54306790 52439258 52244021
 [9] 51834051 51046829

Smallest eigenvalues:
 [1]  0.53286182  0.46920090  0.42146889  0.40534027  0.39012195  0.27968883
 [7]  0.26849185  0.15613849  0.01780754 -0.01079647

Largest  eigenvalues:
 [1] 64755773 59930939 57427084 56056610 55116066 53365782 52718185 52155644
 [9] 51742084 51672283

Smallest eigenvalues:
 [1]  0.5055738  0.4800702  0.4302868  0.4250121  0.4168078  0.4007920
 [7]  0.3421753  0.1133964 -0.4361021 -8.8812634

Largest  eigenvalues:
 [1] 65187881 60564117 57842139 57111328 55258579 53272425 53242773 53154156
 [9] 51762991 51696936

Smallest eigenvalues:
 [1]   0.27662826   0.21596750   0.08515786   0.01854048  -0.01242206
 [6]  -0.13177049  -0.44412948  -0.65678626  -0.75645412 -17.51209710

Largest  eigenvalues:
 [1] 65337417 60241909 56966212 56592948 54484564 53066891 52462962 51933972
 [9] 51334728 51245676

Smallest eigenvalues:
 [1]  0.563739560  0.447134514  0.407241252  0.401656389  0.348456630
 [6]  0.293311330  0.256176858  0.224783826  0.012109739 -0.006663791

Largest  eigenvalues:
 [1] 65688085 60546252 58187565 56871095 54961276 53732990 52997255 52130650
 [9] 52070542 51492391

Smallest eigenvalues:
 [1]  0.42986404  0.36767492  0.28693080  0.24349950  0.23147894  0.21107853
 [7]  0.19085499  0.11799006  0.03368411 -1.37220754

Largest  eigenvalues:
 [1] 65312288 61264969 57973818 56419678 56403982 54745090 53280421 52626794
 [9] 52427761 52079295

Smallest eigenvalues:
 [1]  0.37465773  0.35965816  0.35349947  0.26876609  0.20938226  0.16680784
 [7]  0.08770754  0.01265497 -0.73606131 -6.45738175

Largest  eigenvalues:
 [1] 63296685 59492829 56349918 54567409 54371156 52695002 51428765 50719490
 [9] 50599165 50465109

Smallest eigenvalues:
 [1]   0.29655500   0.24376786   0.13905556   0.07580608  -0.61822502
 [6]  -0.81590333  -1.60298127  -3.82197167  -4.89840002 -10.79176979

Largest  eigenvalues:
 [1] 65726498 60697895 58148637 55924085 55784091 54446787 52829627 52657213
 [9] 52103003 51649252

Smallest eigenvalues:
 [1]  0.4967624  0.4151527  0.3899235  0.3847903  0.3663412  0.3645295
 [7]  0.3067189  0.2630492  0.1228690 -0.5911202

Largest  eigenvalues:
 [1] 62931446 60014696 57684440 55030737 54921580 53274199 52265258 51449345
 [9] 51324662 51135905

Smallest eigenvalues:
 [1]  0.5175794  0.4866245  0.4217284  0.3787368  0.3714231  0.3299036
 [7]  0.3205535  0.2464447  0.2051846 -0.7782507

Largest  eigenvalues:
 [1] 62982466 59707205 56527780 55269602 54664204 53047764 51743112 51450948
 [9] 51204344 50825625

Smallest eigenvalues:
 [1]  0.5923287  0.5170791  0.4890658  0.4174978  0.3868042  0.3862984
 [7]  0.3549069  0.3270727  0.2503074 -0.3910644

Largest  eigenvalues:
 [1] 63708920 60157345 57088009 55584728 55426886 53489407 52236718 52006099
 [9] 51424483 51031211

Smallest eigenvalues:
 [1]  0.34331215  0.29768579  0.29571309  0.17665506  0.14946862  0.01307183
 [7] -0.08212541 -0.47708149 -1.34392765 -9.07828358

Largest  eigenvalues:
 [1] 63693719 60786766 58117203 55436852 55275336 53873719 52657820 52445284
 [9] 51867990 51607802

Smallest eigenvalues:
 [1]  0.52147381  0.46908380  0.42995634  0.42661575  0.36464881  0.30499518
 [7]  0.30339189  0.14064780  0.03851321 -3.19800498

Largest  eigenvalues:
 [1] 63360255 59920491 56718929 55354704 55293135 53488277 52231951 51750700
 [9] 51393812 51054783

Smallest eigenvalues:
 [1]  0.5773097  0.5166810  0.4548954  0.4349956  0.4335509  0.3909374
 [7]  0.3675562  0.2591006  0.2202154 -0.1237997

Largest  eigenvalues:
 [1] 63458025 60535725 57492574 55733391 55501661 54004070 52617085 51993703
 [9] 51476977 51317794

Smallest eigenvalues:
 [1]  0.40968398  0.35411264  0.31820302  0.24463616  0.19075035  0.12670892
 [7]  0.03809146 -0.25516592 -0.62598796 -5.10253827

Largest  eigenvalues:
 [1] 64420158 59795993 56813006 55344506 54559576 52829983 51600430 51451542
 [9] 51062802 50938200

Smallest eigenvalues:
 [1]  0.54996490  0.53709487  0.50980109  0.42660980  0.38797934  0.34306404
 [7]  0.33244315  0.32252642  0.22530047 -0.08631331

Largest  eigenvalues:
 [1] 65473235 60088850 57084299 55877840 54925934 53333597 52046965 51808276
 [9] 51744133 51239453

Smallest eigenvalues:
 [1]  0.383432317  0.369824010  0.329982482  0.273084182  0.110635175
 [6]  0.004946738 -0.044299684 -1.493547709 -1.941855283 -3.500027698

Largest  eigenvalues:
 [1] 65243667 60906268 58076759 56660188 55632592 54264415 52796578 52469313
 [9] 52270895 51866971

Smallest eigenvalues:
 [1]  0.5967675  0.5338444  0.3413342  0.3186640  0.2714519  0.2680787
 [7]  0.2600090  0.2044596 -0.2883868 -1.2271485

Largest  eigenvalues:
 [1] 64541085 60058494 57220054 56152082 54999387 53498364 52289013 52217953
 [9] 51901497 51161671

Smallest eigenvalues:
 [1]  0.5043068  0.4496201  0.4076051  0.3432926  0.2913410  0.2430115
 [7]  0.1270324 -0.2639423 -0.3134329 -1.5769235

Largest  eigenvalues:
 [1] 65266961 60365342 56762083 56637000 54963151 53287142 52568579 51890928
 [9] 51809909 50916874

Smallest eigenvalues:
 [1]  0.48448377  0.47064766  0.41980463  0.34779832  0.30066665  0.26384865
 [7]  0.22789057  0.07499376 -0.07684330 -0.30797073

Largest  eigenvalues:
 [1] 65844021 60397715 58030446 57056452 55004358 53164704 53058134 52913449
 [9] 52114849 51904190

Smallest eigenvalues:
 [1]   0.38659037   0.35025000   0.30883234   0.21083425   0.17647958
 [6]   0.12521346   0.10165116   0.02327131  -1.39496036 -49.41586896

Largest  eigenvalues:
 [1] 65323713 60930496 57663971 56580326 56037125 54429600 52850046 52639791
 [9] 52634834 52065373

Smallest eigenvalues:
 [1]  0.4203997  0.4020511  0.3957960  0.3546598  0.3376361  0.3259472
 [7]  0.2579137  0.1929515  0.1621469 -5.1531192

Largest  eigenvalues:
 [1] 63228742 59491266 56786189 55216033 54837299 53552529 51859725 51354193
 [9] 50924931 50417382

Smallest eigenvalues:
 [1]  0.59439585  0.55838376  0.50000170  0.39503961  0.35127874  0.34264285
 [7]  0.32296369  0.29056436  0.23524513 -0.04651653

Largest  eigenvalues:
 [1] 63577621 60011058 57430459 55371885 55352261 53734389 52277045 51846993
 [9] 51524993 51071770

Smallest eigenvalues:
 [1]  0.52748041  0.52085323  0.47282492  0.46016881  0.32532316  0.32355459
 [7]  0.31122752  0.26143783 -0.04452624 -1.09048076

Largest  eigenvalues:
 [1] 63649752 60463773 57507102 56300753 55602775 54561214 52709651 52331130
 [9] 51624019 51133269

Smallest eigenvalues:
 [1]  0.48199996  0.42465156  0.34396084  0.29845772  0.29826492  0.26976838
 [7]  0.26401978  0.04235792 -1.51236133 -2.94093567

Largest  eigenvalues:
 [1] 64155790 59516753 56550482 55988703 54791713 53150186 51991478 51704450
 [9] 51581074 50565427

Smallest eigenvalues:
 [1]  0.3752704  0.2700645  0.2545741  0.2491218  0.2314775  0.2027098
 [7]  0.1196420 -0.1778295 -1.1648163 -1.3406418

Largest  eigenvalues:
 [1] 63962414 61109501 58043067 56528210 55467432 54788579 52807508 52593739
 [9] 51827295 51408134

Smallest eigenvalues:
 [1]  0.34788149  0.33487322  0.32489211  0.28086913  0.20070571  0.19130303
 [7]  0.13929396  0.10583794  0.06913999 -0.80719810

Largest  eigenvalues:
 [1] 63206745 60089953 57103197 55476322 55076247 53754875 52547994 52156477
 [9] 51581934 51291721

Smallest eigenvalues:
 [1]  0.5489862  0.4958384  0.3754370  0.3634000  0.2586754  0.2459261
 [7]  0.2343000  0.2309345  0.1146095 -0.1314114

Largest  eigenvalues:
 [1] 64027934 60653198 57432371 56003729 55622074 53914822 52706591 52093004
 [9] 52092036 51254230

Smallest eigenvalues:
 [1]  0.3946377  0.3539254  0.3196846  0.2481407  0.2326993  0.2322944
 [7]  0.2103728  0.1694675 -0.8113792 -5.9997816

Largest  eigenvalues:
 [1] 62120489 59394366 56257973 54897705 54188380 53165380 51818076 50758267
 [9] 50282818 50052350

Smallest eigenvalues:
 [1]  0.53707202  0.48932306  0.40819672  0.40196587  0.37362444  0.34277781
 [7]  0.30865320  0.25270616  0.17770408 -0.06253088

Largest  eigenvalues:
 [1] 64644290 59781467 56933636 55909137 54942887 53198391 52002067 51560865
 [9] 51390085 50634680

Smallest eigenvalues:
 [1]  0.5838101  0.5530808  0.3613776  0.3477666  0.3194009  0.3018902
 [7]  0.2508838  0.1881792  0.1345991 -0.6132193

Largest  eigenvalues:
 [1] 64521723 60424218 57548315 55735333 55243046 53582289 52272658 51761120
 [9] 51725538 51264195

Smallest eigenvalues:
 [1]  0.4256473  0.3931636  0.3565357  0.3544706  0.2727139  0.1972685
 [7]  0.1954288  0.1559285 -0.4121790 -0.7174116

Largest  eigenvalues:
 [1] 64743195 60513746 57310242 56191215 55680830 53523236 53152410 52311618
 [9] 52306146 51837495

Smallest eigenvalues:
 [1]   0.03512497  -2.28955971  -3.56035025  -3.78237017  -4.16686291
 [6]  -5.65276404  -5.75583044 -30.47610863 -35.99737529 -70.30215168

Largest  eigenvalues:
 [1] 64979059 59927071 57040172 56609349 54576328 52971318 52873811 52078847
 [9] 51937156 51124465

Smallest eigenvalues:
 [1]  0.4745703  0.4492614  0.3975022  0.3762097  0.3367198  0.3099774
 [7]  0.2588097 -0.2679703 -0.3065810 -1.0882526

Largest  eigenvalues:
 [1] 65531240 60139321 57570954 56602994 55229681 53534052 52804055 52730052
 [9] 51965980 51697491

Smallest eigenvalues:
 [1]  0.57438758  0.47576818  0.47412315  0.33665090  0.22414532  0.19931718
 [7]  0.04983179 -0.25040016 -0.28139087 -0.48746474

Largest  eigenvalues:
 [1] 64642950 59978637 57336755 56279712 54909101 53279481 52223158 52131479
 [9] 51884185 51154289

Smallest eigenvalues:
 [1]  0.471223606  0.443878680  0.379929702  0.221257858  0.190548867
 [6]  0.184841202  0.070488609  0.021771895 -0.005558447 -0.355305018

Largest  eigenvalues:
 [1] 62732318 60383453 57322100 56037109 54269251 54145142 52351919 51824191
 [9] 50797277 50740398

Smallest eigenvalues:
 [1]  0.31202282  0.29779464  0.23817086  0.21194679  0.19063729  0.16796064
 [7] -0.07426175 -0.81794293 -3.73933198 -4.12421016

Largest  eigenvalues:
 [1] 66684690 60682149 58609066 56878427 55264730 53790713 52840685 52799296
 [9] 52166320 52096862

Smallest eigenvalues:
 [1]  0.3620760  0.3113102  0.2995721  0.2950472  0.2329229  0.1873973
 [7] -0.6881733 -1.5603092 -6.0852349 -6.3392510

Largest  eigenvalues:
 [1] 65256836 60408090 57713954 56454726 55730408 54309879 52366279 52288782
 [9] 52248147 51439908

Smallest eigenvalues:
 [1]  0.4459016  0.3807232  0.3576178  0.3353257  0.2629456  0.2070865
 [7]  0.1476873 -0.2393412 -0.5145918 -0.7855670

Largest  eigenvalues:
 [1] 63023767 60309143 57494801 55430197 54958970 53717248 52277383 52154793
 [9] 51551160 51437789

Smallest eigenvalues:
 [1]  0.5187706  0.4642415  0.3359671  0.2477922  0.2285410  0.1859766
 [7]  0.1714449  0.1456001 -0.1751883 -1.0665905

Largest  eigenvalues:
 [1] 65373793 60987124 58138293 56265139 55987159 54749104 53310210 52467950
 [9] 52219920 51985931

Smallest eigenvalues:
 [1]  0.4262290  0.4024308  0.3742407  0.2634124  0.2550825  0.1190769
 [7] -0.1349040 -0.1685421 -0.7925196 -7.6016656

Largest  eigenvalues:
 [1] 62819148 60788241 56966599 55944709 55535637 53559968 52433122 51817826
 [9] 51598629 50626433

Smallest eigenvalues:
 [1]  0.55577240  0.43446897  0.41902560  0.33993349  0.32170116  0.23709011
 [7]  0.17652381  0.09464753  0.01828675 -0.09441767

Largest  eigenvalues:
 [1] 63526255 60457112 57401948 55704414 54894829 53845038 52425722 52035579
 [9] 51266485 51034109

Smallest eigenvalues:
 [1]  0.4324403  0.4208085  0.4133311  0.3539754  0.2394450  0.1903392
 [7]  0.1801038  0.1611402  0.1572008 -1.9735867

Largest  eigenvalues:
 [1] 65138153 59657959 57116144 56764834 54472966 53239463 52530811 51860585
 [9] 51590578 51139438

Smallest eigenvalues:
 [1]  0.47356042  0.39096753  0.36568296  0.36123935  0.31504894  0.23708620
 [7]  0.18704086  0.09624224 -0.78948090 -1.29149872

Largest  eigenvalues:
 [1] 64034350 59882415 56942354 55741970 55171011 53304338 52593904 51816111
 [9] 51768567 51490362

Smallest eigenvalues:
 [1]  0.4108492  0.3877276  0.3725132  0.2686506  0.2656074  0.2435019
 [7]  0.1674495 -0.2545117 -0.5957153 -0.6241742

Largest  eigenvalues:
 [1] 66326526 59597349 57476267 56827425 54580306 53226231 52836348 51784316
 [9] 51732317 51189121

Smallest eigenvalues:
 [1]  0.40790431  0.38059126  0.35759345  0.33178546  0.30666632  0.27075535
 [7]  0.17069240  0.08667056 -1.16944187 -7.02873219

Largest  eigenvalues:
 [1] 65193483 59993545 57024317 55793442 55251426 53734860 51938969 51930717
 [9] 51697989 50940859

Smallest eigenvalues:
 [1]  0.4073014  0.3623563  0.3471461  0.3115334  0.2912702  0.2367067
 [7]  0.1772343  0.1739464  0.1491958 -0.7247349

Largest  eigenvalues:
 [1] 62935510 60235648 57734397 55608469 55066275 53944302 51864927 51795751
 [9] 51108338 50912349

Smallest eigenvalues:
 [1]  0.4699147  0.3793932  0.3763677  0.3609598  0.3235279  0.3142769
 [7]  0.2687971  0.2513977  0.1711949 -2.4107203

Largest  eigenvalues:
 [1] 65019610 60862637 57686846 56629285 56005835 54355129 52869719 52542874
 [9] 52455601 51829018

Smallest eigenvalues:
 [1]  0.4921833  0.4446038  0.4009392  0.3940784  0.3670845  0.3387744
 [7]  0.3176323  0.1741172  0.1498292 -2.4320196

Largest  eigenvalues:
 [1] 64427681 60540069 57425278 56487165 55525908 53825368 52595474 52400545
 [9] 52340120 51591104

Smallest eigenvalues:
 [1]  0.4875495  0.4843307  0.4455267  0.4246734  0.4032467  0.3781196
 [7]  0.3406281  0.2605955  0.1958454 -0.9397968

Largest  eigenvalues:
 [1] 64362034 59888859 57072472 55913244 55117746 53452212 51773877 51728354
 [9] 51651998 50827553

Smallest eigenvalues:
 [1]  0.40264033  0.31325205  0.30628064  0.28088188  0.25733521  0.17447651
 [7]  0.16649813 -0.06481802 -0.72899936 -6.54224088

Largest  eigenvalues:
 [1] 61372784 59105290 56549859 54243774 54162652 52559717 51275378 51186962
 [9] 50428687 50236378

Smallest eigenvalues:
 [1]   0.2792596   0.2201584   0.1951173   0.1753320   0.0265760  -2.2120992
 [7]  -5.7463623 -12.7346491 -21.2329126 -21.5134892

Largest  eigenvalues:
 [1] 65200766 60058219 57706057 55964560 55079918 53538228 52380583 52045752
 [9] 51519894 51434454

Smallest eigenvalues:
 [1]  0.29641363  0.19853855  0.19482634  0.16883003  0.13821027  0.01942460
 [7] -0.03854068 -0.41909868 -3.23326978 -7.15120234

Largest  eigenvalues:
 [1] 63570573 59868792 56337855 55963439 54280394 52766669 51814269 51635003
 [9] 51211637 50357496

Smallest eigenvalues:
 [1]   0.4453602   0.3889695   0.2696852   0.1979118   0.1868589   0.1654724
 [7]   0.1209853  -1.4384469  -2.9832532 -10.9793433

Largest  eigenvalues:
 [1] 64870798 59732786 56444227 55505074 54633797 52982657 51730431 51518656
 [9] 51183754 51017705

Smallest eigenvalues:
 [1]  0.4793919  0.4616651  0.3741029  0.3169623  0.2885599  0.2753860
 [7]  0.1927286  0.1137149 -0.1574263 -1.3859297

Largest  eigenvalues:
 [1] 64104119 60136173 56992729 56122838 54963512 53041919 52376500 52077161
 [9] 51921265 51317676

Smallest eigenvalues:
 [1]  0.42056618  0.41677220  0.38714762  0.36220404  0.29625758  0.26425761
 [7]  0.15729375  0.08177521  0.06367278 -5.68002275

Largest  eigenvalues:
 [1] 62381135 59892352 56944626 55331162 54865099 53619296 52009388 51992231
 [9] 51088411 50925634

Smallest eigenvalues:
 [1]  0.60043450  0.55229516  0.55072741  0.46245176  0.38477186  0.33219781
 [7]  0.32344441  0.26941693  0.26315159 -0.05605375

Largest  eigenvalues:
 [1] 63908392 60840590 57686738 56164601 55483676 53618823 52165064 52121277
 [9] 52005600 50962834

Smallest eigenvalues:
 [1]  0.40941992  0.39970536  0.25718644  0.20553070  0.05825044 -0.21487019
 [7] -0.40347000 -0.67216517 -1.20492051 -1.20729750

Largest  eigenvalues:
 [1] 64022154 60425718 57421453 55930293 55457524 53555159 52683443 52070640
 [9] 51934521 51644078

Smallest eigenvalues:
 [1]   0.493962162   0.480239136   0.388753924   0.383544457   0.316339893
 [6]   0.266802151  -0.005463708  -0.057161030  -0.454866654 -11.584169284

Largest  eigenvalues:
 [1] 64550072 60731968 57726750 55692504 55617985 54160713 52769488 52157680
 [9] 51755109 51610363

Smallest eigenvalues:
 [1]  0.40228173  0.31552111  0.29669447  0.26419610  0.20531856  0.06742672
 [7] -0.59135502 -1.50742033 -3.62198587 -9.01804436

Largest  eigenvalues:
 [1] 65242435 60689217 58535715 56848494 55350011 54038897 52858515 52711182
 [9] 52412557 51846831

Smallest eigenvalues:
 [1]   0.4108772   0.3815098   0.3177356   0.2919447   0.2785749   0.2671502
 [7]   0.1958608   0.1509537  -0.2691563 -34.3063728

Largest  eigenvalues:
 [1] 64644945 60258691 57112245 56584953 54885143 53284782 52625848 51745499
 [9] 51709720 50812727

Smallest eigenvalues:
 [1]  0.44570733  0.43136179  0.41884838  0.40844273  0.26684272  0.16679687
 [7]  0.02689899 -0.26363691 -0.56835588 -6.17513348

Largest  eigenvalues:
 [1] 65015620 60289391 57240238 56258634 55224556 53115947 52386670 52055030
 [9] 51817682 51229007

Smallest eigenvalues:
 [1]  0.39076658  0.30620139  0.28027214  0.26838465  0.15545927  0.03372245
 [7] -0.30181851 -0.59014368 -1.30480662 -3.89361080

Largest  eigenvalues:
 [1] 63274055 59328273 56707389 55363613 54737784 52972874 51899737 51542285
 [9] 51269827 50535279

Smallest eigenvalues:
 [1]  0.5161461  0.4873729  0.4869183  0.4456784  0.3816664  0.3645422
 [7]  0.3024546  0.2536135  0.1387770 -0.3952990

Largest  eigenvalues:
 [1] 63583667 59866340 56958344 55914915 54657952 53011737 51908880 51746140
 [9] 51031240 50454538

Smallest eigenvalues:
 [1]  0.4386390  0.3911951  0.3651583  0.3458550  0.3192719  0.2740766
 [7]  0.2487285  0.2103029 -0.5463044 -0.9132883

Largest  eigenvalues:
 [1] 65842884 60379833 58197482 57211775 54905829 53728715 53197779 51953614
 [9] 51758676 51267480

Smallest eigenvalues:
 [1]  0.51474003  0.42466393  0.36673532  0.35004713  0.34442364  0.31938393
 [7]  0.28264187  0.26385162  0.01473139 -1.65254526

Largest  eigenvalues:
 [1] 64232147 60026593 57159312 56536769 54811369 53353597 52431513 52221948
 [9] 51986291 51028120

Smallest eigenvalues:
 [1]  0.36417741  0.30820353  0.27207555  0.26293412  0.23533050  0.21430500
 [7]  0.15797233  0.06621228 -0.14256016 -1.40739999

Largest  eigenvalues:
 [1] 66280439 60256873 58007988 56904667 55187195 53831909 52908858 52656650
 [9] 51696109 51510384

Smallest eigenvalues:
 [1]  0.5416678  0.5261572  0.4922832  0.4147584  0.4141650  0.3949528
 [7]  0.3035864  0.2643716  0.2221183 -0.1620976

Largest  eigenvalues:
 [1] 64133405 60483524 57472989 55525894 55325342 53689331 51888854 51774456
 [9] 51703666 51002115

Smallest eigenvalues:
 [1]   0.44371097   0.42403549   0.37521802   0.29202457   0.28603542
 [6]   0.25322918   0.23373114   0.07113422  -4.62909282 -15.62692252

Largest  eigenvalues:
 [1] 63790069 60537124 57091706 55872700 55198709 54044540 51862734 51630663
 [9] 51246453 50530531

Smallest eigenvalues:
 [1]   0.38929995   0.37506573   0.36868954   0.32004458   0.31589619
 [6]   0.27434874   0.18483187   0.17684090  -0.03761006 -14.14437463

Largest  eigenvalues:
 [1] 62557588 59625581 56891784 55119558 54596424 53330207 51798207 51445110
 [9] 50922762 50766874

Smallest eigenvalues:
 [1]  0.5272973  0.3849396  0.3841447  0.3205607  0.3150492  0.3093808
 [7]  0.2720532 -0.4080563 -0.7311009 -0.7398283

Largest  eigenvalues:
 [1] 65002529 60346942 57757186 56607651 55373300 53805874 52818378 52730570
 [9] 52126266 51251488

Smallest eigenvalues:
 [1]   0.4527231   0.3520761   0.3125946   0.2835301   0.2639696   0.2433599
 [7]   0.2346522   0.2129127   0.2121767 -47.0272980

Largest  eigenvalues:
 [1] 63578345 59846460 56995950 55783146 54932017 53273873 51842079 51823057
 [9] 51761321 50978558

Smallest eigenvalues:
 [1]  0.51053661  0.49367922  0.46542859  0.43739684  0.38594699  0.30683133
 [7]  0.24551698  0.23853101 -0.05231138 -0.20058894

Largest  eigenvalues:
 [1] 64472977 60302040 57456427 55974053 54856355 53509806 52053331 52009115
 [9] 51746006 51239364

Smallest eigenvalues:
 [1]  0.55243864  0.50350228  0.48772750  0.39806217  0.35248170  0.30528158
 [7]  0.21498327  0.20850888  0.01982676 -0.94523494

Largest  eigenvalues:
 [1] 63876450 60715516 57608421 55852721 55762732 54294908 52550423 52157952
 [9] 51882153 51274727

Smallest eigenvalues:
 [1]   0.34765242   0.23475870   0.20018750   0.19615798   0.17217104
 [6]   0.07853328   0.07581293  -0.25391967 -14.60019297 -23.23722275

Largest  eigenvalues:
 [1] 64846506 60100147 56859529 56326514 55396860 53765321 52289331 52232157
 [9] 51755971 51339123

Smallest eigenvalues:
 [1]  0.35915809  0.34183643  0.29880684  0.29326309  0.02126389 -0.02008096
 [7] -0.07364751 -0.90829768 -0.93172381 -1.97376623

Largest  eigenvalues:
 [1] 64648089 59284634 56695111 55407157 53907633 52321700 51802478 51282756
 [9] 50899172 50868645

Smallest eigenvalues:
 [1]  0.5945667  0.5912657  0.5732336  0.5059641  0.4862638  0.3333659
 [7]  0.3173061  0.2106485  0.1670870 -0.9075313

Largest  eigenvalues:
 [1] 64689216 60263316 56858979 56217166 55175319 53330521 52191077 52008612
 [9] 51764950 50826176

Smallest eigenvalues:
 [1]  0.53067501  0.46535419  0.39059203  0.36303622  0.29862882  0.28498252
 [7]  0.19101920  0.18783262  0.08313483 -0.01668797

Largest  eigenvalues:
 [1] 63100317 61104240 58104763 56025735 55097270 54584448 52647018 52449401
 [9] 51407199 51256021

Smallest eigenvalues:
 [1]  0.4649662  0.4456508  0.4451130  0.3995442  0.3427075  0.2968905
 [7]  0.2295695  0.1795657  0.1278092 -0.5961903

Largest  eigenvalues:
 [1] 65700641 60157099 57324520 56436964 55339609 53508899 52524768 52437061
 [9] 51532328 51231568

Smallest eigenvalues:
 [1]  0.5577856  0.4527810  0.4458934  0.3835374  0.3776193  0.2802705
 [7]  0.2154514  0.1445144  0.1419363 -0.3563632

Largest  eigenvalues:
 [1] 65223421 60895085 57957820 56144633 56035443 54525575 52900697 52616035
 [9] 52215987 51968281

Smallest eigenvalues:
 [1]  0.39782567  0.28823019  0.28446353  0.22069442  0.21553641  0.16863895
 [7] -0.05032267 -0.31141126 -5.81575747 -7.69533560

Largest  eigenvalues:
 [1] 64266262 60453536 57504345 55727525 55579695 54127336 52721205 52502688
 [9] 51816277 51631943

Smallest eigenvalues:
 [1]  0.44744161  0.38635530  0.23092578  0.18898982  0.12466762  0.09420096
 [7] -0.37322925 -0.58675489 -0.67412324 -0.68564567

Largest  eigenvalues:
 [1] 62952282 59101338 56355655 55410283 54201069 52615221 51341441 51200414
 [9] 51149735 50090481

Smallest eigenvalues:
 [1]   0.4273844   0.3784932   0.3661989   0.3221397   0.2524620   0.2348463
 [7]   0.2198620   0.1243170  -0.1306255 -25.9120523

Largest  eigenvalues:
 [1] 62738387 59750516 56664971 55210634 55045756 53362807 51999932 51205489
 [9] 51059326 50578585

Smallest eigenvalues:
 [1]  0.44173118  0.41766847  0.29663689  0.21335419  0.20210994  0.19522354
 [7]  0.12163997  0.08712377 -0.87484163 -0.94663227

Largest  eigenvalues:
 [1] 63228112 60321751 57075243 55574710 55039494 53586446 51891349 51584565
 [9] 50855745 50627836

Smallest eigenvalues:
 [1]  0.54377460  0.50828821  0.48854719  0.44163766  0.39240959  0.34669646
 [7]  0.34436526  0.05140154 -0.11122891 -0.12596470

Largest  eigenvalues:
 [1] 64972987 59924104 57022200 56462457 54575562 53044294 52397338 51748978
 [9] 51333843 50759189

Smallest eigenvalues:
 [1]  0.4501406  0.3606449  0.3351489  0.3155514  0.2163558  0.2070481
 [7]  0.1606351  0.1485936 -0.1166917 -0.2877739

Largest  eigenvalues:
 [1] 67238662 60641681 57599752 56898376 55157188 53462277 53003532 52552273
 [9] 52034346 51949087

Smallest eigenvalues:
 [1]  0.4855776  0.4711871  0.4461184  0.3601130  0.2894634  0.2743768
 [7]  0.2119518 -0.1307573 -0.2655882 -0.9586734

Largest  eigenvalues:
 [1] 64497109 59896533 57400680 55305819 55219157 53409811 52068333 51737399
 [9] 51573997 50837992

Smallest eigenvalues:
 [1]   0.397829888   0.378073963   0.253567315   0.238277959  -0.004018831
 [6]  -0.052295377  -0.718975220  -4.879905883  -8.571938271 -21.245612591

Largest  eigenvalues:
 [1] 65227248 60081534 57273826 56045157 54716364 53229891 52335017 51657238
 [9] 51447147 50440667

Smallest eigenvalues:
 [1]  0.5777902  0.5285264  0.4764035  0.4534884  0.4225118  0.3819935
 [7]  0.2901142  0.1287401 -0.1943729 -1.4644464

Largest  eigenvalues:
 [1] 64501969 60242924 57223600 56167665 55240134 53424745 52657127 52244620
 [9] 51582444 51246166

Smallest eigenvalues:
 [1]  0.4123787  0.3451237  0.3297252  0.3157962  0.2970803  0.2515298
 [7]  0.2125220  0.1820318 -1.5221512 -4.7396950

Largest  eigenvalues:
 [1] 64328113 60651351 57779927 55547709 55502927 54104763 52402784 51958694
 [9] 51635639 51565368

Smallest eigenvalues:
 [1]   0.4577761   0.4134344   0.3510479   0.3415856   0.3107431   0.2597804
 [7]   0.1743676   0.1305305  -1.8441918 -28.0020569

Largest  eigenvalues:
 [1] 61973462 59664291 56461507 55476436 54390708 53466216 51743112 51099796
 [9] 50388622 50217819

Smallest eigenvalues:
 [1]  0.5247866  0.4481411  0.3969670  0.3632418  0.3431483  0.2947796
 [7]  0.2111178 -0.2536880 -0.4566583 -0.8078062

Largest  eigenvalues:
 [1] 65334554 60569274 58060601 56851042 55045442 53257582 52875732 52745624
 [9] 51926352 51763399

Smallest eigenvalues:
 [1]  0.5285832  0.5109925  0.4110934  0.3956321  0.3101972  0.3050851
 [7]  0.2164226  0.2047794  0.1906650 -0.5883761

Largest  eigenvalues:
 [1] 64711578 60930732 57488225 55999436 55603184 54019738 52340364 52305763
 [9] 52104855 51531114

Smallest eigenvalues:
 [1]   0.4575469   0.4278374   0.3985803   0.3787255   0.3161689   0.3017975
 [7]   0.2532425   0.2508443  -0.2244553 -11.3013510

Largest  eigenvalues:
 [1] 64409557 60146794 57524712 56331382 55217776 53678895 52329437 51929172
 [9] 51903538 50804662

Smallest eigenvalues:
 [1]  0.5660977  0.5614655  0.5025169  0.4962164  0.4902495  0.4348534
 [7]  0.2947021  0.2288873  0.1432563 -0.0124105

Largest  eigenvalues:
 [1] 64272907 60490907 57640892 55890379 55139834 53237009 52178205 52093895
 [9] 51549961 51073268

Smallest eigenvalues:
 [1]  0.4431478  0.4399100  0.4218137  0.4167145  0.2463045  0.1689906
 [7] -0.0104216 -0.2808190 -0.8529293 -3.8373678

Largest  eigenvalues:
 [1] 64369733 60285334 57746115 55893417 55085712 53579532 52270457 52075367
 [9] 51783573 51100670

Smallest eigenvalues:
 [1]   0.3130513   0.2887261   0.2371672   0.1944272   0.1386723   0.1364611
 [7]   0.1232128  -1.9232410  -7.9194896 -13.1183649

Largest  eigenvalues:
 [1] 64122534 60696893 57585419 55828909 55245155 54151600 52613778 52106942
 [9] 51752157 51433019

Smallest eigenvalues:
 [1]   0.43999769   0.40226682   0.39649554   0.27970738   0.05430193
 [6]  -0.22573704  -1.05289146  -2.37022721 -11.90138962 -16.72403737

Largest  eigenvalues:
 [1] 65449488 59823464 56982782 56805929 54551980 52740904 52379025 51820153
 [9] 51381166 50837962

Smallest eigenvalues:
 [1]  0.579456899  0.502435226  0.482807395  0.421048881  0.410055727
 [6]  0.381170650  0.261967219  0.178262799 -0.004355218 -0.480903358

Largest  eigenvalues:
 [1] 64438436 60590422 57406434 55759978 55464624 53731275 52880215 51914190
 [9] 51527865 51403591

Smallest eigenvalues:
 [1]   0.407300773   0.392086813   0.325684139   0.273974301   0.256428816
 [6]   0.164179897  -0.004469679  -0.671087013  -1.378044525 -20.738203116

Largest  eigenvalues:
 [1] 64822376 60634447 57631224 55769033 55603540 54267664 52559980 52310632
 [9] 51797851 51487891

Smallest eigenvalues:
 [1]  0.4137713  0.3905699  0.3565862  0.3275166  0.2977538  0.2717841
 [7]  0.1819313  0.0169558 -0.1748779 -0.1783005

Largest  eigenvalues:
 [1] 65922539 60860854 57672089 56012614 55589909 53768319 52651681 52152045
 [9] 51932414 51794458

Smallest eigenvalues:
 [1]  0.473353171  0.386313278  0.373284754  0.329610294  0.321103884
 [6]  0.254320967  0.245538546  0.222118931  0.002710441 -1.949912830

Largest  eigenvalues:
 [1] 65590939 60386123 57607027 56710983 55142854 53711026 52580888 52422018
 [9] 51947321 51574801

Smallest eigenvalues:
 [1]  0.4945280  0.4238950  0.3803603  0.2546834  0.2224167  0.2060694
 [7] -0.3301968 -0.4081751 -1.7085810 -3.1578185

Largest  eigenvalues:
 [1] 66363963 60972172 58399351 56724628 55903984 54118487 52994515 52849238
 [9] 52383466 52052659

Smallest eigenvalues:
 [1]  0.42914077  0.35112878  0.31436844  0.30790343  0.24369747  0.24065081
 [7]  0.19301158  0.09533672 -0.15580056 -5.59920431

Largest  eigenvalues:
 [1] 65193948 59359400 56842649 56018359 54657947 53084381 51988950 51280754
 [9] 51181011 50571546

Smallest eigenvalues:
 [1]  0.44540364  0.39647879  0.38906845  0.28337812  0.24560944  0.21852804
 [7]  0.17799999  0.09528115 -0.14839172 -0.31872084

Largest  eigenvalues:
 [1] 66792483 61350523 58455361 56892051 55538783 53790808 53077143 52875836
 [9] 52053187 51988881

Smallest eigenvalues:
 [1]  0.55952852  0.51764265  0.50001523  0.46404429  0.44538113  0.44402248
 [7]  0.24070330  0.23478026  0.05481448 -0.04383853

Largest  eigenvalues:
 [1] 62692441 60109822 56752820 55453947 55236769 53376613 52221842 51651821
 [9] 51206136 50448952

Smallest eigenvalues:
 [1]  0.6267241  0.5998844  0.5530882  0.5524737  0.4416732  0.4369281
 [7]  0.3279452  0.2550960  0.1971534 -0.8838666

Largest  eigenvalues:
 [1] 64761478 60403651 57609591 56257067 55162259 53729655 52228340 52002230
 [9] 51812555 50983509

Smallest eigenvalues:
 [1]  0.4826473  0.4228256  0.3656121  0.3600153  0.3477249  0.3439085
 [7]  0.2083771  0.1947293 -0.5610049 -2.6252851

Largest  eigenvalues:
 [1] 64008134 59959024 57243562 56178801 54866342 53224151 52107288 52055389
 [9] 51687140 50616711

Smallest eigenvalues:
 [1]  0.6159226  0.5157152  0.5116598  0.4669934  0.4399881  0.3838208
 [7]  0.3699063  0.3082080  0.1883525 -0.1889362

Largest  eigenvalues:
 [1] 65133528 61181729 58309661 56526524 56293937 54673842 53450112 52625344
 [9] 52499007 51921232

Smallest eigenvalues:
 [1]  0.4760437  0.4668003  0.4293443  0.3952245  0.3801807  0.3672524
 [7]  0.3519612  0.1837539  0.1387142 -0.6580002

Largest  eigenvalues:
 [1] 64887470 61097338 58163693 56198046 56038588 54481068 52530406 52495724
 [9] 52176568 51678814

Smallest eigenvalues:
 [1]  0.46768616  0.45620225  0.39409128  0.35109722  0.34220883  0.31387560
 [7]  0.30997247  0.11256245  0.06658107 -2.99363539

Largest  eigenvalues:
 [1] 64334090 59488325 56631915 55969789 54474328 52777639 51983950 51483351
 [9] 51476566 50541576

Smallest eigenvalues:
 [1]  0.43370938  0.37139639  0.36564579  0.29066053  0.24592875  0.24374540
 [7]  0.21965733  0.09210695 -1.32531585 -7.57687311

Largest  eigenvalues:
 [1] 64922553 60111053 57321327 55982375 55029462 53636310 52062716 51779950
 [9] 51730159 50806505

Smallest eigenvalues:
 [1]   0.40150300   0.35584018   0.30906548   0.23974026   0.16015790
 [6]   0.06549485  -0.01829593  -0.90373968  -1.40924301 -11.73826233

Largest  eigenvalues:
 [1] 65594886 60841569 58168537 56319756 55590571 54082489 52811001 52331485
 [9] 52074493 51587397

Smallest eigenvalues:
 [1]  0.51077279  0.47981713  0.46476457  0.45878954  0.43980515  0.40873839
 [7]  0.40144307  0.31094595  0.08014935 -0.13509335

Largest  eigenvalues:
 [1] 63646959 59607637 57339683 55419658 54936795 53229512 51584319 51530131
 [9] 51421068 50469507

Smallest eigenvalues:
 [1]  0.3073931  0.2930366  0.2597274  0.2550049  0.2085749  0.1056647
 [7] -0.2352336 -0.4998183 -1.3890788 -4.3409479

Largest  eigenvalues:
 [1] 65416691 59465517 57051025 56035790 54260323 52730294 52149977 51766651
 [9] 51470333 51088403

Smallest eigenvalues:
 [1]   0.4190005   0.3460691   0.3336302   0.3272618   0.2213292   0.1830725
 [7]  -1.0805507  -3.0684524  -3.3445998 -10.3133783

Largest  eigenvalues:
 [1] 65737787 60089277 57436722 57309202 54759970 53183730 53151518 52437514
 [9] 52249643 51672466

Smallest eigenvalues:
 [1]   0.36984410   0.32354837   0.24748929   0.22111587   0.14126368
 [6]   0.13077740   0.10501490   0.06099851  -0.61134840 -14.18339231

Largest  eigenvalues:
 [1] 65764822 59896029 57470203 56665039 54688670 53054987 52707939 51908814
 [9] 51627244 51108944

Smallest eigenvalues:
 [1]  0.5819184  0.5608733  0.3754795  0.3612453  0.3017642  0.2798739
 [7]  0.2691494  0.2636202  0.2414923 -1.4905963

Largest  eigenvalues:
 [1] 65110472 60612278 57822830 56161695 55523546 54173962 52314028 52294596
 [9] 52235862 51311441

Smallest eigenvalues:
 [1]  0.3524496  0.3458904  0.3260322  0.3108317  0.2751863  0.2682491
 [7]  0.2303524  0.1790908 -0.6312919 -1.5618378

Largest  eigenvalues:
 [1] 64602493 60763712 57862391 56431761 55977201 54216431 52373058 52224317
 [9] 52088643 51186602

Smallest eigenvalues:
 [1]  0.4629705  0.4458128  0.4374147  0.3750568  0.3426212  0.3401255
 [7]  0.2391934  0.1461593  0.0739874 -0.2468892

Largest  eigenvalues:
 [1] 64424944 61143015 57717909 56311141 55838433 54251583 52467238 52125546
 [9] 51997919 51275565

Smallest eigenvalues:
 [1]  0.47285252  0.43627100  0.38707403  0.32341508  0.31561133  0.19820748
 [7]  0.13297387  0.02921038 -0.09971439 -3.74691374

Largest  eigenvalues:
 [1] 61722328 59500264 56818489 54664848 54394991 52931245 51660575 51550804
 [9] 50814602 50625100

Smallest eigenvalues:
 [1]  0.4035618  0.3801351  0.3149668  0.3064326  0.3054499  0.2614515
 [7]  0.2355876  0.2210825 -0.4099762 -0.9586278

Largest  eigenvalues:
 [1] 64106118 60272910 57575847 55655209 55192127 53702907 51909633 51723919
 [9] 51719551 51042130

Smallest eigenvalues:
 [1]  0.47131514  0.45438683  0.35194818  0.27723457  0.25839899  0.24195155
 [7]  0.22931960 -0.00658627 -0.17208871 -0.17659668

Largest  eigenvalues:
 [1] 65248965 60892989 58104344 55747389 55560101 54328809 52647524 52370895
 [9] 51816747 51663061

Smallest eigenvalues:
 [1]  0.5154123  0.4797545  0.3853984  0.3600652  0.3122994  0.2819511
 [7]  0.2778904  0.2715248 -0.8974183 -1.5345765

Largest  eigenvalues:
 [1] 64862637 59754598 57172231 55934843 54958512 53573132 51990718 51950527
 [9] 51677258 51116495

Smallest eigenvalues:
 [1]  0.4214306  0.4110650  0.4050761  0.3763895  0.3110774  0.2695821
 [7]  0.1962728  0.1687833  0.1519829 -0.1058320

Largest  eigenvalues:
 [1] 64238636 60048155 57359374 55482445 55406002 53809849 52232140 51978960
 [9] 51547965 51201307

Smallest eigenvalues:
 [1]   0.277144729   0.214681764   0.159625608   0.076487123   0.022964958
 [6]   0.005611657  -0.111955304  -0.861141442 -15.397538787 -17.238356175

Largest  eigenvalues:
 [1] 62449725 60143066 56267634 55237774 55162765 53416462 51961707 51875288
 [9] 50966727 50446254

Smallest eigenvalues:
 [1]  0.5100599  0.4865241  0.4829214  0.4238372  0.4060621  0.3861233
 [7]  0.3376398  0.3364275  0.2984327 -1.1160096

Largest  eigenvalues:
 [1] 65260449 60596029 57727287 56696319 55462784 53943489 52572445 52297343
 [9] 51834597 51258823

Smallest eigenvalues:
 [1]  0.57145427  0.55753269  0.53459171  0.53095143  0.44756498  0.37224306
 [7]  0.35544234  0.32169649  0.31249705 -0.05275244

Largest  eigenvalues:
 [1] 65558192 61059809 58282166 57127677 55603915 53980074 53089171 52803432
 [9] 52324969 51803867

Smallest eigenvalues:
 [1]  0.37653562  0.36138815  0.35813638  0.27276133  0.19882070 -0.07922013
 [7] -0.30848050 -1.08283429 -3.13802442 -9.46730544

Largest  eigenvalues:
 [1] 63085319 60049489 56991183 55248438 55220761 53434653 52200551 51831758
 [9] 51249734 51036070

Smallest eigenvalues:
 [1]  0.5203221  0.4873814  0.4515710  0.4095868  0.3490400  0.2566253
 [7]  0.2142105  0.1203538 -0.4237941 -0.4264951

Largest  eigenvalues:
 [1] 64156010 60635895 58362659 55865418 55442212 54608723 52762325 52204606
 [9] 51595217 51412822

Smallest eigenvalues:
 [1]  0.4032245  0.3893146  0.3863251  0.3032663  0.2595042  0.2593872
 [7]  0.2391131  0.2389307  0.2120504 -0.9185261

Largest  eigenvalues:
 [1] 64574369 60691638 57758946 55713216 55647294 54280606 52424015 52010041
 [9] 51820598 51168637

Smallest eigenvalues:
 [1]  0.36192509  0.26728992  0.03431254 -0.01634378 -0.04062130 -0.08608666
 [7] -0.44391988 -0.66291506 -1.10601940 -1.15066329

Largest  eigenvalues:
 [1] 62087352 60191546 56866220 55555559 55180859 53718368 52364337 51850741
 [9] 50922203 50808616

Smallest eigenvalues:
 [1]  0.3772597510  0.3292329620  0.2687995420  0.2523414433  0.2378080414
 [6]  0.2186807557  0.0560499362  0.0003070804 -2.6481189196 -6.3232371937

Largest  eigenvalues:
 [1] 63782306 60608112 57859641 55782364 55779705 54129684 52668698 52177968
 [9] 51786156 51648349

Smallest eigenvalues:
 [1]  0.5233690  0.4437868  0.4241692  0.4111181  0.4055430  0.3617718
 [7]  0.3509802  0.3417824  0.3302832 -0.4323087

Largest  eigenvalues:
 [1] 63482282 59878366 56893612 55701351 54776503 53199528 51696878 51464134
 [9] 51183533 50362063

Smallest eigenvalues:
 [1]  0.4488624  0.4088865  0.3980209  0.3884198  0.3125796  0.2777834
 [7]  0.2760359  0.2501593  0.1885041 -1.3077888

Largest  eigenvalues:
 [1] 64149204 60041350 56955629 56047051 54999193 53376109 51993359 51850399
 [9] 51711345 51028895

Smallest eigenvalues:
 [1]  0.4166548  0.2597084  0.2583535  0.2320402  0.2255468  0.1859566
 [7]  0.1799141 -2.1804519 -4.1661929 -6.1697151

Largest  eigenvalues:
 [1] 64882251 59920192 56949407 56574538 54648363 53160227 52342638 52232011
 [9] 51734730 50997739

Smallest eigenvalues:
 [1]   0.5272917   0.4095600   0.3948305   0.3046950   0.2475154   0.2275251
 [7]  -0.1532177  -0.3268616  -0.7947572 -19.8696438

Largest  eigenvalues:
 [1] 65358244 60066596 57055828 55849338 54942025 53381722 52059797 52009717
 [9] 51628753 51226113

Smallest eigenvalues:
 [1]  0.50273204  0.50209258  0.46063776  0.37593047  0.36467257  0.35484522
 [7]  0.26495825  0.23441842 -0.02816597 -0.40853757

Largest  eigenvalues:
 [1] 62632943 59753858 56714706 55162487 54708107 53279468 51918442 51717350
 [9] 50859528 50612904

Smallest eigenvalues:
 [1]  0.47437986  0.44415297  0.43620424  0.40146302  0.38365035  0.34035738
 [7]  0.32023747  0.08923091 -0.01309224 -0.12941651

Largest  eigenvalues:
 [1] 63703038 60259754 57314930 55437871 54815591 53387231 51959068 51488468
 [9] 51477153 51118986

Smallest eigenvalues:
 [1]  0.4210618  0.4166619  0.3982851  0.2895063  0.2790783  0.2592374
 [7]  0.1796040  0.1664031  0.1333599 -0.1070419

Largest  eigenvalues:
 [1] 64587864 61193033 58200081 56047958 55685895 54144612 52822672 52197810
 [9] 52170049 51940656

Smallest eigenvalues:
 [1]  0.4844979  0.4515795  0.3957639  0.3685315  0.3619856  0.2719537
 [7]  0.2345142 -0.1887088 -0.2779968 -0.5223525

Largest  eigenvalues:
 [1] 63709288 59778623 57400401 55296419 54912841 53616548 51897370 51476591
 [9] 51207765 50669660

Smallest eigenvalues:
 [1]  0.47636033  0.41777917  0.41485096  0.36978931  0.32379331  0.31066984
 [7]  0.28828535  0.20830662  0.15596870 -0.03956168

Largest  eigenvalues:
 [1] 64191901 59420600 57241350 55558927 54466917 53029562 51836568 51712867
 [9] 51253439 50822922

Smallest eigenvalues:
 [1]   0.4408627   0.4142176   0.4055389   0.3828166   0.3689204   0.3423735
 [7]   0.3056915   0.2727094  -0.3386079 -35.0000879

Largest  eigenvalues:
 [1] 66204329 60463825 57849191 57064284 55079541 53692004 53074905 51940792
 [9] 51891991 51084282

Smallest eigenvalues:
 [1]  0.4481405  0.3482361  0.3100445  0.2780136  0.2669352  0.2583741
 [7] -0.1721777 -0.4230542 -3.6672215 -5.0348088

Largest  eigenvalues:
 [1] 65302807 59940230 57841173 56458913 55204677 53999009 52710915 52391616
 [9] 52386422 51826046

Smallest eigenvalues:
 [1]  0.3431130  0.3033891  0.3020519  0.2658873  0.2407580  0.2294935
 [7] -0.6470565 -0.7433620 -1.3538775 -8.8507396

Largest  eigenvalues:
 [1] 62330565 59868631 57460374 55868313 54143647 54070883 52339890 52045901
 [9] 50999348 50683380

Smallest eigenvalues:
 [1]   0.259414034   0.235911394   0.182107200   0.142726388   0.130404902
 [6]   0.029811818   0.023267256   0.007202171  -0.994741717 -21.206815907

Largest  eigenvalues:
 [1] 62877784 60705250 57741091 55542502 55186497 53948591 52171000 51819497
 [9] 51353228 51205627

Smallest eigenvalues:
 [1]  0.5737969  0.4855040  0.4784855  0.4346783  0.3908720  0.3289955
 [7]  0.3010678  0.2782222  0.2361162 -1.1183358

Largest  eigenvalues:
 [1] 65216103 61054494 57854856 56793021 55371383 53880409 52798391 52707747
 [9] 52163630 51912475

Smallest eigenvalues:
 [1]  0.5294325  0.4635894  0.4617910  0.4325612  0.4084160  0.3373342
 [7]  0.2814365  0.2560524  0.1294240 -0.1843345

Largest  eigenvalues:
 [1] 65449410 60014994 57825275 56587435 54687188 53050099 52825876 51791074
 [9] 51467864 50887624

Smallest eigenvalues:
 [1]   0.4221387   0.4184757   0.4086284   0.3485475   0.3457772   0.2967528
 [7]   0.1941861   0.1921846  -0.5077250 -21.1804028

Largest  eigenvalues:
 [1] 64988465 60352046 57684700 56518824 55109053 53392058 52701138 51982890
 [9] 51888836 50972132

Smallest eigenvalues:
 [1]  0.5082897  0.4282380  0.4250931  0.4011988  0.3824082  0.3780757
 [7]  0.3031114  0.1892091  0.1795391 -1.7545148

Largest  eigenvalues:
 [1] 62917392 60240179 57547923 55380784 54903530 53808175 51886213 51787727
 [9] 51064877 50910118

Smallest eigenvalues:
 [1]  0.6067477  0.5927991  0.5574038  0.5474962  0.4485107  0.3760682
 [7]  0.2543690  0.2059890  0.1842158 -0.8582076

Largest  eigenvalues:
 [1] 64328609 60026389 56836071 55823284 54973607 53315746 51705917 51629483
 [9] 51386606 50498134

Smallest eigenvalues:
 [1]   0.12910512   0.07293391   0.06951283  -0.05119517  -0.34512771
 [6]  -1.88304651  -9.40686953 -27.09433150 -33.18028364 -48.11054503

Largest  eigenvalues:
 [1] 65153055 60164456 56442164 56310870 55170708 53288162 52298985 52261900
 [9] 52154918 51110187

Smallest eigenvalues:
 [1]  0.37225355  0.34600652  0.34468136  0.31751447  0.28717586  0.08619961
 [7]  0.07734499  0.05279732 -1.03268731 -3.56855177

Largest  eigenvalues:
 [1] 62680167 59026230 56573960 54997849 54694230 53055512 51846640 51479952
 [9] 50871104 50478001

Smallest eigenvalues:
 [1]  0.45239730  0.42975724  0.41104833  0.36258756  0.32181852  0.26670411
 [7]  0.23487867  0.05102641 -0.17237684 -0.29572263

Largest  eigenvalues:
 [1] 62220890 59303055 56861079 54802973 54441244 52855126 51857810 51233709
 [9] 50933831 50785243

Smallest eigenvalues:
 [1]  0.3818677  0.3782604  0.3633752  0.3357047  0.2888086  0.2556823
 [7]  0.2234954  0.1470575  0.1369593 -0.8735760

Largest  eigenvalues:
 [1] 63566785 60083765 57099975 55489036 55235344 53896763 52321413 51908615
 [9] 51385316 51165763

Smallest eigenvalues:
 [1]  0.4966688  0.4788885  0.3355494  0.3007781  0.2672923  0.2261897
 [7]  0.2238763  0.1019961 -1.0912447 -6.6039892

Largest  eigenvalues:
 [1] 64653666 60869496 57258495 56228121 55780385 53967814 52447747 52254164
 [9] 51917458 51453584

Smallest eigenvalues:
 [1]  0.4381800  0.4316199  0.3983476  0.3187999  0.2771435  0.2724599
 [7]  0.2346466 -0.1702307 -0.3342011 -0.6965179

Largest  eigenvalues:
 [1] 64594942 60348314 57792539 56532087 55357813 53889448 52964796 52564120
 [9] 52142880 51682595

Smallest eigenvalues:
 [1]  0.4496823  0.4016000  0.3382060  0.3209556  0.3098294  0.2719140
 [7]  0.2412580  0.1896744 -0.1484066 -2.0483270

Largest  eigenvalues:
 [1] 63997836 60440199 57335456 56061634 55668833 53991379 52219031 52098254
 [9] 52005859 50985152

Smallest eigenvalues:
 [1]  0.4811915  0.4304199  0.3407603  0.3148029  0.2680707  0.2468190
 [7]  0.2433870  0.1324856  0.1152177 -0.1885876

Largest  eigenvalues:
 [1] 63562644 60086269 57788449 55269061 55220238 53850732 52230843 52143408
 [9] 51429268 51262170

Smallest eigenvalues:
 [1]  0.43073613  0.39598935  0.33275605  0.30962494  0.27688007  0.23739327
 [7]  0.19458683  0.02997172 -0.05313936 -0.28813060

Largest  eigenvalues:
 [1] 64527663 61100911 57750556 56518302 55405523 53767320 52422619 52388936
 [9] 51715561 51329513

Smallest eigenvalues:
 [1]  0.4527159  0.4336027  0.4120107  0.3264515  0.2806342  0.2378237
 [7]  0.1783002 -0.1671808 -0.2362833 -5.3096692

Largest  eigenvalues:
 [1] 61972903 60005066 56538383 55233509 54318343 53454239 52027901 51511951
 [9] 50551854 50315658

Smallest eigenvalues:
 [1]  0.4417027  0.3347862  0.3318064  0.3074318  0.2699170  0.2271045
 [7]  0.2229960  0.1944539 -1.7985666 -4.7750955

Largest  eigenvalues:
 [1] 64265014 60124704 57239178 56157164 54913847 53564161 52347347 52224350
 [9] 52190012 51355914

Smallest eigenvalues:
 [1]  0.47951890  0.47565483  0.43251610  0.34003769  0.31453153  0.12543344
 [7]  0.10880617  0.08034982 -0.23906263 -0.25008458

Largest  eigenvalues:
 [1] 64350979 59859908 57085181 56078613 54226984 52761362 52079246 51814823
 [9] 51413064 50955594

Smallest eigenvalues:
 [1]  0.5019727  0.4918704  0.3884751  0.3039743  0.2629069  0.1860632
 [7]  0.1098385 -0.1473894 -0.9991205 -4.6168133

Largest  eigenvalues:
 [1] 63305817 60798931 57621039 56131025 55187364 54301559 52956833 52296974
 [9] 51988309 51344844

Smallest eigenvalues:
 [1]  0.50341827  0.47562266  0.46253639  0.40748343  0.34715293  0.31451924
 [7]  0.30546726  0.24999597  0.01766297 -1.45991536

Largest  eigenvalues:
 [1] 65427219 60458005 57412597 56859672 55327476 53704865 52904921 52425012
 [9] 51836097 51417679

Smallest eigenvalues:
 [1]  0.3351082  0.2863840  0.2438458  0.2166721  0.2130028  0.1592809
 [7] -0.2582428 -4.6442186 -7.5484116 -8.3979607

Largest  eigenvalues:
 [1] 66474731 61071583 58821985 57012305 55678299 54316549 52989560 52901448
 [9] 52556932 52246237

Smallest eigenvalues:
 [1]  0.4002648  0.3428217  0.3320428  0.3271492  0.2514968  0.2120884
 [7]  0.1016588 -0.2699683 -1.6983558 -6.6061162

Largest  eigenvalues:
 [1] 66065561 59791156 56893225 56787147 54470057 52988021 52519534 51363955
 [9] 51317347 50587361

Smallest eigenvalues:
 [1]  0.57368883  0.51412926  0.40952501  0.35193654  0.31713598  0.30383883
 [7]  0.28670960  0.17305459  0.06471892 -0.48991242

Largest  eigenvalues:
 [1] 63811778 60105002 57330817 55434262 54714645 53254830 51953399 51625900
 [9] 51485871 50917303

Smallest eigenvalues:
 [1]  0.5223011  0.4422109  0.4303282  0.4099498  0.4033249  0.3882165
 [7]  0.3328612  0.2392868  0.2249731 -0.7703900

Largest  eigenvalues:
 [1] 64005988 61088038 57811873 56237333 55856227 54235906 52552181 52402561
 [9] 52098404 51342715

Smallest eigenvalues:
 [1]  0.53425894  0.48777593  0.47289628  0.45649236  0.43235734  0.41169416
 [7]  0.23800134  0.16890563  0.02712257 -4.13467303

Largest  eigenvalues:
 [1] 63558925 59683960 57096125 55326559 55323519 53734377 52097261 52057624
 [9] 51323889 51040636

Smallest eigenvalues:
 [1]   0.11308089   0.08086033   0.05926124  -0.06016864  -0.20375368
 [6]  -0.45388423  -0.48104215  -6.55025643  -8.53189029 -13.72622378

Largest  eigenvalues:
 [1] 60203992 59667671 57183170 55558366 53778750 53539625 51805577 51783634
 [9] 50886306 50188598

Smallest eigenvalues:
 [1]  0.6042306  0.5946579  0.5763476  0.4978116  0.4056226  0.2799841
 [7]  0.2220836  0.1684605 -0.9054644 -1.3985510

Largest  eigenvalues:
 [1] 65266362 60365648 57316716 56578301 55199894 53460254 52474940 52264363
 [9] 52036026 51211656

Smallest eigenvalues:
 [1]   0.33016698   0.31910528   0.31804658   0.25808180   0.22520935
 [6]   0.08478568   0.02300430  -1.50545489  -3.97236433 -12.94926674

Largest  eigenvalues:
 [1] 66743039 60618127 58054794 57125957 55237153 53445825 53378151 52278860
 [9] 52014812 51365546

Smallest eigenvalues:
 [1]   0.1735173   0.1715748  -0.1342431  -0.1597266  -0.2054492  -2.8952218
 [7] -10.7840417 -14.1758333 -18.0135490 -45.6083195

Largest  eigenvalues:
 [1] 64138061 60309180 57625721 55555563 55094754 53900992 52416953 52335947
 [9] 51403954 51311170

Smallest eigenvalues:
 [1]  0.57309293  0.44400917  0.44251446  0.23416016  0.20330501  0.02873755
 [7] -0.03499777 -0.07899451 -0.71605283 -9.51492122

Largest  eigenvalues:
 [1] 63725117 60096339 57044148 55605588 55296935 53597972 52377618 52056956
 [9] 51639836 51228933

Smallest eigenvalues:
 [1]  0.311450710  0.308014161  0.250101929  0.159539669  0.147845101
 [6] -0.001237055 -0.020688332 -0.903911591 -1.458401957 -2.481793939

Largest  eigenvalues:
 [1] 64610281 59993688 56506071 56059537 54536632 52879752 52107641 51544599
 [9] 51427655 50596643

Smallest eigenvalues:
 [1]   0.1872282   0.1579812  -0.2458350  -0.3544927  -0.4591195  -0.7787538
 [7]  -1.3174774  -8.8873714 -13.9008192 -45.2157935

Largest  eigenvalues:
 [1] 63120365 61160335 57527503 56025955 54968204 54341334 52253122 52129928
 [9] 51002782 50883681

Smallest eigenvalues:
 [1]  0.44063593  0.43249308  0.37115635  0.33283345  0.28408980  0.26166240
 [7]  0.17621458 -0.07496801 -0.43992879 -0.77208740

Largest  eigenvalues:
 [1] 65235758 60405393 58106427 56865862 54876283 53201297 52729928 52399719
 [9] 51871340 51615993

Smallest eigenvalues:
 [1]  0.5026744  0.4855860  0.3991645  0.3829994  0.3601882  0.3062121
 [7]  0.2815905  0.2577905  0.1946266 -0.8318331

Largest  eigenvalues:
 [1] 65908125 59662722 56591735 56327336 54420293 52682685 52338597 51785282
 [9] 51510040 51030351

Smallest eigenvalues:
 [1] -0.07833204 -0.22851411 -0.43475687 -0.56387118 -1.24443253 -1.86830562
 [7] -1.86846587 -2.06105839 -2.97130135 -9.29840438

Largest  eigenvalues:
 [1] 63922135 60755539 57674741 55993591 55782357 54203302 52591939 52513450
 [9] 51936391 51668677

Smallest eigenvalues:
 [1]  0.3949043  0.3722751  0.3620888  0.3573198  0.3550337  0.2158414
 [7] -0.8612041 -0.9034753 -3.6333080 -5.0483643

Largest  eigenvalues:
 [1] 65081248 59878627 57466677 56299282 54724920 53045273 52373184 52336020
 [9] 51591981 51463356

Smallest eigenvalues:
 [1]  0.46041997  0.42956390  0.30742440  0.30708329  0.16968009  0.11858813
 [7] -0.02366868 -0.36030556 -0.50952099 -6.73914304

Largest  eigenvalues:
 [1] 64728409 59521913 56998297 55545598 54096031 52596825 52017726 51727375
 [9] 51183439 51032262

Smallest eigenvalues:
 [1]  0.5228137  0.5136512  0.5100477  0.4758227  0.4681192  0.4335429
 [7]  0.3860520  0.2912431  0.2538382 -0.5944993

Largest  eigenvalues:
 [1] 63993162 60587833 57122163 56311162 55355661 53639219 52275395 52071700
 [9] 51988670 51215584

Smallest eigenvalues:
 [1]  0.41861770  0.35889258  0.31835313  0.31077346  0.25839709  0.17377898
 [7]  0.05758828 -0.05755575 -0.10683318 -0.41837805

Largest  eigenvalues:
 [1] 61275159 60010721 57106995 55782390 53857925 53816823 52144297 51623684
 [9] 50730371 50686008

Smallest eigenvalues:
 [1]   0.4842106   0.4727960   0.4235241   0.3743658   0.2943528   0.2790244
 [7]   0.2174392   0.1951370  -1.6850298 -29.5821733

Largest  eigenvalues:
 [1] 63811226 59939656 57051267 55643304 55142257 53280007 52132599 51657246
 [9] 51541495 51022965

Smallest eigenvalues:
 [1]  0.4668311  0.4531328  0.3611645  0.2852611  0.2818005  0.2649809
 [7]  0.1932553 -0.0333744 -0.2051055 -1.5172173

Largest  eigenvalues:
 [1] 64699488 59422617 56593254 55971313 54259860 52791243 52000611 51680095
 [9] 51184343 50827453

Smallest eigenvalues:
 [1]  0.4974162  0.4607634  0.4111369  0.3812524  0.3495022  0.2679391
 [7]  0.2487249  0.1854849 -0.2348013 -6.0789563

Largest  eigenvalues:
 [1] 63525673 60405429 57531887 55651021 55440330 54131804 52333415 52303281
 [9] 51565656 51242176

Smallest eigenvalues:
 [1]  0.4121963  0.4092734  0.3806980  0.3575207  0.2573680  0.2354548
 [7]  0.1720906  0.1185910 -0.3438910 -0.6660165

Largest  eigenvalues:
 [1] 65121656 61135684 58455424 56536342 55851432 54276180 53101072 52543997
 [9] 52034390 51916285

Smallest eigenvalues:
 [1]  0.4342009  0.3989505  0.3852095  0.3091908  0.3063040  0.2962070
 [7]  0.2270725  0.2221306 -0.7151561 -1.1500861

Largest  eigenvalues:
 [1] 64962457 59879953 57827566 56144945 55001552 53920448 52183031 52139025
 [9] 51769687 51190569

Smallest eigenvalues:
 [1]  0.4837691  0.4318162  0.4270993  0.3581527  0.3362051  0.3085269
 [7]  0.2935498  0.2416242  0.1891279 -1.1688314

Largest  eigenvalues:
 [1] 64628789 59860891 57237313 55540903 54904925 53431359 52075358 51669393
 [9] 51655421 51257737

Smallest eigenvalues:
 [1]   0.29248756   0.19965439   0.19247584   0.08293757   0.08224070
 [6]  -0.03897466  -0.03994578  -3.27708633  -8.37655305 -18.71079443

Largest  eigenvalues:
 [1] 63071067 58713267 55994656 55243424 53857442 52663337 51408405 51123366
 [9] 50884044 50045346

Smallest eigenvalues:
 [1]  0.3970637  0.3937481  0.3480658  0.3181406  0.3081975  0.3016968
 [7]  0.2863138  0.2297331  0.1835831 -2.9488796

Largest  eigenvalues:
 [1] 65114829 60428118 57096136 57033364 54940409 53441669 52799333 52540473
 [9] 52009455 51656471

Smallest eigenvalues:
 [1]  0.4821478  0.4321006  0.4307401  0.3063427  0.2404440  0.1870286
 [7]  0.1689045  0.1511480  0.1267058 -0.2770814

Largest  eigenvalues:
 [1] 63705043 60319918 57271441 55266267 55221658 53423604 52897570 51790072
 [9] 51718034 51469796

Smallest eigenvalues:
 [1]  0.4709553  0.4686872  0.4171933  0.4034580  0.3093342  0.2728820
 [7]  0.1629109  0.1152926 -0.6973689 -1.3624365

Largest  eigenvalues:
 [1] 65073384 59731159 57333085 56096258 54826182 53325745 52122491 52050217
 [9] 51911350 51202078

Smallest eigenvalues:
 [1]   0.27250745   0.21846706   0.20965168   0.09725675  -0.00939362
 [6]  -0.43955782 -14.23894000 -16.07056221 -57.87512347 -68.26835266

Largest  eigenvalues:
 [1] 63003664 59381268 56182687 54650493 54540268 52969259 51762313 51477914
 [9] 50803443 50577504

Smallest eigenvalues:
 [1]  0.54667633  0.38980251  0.33372748  0.31956173  0.29728659  0.26991633
 [7]  0.26944734 -0.08663531 -1.04504535 -1.18452027

Largest  eigenvalues:
 [1] 62385185 59565030 57341102 55291269 54545542 53507424 52374201 51826888
 [9] 50835599 50691868

Smallest eigenvalues:
 [1]  0.550223391  0.525924343  0.517918325  0.506911687  0.465598629
 [6]  0.424860826  0.375987183  0.080182941  0.001190248 -0.014031902

Largest  eigenvalues:
 [1] 65399013 59878085 57142158 56207364 54622400 52893762 52387161 51552133
 [9] 51525100 50741746

Smallest eigenvalues:
 [1]  0.366823762  0.319180191  0.293875423  0.272850953  0.236965141
 [6]  0.232195740  0.193625525  0.164064308 -0.006541406 -0.333933932

Largest  eigenvalues:
 [1] 63775035 59217021 57019931 55091508 54479672 53123552 51377346 51325381
 [9] 51078430 50358138

Smallest eigenvalues:
 [1]  0.4907138  0.4516266  0.4079258  0.3676228  0.3068431  0.2120014
 [7]  0.1670168 -0.3884251 -2.8482545 -3.9321699

Largest  eigenvalues:
 [1] 63525808 60044342 56767935 55036768 54909498 53108451 51765105 51022970
 [9] 50989216 50703666

Smallest eigenvalues:
 [1]  0.56765003  0.52402795  0.46992327  0.36465294  0.30585874  0.30289750
 [7]  0.23509138  0.21745366  0.20829651 -0.06848167

Largest  eigenvalues:
 [1] 63041871 60208038 56844993 55548294 55172206 53708312 52054080 51878742
 [9] 51290547 50866992

Smallest eigenvalues:
 [1]  0.5584792  0.4906320  0.4089252  0.3770547  0.3339411  0.2092842
 [7]  0.1103486 -0.2060481 -0.4229839 -1.0691039

Largest  eigenvalues:
 [1] 64929348 60217277 57422070 56502244 54983184 53422258 52442049 52080673
 [9] 51573806 50969657

Smallest eigenvalues:
 [1]  0.5889441  0.5215414  0.4411243  0.4157165  0.3190951  0.3016080
 [7]  0.2593738  0.2485206 -0.1325038 -0.5351529

Largest  eigenvalues:
 [1] 65226507 59981115 56808633 56352941 54701185 52996120 52427966 51801599
 [9] 51760707 51047748

Smallest eigenvalues:
 [1]   0.39718859   0.35128678   0.33118365   0.25306610   0.19290664
 [6]   0.04594924  -0.43040197  -5.50962085 -12.21644820 -38.49245698

Largest  eigenvalues:
 [1] 62769956 59683171 56394355 54931698 54836453 52811957 51783522 51095392
 [9] 50836240 50387211

Smallest eigenvalues:
 [1]  0.4789005  0.4559953  0.3990029  0.2907194  0.2507092  0.2474317
 [7]  0.2391723 -0.4709886 -0.7793261 -2.6247577

Largest  eigenvalues:
 [1] 67132127 60650125 58580230 57394993 55255674 53606872 53550940 52884531
 [9] 52216156 52054333

Smallest eigenvalues:
 [1]  0.5563766  0.5053720  0.3644869  0.3376697  0.2914989  0.2892991
 [7]  0.2543838  0.1308287  0.1098330 -0.9911260

Largest  eigenvalues:
 [1] 65965642 60953694 58391069 57303180 55520031 54112145 53246459 52755659
 [9] 52451211 51736276

Smallest eigenvalues:
 [1]  0.43576162  0.41867014  0.35206250  0.28186734  0.27241947  0.22117037
 [7]  0.14696657  0.13024964  0.09817621 -0.45435093

Largest  eigenvalues:
 [1] 63333058 60437452 57138114 55507087 55225999 53883635 52401455 52300670
 [9] 51375277 51245704

Smallest eigenvalues:
 [1]  0.4979374  0.4661988  0.4570703  0.3672545  0.2917200  0.2315145
 [7]  0.2106453  0.1749869 -0.1315438 -0.3352843

Largest  eigenvalues:
 [1] 62976081 59466654 56488345 54910953 54618364 52885919 51474137 51050076
 [9] 50957164 50311061

Smallest eigenvalues:
 [1]  0.46079882  0.44038488  0.32332373  0.29822588  0.18894853  0.16291772
 [7] -0.02099049 -0.14208520 -0.83208624 -2.29881614

Largest  eigenvalues:
 [1] 65374307 60247216 57667844 56506216 55020699 53571552 52430179 52394908
 [9] 52322313 51595311

Smallest eigenvalues:
 [1]  0.42016858  0.31741860  0.30699500  0.24756346  0.23962368  0.23007383
 [7]  0.17421150  0.05369563 -0.21341390 -0.25729259

Largest  eigenvalues:
 [1] 64886803 59489955 57131947 55706658 54690895 53328189 51783974 51703330
 [9] 51236363 50717543

Smallest eigenvalues:
 [1]  0.4225963  0.2895787  0.2838451  0.2690289  0.1845481  0.1728189
 [7]  0.1030672  0.0723467 -0.8260505 -1.2289281

Largest  eigenvalues:
 [1] 64925557 60564137 57899968 55598272 55479431 53968439 52934865 52064048
 [9] 51983777 51731481

Smallest eigenvalues:
 [1]   0.4667609   0.4374028   0.3997889   0.3994561   0.3443882   0.3341805
 [7]   0.2868249   0.2244484  -1.0876611 -20.4349850

Largest  eigenvalues:
 [1] 63508902 59989291 57127841 55847374 55292775 53597121 51983273 51952960
 [9] 51775511 50937437

Smallest eigenvalues:
 [1]  0.55385261  0.51342060  0.43817217  0.41574485  0.38453103  0.27942107
 [7]  0.27320378  0.27271548  0.25904802 -0.09261359

Largest  eigenvalues:
 [1] 65307788 60735843 57810156 56834105 55341693 53717776 52910471 52409389
 [9] 52149470 51339824

Smallest eigenvalues:
 [1]  0.52230262  0.51970535  0.47814213  0.36908567  0.30457429  0.30328106
 [7]  0.21061115  0.06329256  0.04996261 -3.47754804

Largest  eigenvalues:
 [1] 62660041 60235726 56907447 55564260 54816992 53781242 52209878 51653991
 [9] 50997388 50780734

Smallest eigenvalues:
 [1]   0.29430075   0.24786529   0.21905304   0.16531437   0.05192744
 [6]  -0.17115461  -0.58350368 -10.60787097 -13.57307915 -27.51346592

Largest  eigenvalues:
 [1] 62323970 59029021 56408397 54375113 54335987 52632027 51572028 51451611
 [9] 50577764 50342695

Smallest eigenvalues:
 [1]  0.50570073  0.50105826  0.41825566  0.39406476  0.38547953  0.38098189
 [7]  0.34199021  0.21766503 -0.09351116 -0.25112799

Largest  eigenvalues:
 [1] 64408718 60099341 57641196 56280002 54637882 53194595 52324811 51832298
 [9] 51686766 51056797

Smallest eigenvalues:
 [1]  0.5150850  0.4606915  0.4496685  0.4290225  0.3603103  0.3312539
 [7]  0.2832682  0.1763414 -0.1717241 -0.3835961

Largest  eigenvalues:
 [1] 65221829 60345850 56999490 56274396 55532917 53682279 52272483 52185730
 [9] 51696216 51081621

Smallest eigenvalues:
 [1]   0.16295783   0.10940209  -0.01431263  -0.17549372  -0.36040939
 [6]  -1.69599575  -6.18910252 -18.44027507 -23.52418014 -93.67638236

Largest  eigenvalues:
 [1] 65285636 60893104 57157784 56991096 55897968 53946619 53307229 52884357
 [9] 51944954 51872070

Smallest eigenvalues:
 [1]  0.4843090  0.4765560  0.3883617  0.3621946  0.3170202  0.2869983
 [7]  0.1916579  0.1580417  0.1226571 -0.4186822

Largest  eigenvalues:
 [1] 64280452 60688772 57660677 56004615 55840809 54180270 52770967 52513343
 [9] 52001747 51784654

Smallest eigenvalues:
 [1]  0.342589171  0.314095355  0.233616744  0.226361277  0.167102884
 [6] -0.004610378 -0.148466286 -1.819808635 -1.841588275 -2.150308435

Largest  eigenvalues:
 [1] 62457458 59824323 57074045 55636193 54186055 53786178 52074826 51549250
 [9] 50679352 50480538

Smallest eigenvalues:
 [1]    0.2738956    0.2128682    0.1976286    0.1761831   -0.6796558
 [6]   -0.7544631   -0.8436561   -1.9246022   -5.7617735 -105.9143133

Largest  eigenvalues:
 [1] 66850801 60694457 57911848 56583953 55477409 53507983 52898952 52149993
 [9] 52085098 50979852

Smallest eigenvalues:
 [1]  0.5554700  0.4687543  0.4515623  0.3623186  0.3377533  0.2771617
 [7]  0.2630704  0.2509233  0.2081849 -0.4036198

Largest  eigenvalues:
 [1] 62895204 60591093 57301275 55764621 55088001 54167445 52742690 51879755
 [9] 51257597 50960591

Smallest eigenvalues:
 [1]  0.4623208  0.3960992  0.3608581  0.3404803  0.3286677  0.2897268
 [7]  0.2542337  0.2232213  0.2099607 -3.4260121

Largest  eigenvalues:
 [1] 64913795 60291265 57452375 56615235 55076075 53488335 52457321 52412587
 [9] 52401743 51433051

Smallest eigenvalues:
 [1]  0.52137701  0.42107219  0.37867713  0.31439916  0.30043682  0.18770837
 [7] -0.06621509 -0.92483527 -2.37304612 -6.54656598

Largest  eigenvalues:
 [1] 64498048 60078515 57297960 56529533 54844369 53134263 52324010 52283285
 [9] 51746366 51170042

Smallest eigenvalues:
 [1]  0.44630930  0.42759673  0.42688949  0.40460563  0.37163615  0.21076585
 [7]  0.17202490  0.14191609  0.02125368 -1.68825280

Largest  eigenvalues:
 [1] 64169735 60441477 57313751 56012294 55298933 53387736 52691360 52039103
 [9] 51655275 51548874

Smallest eigenvalues:
 [1]  0.3696885  0.3404754  0.2852101  0.2374753  0.1301295 -0.2279523
 [7] -0.2763966 -0.5377590 -1.1613819 -3.6757600

Largest  eigenvalues:
 [1] 65574655 60627445 58126389 56092139 55364498 53775197 52960896 52259757
 [9] 52017150 51926825

Smallest eigenvalues:
 [1]  0.3875723  0.3769951  0.3533727  0.3457456  0.2687831  0.2387556
 [7]  0.1367731  0.1345906 -0.9472159 -1.0323866

Largest  eigenvalues:
 [1] 65757496 60775256 58189688 56355558 55608083 54240914 52412895 52397984
 [9] 52336372 51661090

Smallest eigenvalues:
 [1]  0.5791801  0.5321776  0.4904700  0.4384957  0.4197904  0.3623652
 [7]  0.2453059  0.1465593  0.1161608 -0.1420097

Largest  eigenvalues:
 [1] 64852201 60368135 57248811 55272037 55108525 53506892 52045478 51488573
 [9] 51477706 51166003

Smallest eigenvalues:
 [1]  0.52243628  0.42608586  0.30303085  0.24741161  0.20387804  0.02763839
 [7] -0.06112667 -0.20349630 -2.05955743 -2.83854690

Largest  eigenvalues:
 [1] 63273189 59392509 56701059 55147590 54860675 52958906 51794029 51479229
 [9] 51248111 50675086

Smallest eigenvalues:
 [1]  0.5351256  0.4543007  0.3853692  0.3263224  0.2809709  0.2667325
 [7]  0.1648275 -0.1159955 -0.2738532 -1.1538587

Largest  eigenvalues:
 [1] 64427683 60698235 57271529 56607305 55429275 53470383 52714555 52481688
 [9] 51867946 51046410

Smallest eigenvalues:
 [1]  0.6031815  0.5559160  0.4584568  0.4124849  0.3863325  0.3495184
 [7]  0.3245471  0.2899357  0.1975683 -0.0352876

Largest  eigenvalues:
 [1] 64280302 60355686 57255172 56218845 55510923 53662182 52524410 52314474
 [9] 51835956 51077251

Smallest eigenvalues:
 [1]  0.24487732  0.21753507  0.19221810  0.17856029  0.09013428 -0.84026871
 [7] -1.25591387 -1.89110812 -3.91100887 -5.60480730

Largest  eigenvalues:
 [1] 65492130 59756004 57284589 56485049 54995108 53463778 52586875 52024990
 [9] 51836361 50786609

Smallest eigenvalues:
 [1]  0.49473185  0.47685649  0.45313630  0.41967156  0.29485566  0.29099290
 [7]  0.24567535  0.23809376  0.02008018 -0.03924129

Largest  eigenvalues:
 [1] 64998887 60133900 57789946 55988230 55054740 53675389 52212469 52083434
 [9] 51985403 51076331

Smallest eigenvalues:
 [1]  0.4895499  0.4804919  0.4710209  0.4374892  0.4097570  0.3207026
 [7]  0.3139825  0.2967670  0.2232518 -0.2950731

Largest  eigenvalues:
 [1] 64191665 59892952 57085198 55717890 55127016 53374738 52233725 51727474
 [9] 51621961 50886650

Smallest eigenvalues:
 [1]  0.5095042  0.4858718  0.4560664  0.3546844  0.3475106  0.3219654
 [7]  0.2721654 -0.3313732 -1.6121342 -2.0792855

Largest  eigenvalues:
 [1] 67396510 60875571 58667186 57760226 55257361 53777342 53746130 52727777
 [9] 52216301 51971187

Smallest eigenvalues:
 [1]  0.5701869  0.5571233  0.4616622  0.4133250  0.3971531  0.3589362
 [7]  0.3393439  0.2717245  0.1910852 -1.8657771

Largest  eigenvalues:
 [1] 64852573 60256431 57153972 56201674 55302096 53819958 52198612 52086247
 [9] 52000434 50916451

Smallest eigenvalues:
 [1]  0.47377439  0.43946254  0.39472870  0.38505714  0.32420693  0.30274886
 [7]  0.27431695  0.22410539  0.13329682 -0.07047193

Largest  eigenvalues:
 [1] 65369469 59386051 56609219 56363255 54236033 52782865 52394333 51524410
 [9] 51275851 50612115

Smallest eigenvalues:
 [1]  0.4717617  0.4049114  0.4031669  0.3579300  0.3046940  0.2768814
 [7]  0.2427820 -0.2199484 -0.5824348 -2.5127247

Largest  eigenvalues:
 [1] 64767877 60526803 57608372 56463659 55165161 53356164 52483942 52262587
 [9] 52080639 51141668

Smallest eigenvalues:
 [1]  0.4697528  0.4641836  0.4607982  0.4359906  0.4033246  0.3991634
 [7]  0.3404617  0.3153652  0.2880753 -0.2278895

Largest  eigenvalues:
 [1] 64938253 60217973 57638866 56257256 55125233 53685919 52346024 52102205
 [9] 51875954 51195039

Smallest eigenvalues:
 [1]  0.4755321  0.4584848  0.4539473  0.3939772  0.3788036  0.3641562
 [7]  0.3595409  0.3313466 -0.2228871 -2.7397324

Largest  eigenvalues:
 [1] 63028655 59970447 57152010 55596003 55140790 53506562 51888122 51671867
 [9] 51409845 50535929

Smallest eigenvalues:
 [1]  0.33889090  0.22070169  0.16345909  0.15426066  0.13532187  0.02392872
 [7] -0.04319617 -0.04913913 -1.02893506 -5.13652364

Largest  eigenvalues:
 [1] 64277489 59968464 57057088 55805533 55804017 53915779 52094887 51764620
 [9] 51732692 50661285

Smallest eigenvalues:
 [1]   0.3571057   0.3279767   0.3121123   0.2685279   0.2562704   0.2393176
 [7]   0.2348980   0.1974721  -3.0385916 -10.6423744

Largest  eigenvalues:
 [1] 64475717 60593456 57679329 55695014 55540867 54115683 52346157 52147853
 [9] 51632276 51541988

Smallest eigenvalues:
 [1]  0.5483500  0.4564222  0.3880366  0.3301862  0.3274144  0.3009116
 [7]  0.2495507  0.1832786 -0.5266163 -3.1807076

Largest  eigenvalues:
 [1] 66564178 59649047 57126631 56854899 54335444 53216986 52530654 51741390
 [9] 51353991 51042168

Smallest eigenvalues:
 [1]  0.4656972  0.4300061  0.4295841  0.3067134  0.3005345  0.2435236
 [7]  0.1771190  0.1168031 -2.1912007 -4.9577529

Largest  eigenvalues:
 [1] 63378742 59788896 57227558 55890768 54864910 53336037 52725611 52163593
 [9] 51692602 51472577

Smallest eigenvalues:
 [1]   0.4171166   0.3774837   0.3622252   0.2245828   0.1381114  -0.1002495
 [7]  -0.1293906  -0.3961462  -3.9126751 -13.5229930

Largest  eigenvalues:
 [1] 63678231 59146676 56544921 54974838 54181085 52529805 51317125 50964456
 [9] 50962658 50423226

Smallest eigenvalues:
 [1]  0.4824038  0.4001162  0.3757384  0.3298817  0.3202459  0.2609935
 [7]  0.2096062  0.1950268  0.1790065 -0.2876235

Largest  eigenvalues:
 [1] 63346947 59693400 57002617 55526453 54781707 53265129 51757518 51660078
 [9] 51573052 50776308

Smallest eigenvalues:
 [1]  0.4017196  0.3099829  0.3060601  0.2550064  0.2056617  0.1627810
 [7]  0.1342936  0.1037703 -1.1493079 -4.2108173

Largest  eigenvalues:
 [1] 65078752 59074422 56526244 56063135 53878681 52572950 52091441 51223415
 [9] 51087864 50476204

Smallest eigenvalues:
 [1]  0.5272416  0.5054613  0.4903513  0.4308589  0.3776353  0.3573757
 [7]  0.2921170  0.2826911 -0.4251678 -2.7358815

Largest  eigenvalues:
 [1] 66599600 60981775 58124208 57774052 55189042 53810531 53364397 52419744
 [9] 52096953 51510495

Smallest eigenvalues:
 [1]  0.44352102  0.36971851  0.36385556  0.31225080  0.26483173  0.25880484
 [7]  0.25820962  0.19419127 -0.01820648 -1.00247676

Largest  eigenvalues:
 [1] 65056606 60215757 57343812 56239633 55337147 53691532 52302398 51991954
 [9] 51808179 50987505

Smallest eigenvalues:
 [1]  0.4244945  0.3552956  0.3220012  0.3077159  0.2877264  0.1979399
 [7]  0.1076089 -0.5034533 -1.0337733 -3.7950455

Largest  eigenvalues:
 [1] 63376511 60223485 57200536 55649710 55574674 53663464 51952046 51761827
 [9] 51469738 51235669

Smallest eigenvalues:
 [1]  0.42132701  0.37521250  0.30924554  0.29312385  0.27712202  0.24223365
 [7]  0.19316044  0.03794398 -0.13643478 -5.47684096

Largest  eigenvalues:
 [1] 65345551 60556261 57809068 56562754 56163572 54244981 52586173 52399029
 [9] 51938387 51240231

Smallest eigenvalues:
 [1]   0.2546413   0.2494736   0.2266284   0.2064892   0.1300866  -0.4342752
 [7]  -0.5593178  -1.2217019 -20.0815033 -39.4685869

Largest  eigenvalues:
 [1] 64884322 59733086 56926564 56654483 54875031 53184780 52477787 51331660
 [9] 51188295 50415105

Smallest eigenvalues:
 [1]   0.4375188   0.3411944   0.3239461   0.3085751   0.2607217   0.2339986
 [7]  -0.1312906  -0.4170674  -1.4996094 -13.2815155

Largest  eigenvalues:
 [1] 63385042 59588275 56911855 54884094 54731446 52916608 51656084 51144916
 [9] 50998802 50541110

Smallest eigenvalues:
 [1]  0.4811541  0.4742101  0.4539463  0.4451578  0.2700403  0.2442770
 [7]  0.1207482 -0.0139907 -0.4748405 -9.7533969

Largest  eigenvalues:
 [1] 64958591 60032158 57060435 55845321 54848867 53094376 52094341 51941215
 [9] 51862042 51214104

Smallest eigenvalues:
 [1]  0.4412282  0.3926182  0.3834597  0.3668619  0.3175575  0.2852846
 [7]  0.2167005  0.1989422  0.0679503 -1.2611754

Largest  eigenvalues:
 [1] 64890205 61156686 58182066 56431292 56236087 54817982 53100533 52761345
 [9] 52159653 51954800

Smallest eigenvalues:
 [1]   0.48549508   0.36848194   0.30088141   0.20034541  -0.09592838
 [6]  -0.36913493  -0.37442737  -1.23779526  -1.81110894 -24.87610184

Largest  eigenvalues:
 [1] 65731682 60396458 57677093 56541092 55534263 53639803 52667410 52300771
 [9] 52181253 51377750

Smallest eigenvalues:
 [1]  0.5517755  0.4154157  0.4103750  0.3795497  0.3781615  0.2874042
 [7]  0.2562975  0.1691774  0.1384625 -1.3797954

Largest  eigenvalues:
 [1] 65211114 60484917 57789617 56365442 55499866 54085952 52807485 52427418
 [9] 52347525 51807585

Smallest eigenvalues:
 [1]  0.244674640  0.215752978  0.213419851  0.212298594  0.196549748
 [6] -0.009611284 -0.038700521 -0.096844955 -1.347646435 -3.740604286

Largest  eigenvalues:
 [1] 68010205 60653718 58542573 57718957 54943626 53936989 53737989 52337973
 [9] 51771129 51672165

Smallest eigenvalues:
 [1]  0.4454781  0.4272542  0.3612084  0.3192339  0.3178917  0.2835763
 [7]  0.2694921  0.2391410  0.2168436 -0.1538713

Largest  eigenvalues:
 [1] 64702745 60367796 57275603 56268228 54893223 53343385 52485105 51731587
 [9] 51700357 50841561

Smallest eigenvalues:
 [1]  0.38710900  0.36272787  0.35542668  0.26672463  0.25187289  0.24226184
 [7]  0.22712123  0.06988783 -0.08184563 -0.80146537

Largest  eigenvalues:
 [1] 64386971 60230569 57505664 55388288 55094147 53723589 52019774 51911124
 [9] 51616110 51072783

Smallest eigenvalues:
 [1]  0.6397911  0.5237817  0.4350590  0.3548538  0.3145444  0.2486016
 [7]  0.2295997  0.1351371 -0.1219736 -0.5428926

Largest  eigenvalues:
 [1] 63167112 59955747 57475063 55286842 55022379 53711398 52316885 51788930
 [9] 51183622 50815085

Smallest eigenvalues:
 [1]   0.4509615   0.4219120   0.3639738   0.3115124   0.3056710   0.2643480
 [7]   0.1988579   0.1818644  -1.2520372 -16.6504080

Largest  eigenvalues:
 [1] 64558552 59914805 56702593 55796313 55080575 53380930 52332457 51906123
 [9] 51837458 51203438

Smallest eigenvalues:
 [1]  0.44798987  0.37484278  0.35734470  0.32751621  0.25422863  0.25162084
 [7]  0.23210663  0.05834778 -0.77380815 -1.31161107

Largest  eigenvalues:
 [1] 64412271 60336826 57178094 55433930 55433145 53783873 52146624 51843072
 [9] 51386199 51126856

Smallest eigenvalues:
 [1]  0.47247321  0.43731939  0.42800514  0.41263904  0.35909698  0.29756946
 [7]  0.20783115  0.17820098  0.16656171 -0.08737491

Largest  eigenvalues:
 [1] 63304381 59504721 56824836 55065685 55031788 53160509 51844310 51478788
 [9] 51142127 50639497

Smallest eigenvalues:
 [1]  0.5364489  0.4888863  0.4646458  0.4430279  0.3219069  0.3114664
 [7]  0.2629622  0.2363482  0.2159001 -0.8350587

Largest  eigenvalues:
 [1] 64451599 59917436 57083911 55842637 54845664 53374339 52299075 51887340
 [9] 51617718 50994941

Smallest eigenvalues:
 [1]  0.4555598  0.4141347  0.3236819  0.2926560  0.2833387  0.2458844
 [7]  0.2417143  0.2177797  0.1739207 -4.7560440

Largest  eigenvalues:
 [1] 66784912 60154879 57631162 57143699 54877237 53514259 53132596 52203781
 [9] 52046813 51459476

Smallest eigenvalues:
 [1]  0.49148507  0.44799225  0.37651062  0.36622368  0.31744605  0.27887903
 [7]  0.25567139  0.17077949 -0.03381753 -0.50289311

Largest  eigenvalues:
 [1] 65571359 60716135 57917675 56443603 55662642 54029117 53414252 52637942
 [9] 52116383 51968468

Smallest eigenvalues:
 [1]  0.470088435  0.464224478  0.391518808  0.389368126  0.375985762
 [6]  0.341729409  0.318103279  0.232783097 -0.001970510 -0.006211456

Largest  eigenvalues:
 [1] 63114465 60325007 57915148 55306710 55178253 53982394 52351739 51762394
 [9] 51368110 50941495

Smallest eigenvalues:
 [1]  0.42907799  0.41610627  0.29064990  0.25543067  0.24003664  0.20508469
 [7]  0.15725446  0.06694527 -0.54133140 -0.82281241

Largest  eigenvalues:
 [1] 67142309 60537948 57827465 57382428 54734914 53449823 53098561 52251383
 [9] 51924484 51690757

Smallest eigenvalues:
 [1]  0.4181066  0.3867627  0.3822281  0.3351218  0.3270386  0.2238736
 [7]  0.1830226  0.1512076 -0.2597841 -6.9723956

Largest  eigenvalues:
 [1] 65069700 59721767 56872295 56333737 54512175 52698862 52400058 51631594
 [9] 51537376 50920317

Smallest eigenvalues:
 [1]  0.3074794  0.3057437  0.2668262  0.2433242  0.1697352 -0.2505308
 [7] -0.3755285 -1.0438328 -1.5444525 -2.6934692

Largest  eigenvalues:
 [1] 65237474 60741912 57672903 56394164 55858527 54327783 52783278 52385975
 [9] 52056787 51626678

Smallest eigenvalues:
 [1]  0.5842321  0.5439385  0.5220422  0.4844043  0.4752812  0.4631421
 [7]  0.4197152  0.2924333  0.2630965 -0.2741088

Largest  eigenvalues:
 [1] 64110132 59749677 56744453 55971926 54796706 53151431 51961119 51794728
 [9] 51605348 50817931

Smallest eigenvalues:
 [1]   0.4161700   0.3987813   0.3890185   0.3483768   0.3017138   0.2951071
 [7]   0.1120481  -0.3732939 -10.5473146 -18.0409035

Largest  eigenvalues:
 [1] 65485083 60200490 57502093 56621302 54726232 53369536 52731891 51485488
 [9] 51459974 50504923

Smallest eigenvalues:
 [1]  0.44456264  0.36018395  0.35957191  0.27792494  0.22881227  0.22025975
 [7]  0.18238699  0.05028327  0.03185821 -6.11217840

Largest  eigenvalues:
 [1] 61702597 59854986 57130846 55983937 54328504 53790224 52109966 51129479
 [9] 50541351 50521184

Smallest eigenvalues:
 [1]  0.4482850  0.4392214  0.4138799  0.3871189  0.3434284  0.3379533
 [7]  0.2350395  0.2264454 -0.6419894 -1.3997029

Largest  eigenvalues:
 [1] 65162788 60259141 58227062 56426661 55227870 54009113 52524208 52495173
 [9] 52165360 51753445

Smallest eigenvalues:
 [1]  0.46648543  0.38176729  0.34760703  0.29687820  0.04288414 -0.02987877
 [7] -0.03561369 -0.10589229 -1.61225924 -2.23537397

Largest  eigenvalues:
 [1] 65039093 59968201 56676752 56228034 54664749 52986433 52295477 52176354
 [9] 51394842 51158536

Smallest eigenvalues:
 [1]  0.41181687  0.35092745  0.33513618  0.26560699  0.25800361  0.23422138
 [7]  0.19919388  0.14672251  0.06517232 -2.73309574

Largest  eigenvalues:
 [1] 61347523 59560434 56796569 55388306 53488630 53379571 51644262 50904266
 [9] 50233030 50081801

Smallest eigenvalues:
 [1]   0.28250919   0.27223589   0.21345274   0.08412727  -0.10838682
 [6]  -0.89789055  -1.85833469  -2.54314852  -4.52537947 -27.49158451

Largest  eigenvalues:
 [1] 62997784 60597268 57140072 55929170 55477783 54286446 52429981 52348776
 [9] 51394000 51246637

Smallest eigenvalues:
 [1]  0.46752938  0.44699365  0.44605889  0.42096413  0.35844914  0.19402009
 [7]  0.18957588  0.16765407  0.08535547 -0.31654780

Largest  eigenvalues:
 [1] 65511982 60049876 56889558 56366133 54988510 53145557 52428362 52190051
 [9] 51989228 51478460

Smallest eigenvalues:
 [1]   0.3911942   0.3051112   0.2374562   0.2033701   0.2027744   0.1955194
 [7]   0.1478828  -0.5445392  -2.1472867 -30.4367665

Largest  eigenvalues:
 [1] 65198905 60354516 57738810 56080783 54758331 53158568 52362712 52089075
 [9] 51939519 51686001

Smallest eigenvalues:
 [1]   0.40859054   0.35185951   0.31981995   0.31713911   0.31588386
 [6]   0.29767602   0.27128695   0.06159938  -0.01686441 -29.71729307

Largest  eigenvalues:
 [1] 63006282 59454193 57069490 55214707 55156510 53388659 51704754 51440939
 [9] 51276479 50576668

Smallest eigenvalues:
 [1]  0.36769598  0.34910195  0.33467407  0.33228324  0.24533693  0.22296072
 [7]  0.17850995  0.06118942 -0.34423999 -2.42058708

Largest  eigenvalues:
 [1] 64965063 60226377 57262266 55873684 55294297 53597414 51804072 51530574
 [9] 51497340 50865848

Smallest eigenvalues:
 [1]  0.4876125  0.4788661  0.4512282  0.3296756  0.3022255  0.2930782
 [7]  0.2866780  0.2715847  0.2200952 -0.4612267

Largest  eigenvalues:
 [1] 61900594 59845930 56840985 55531103 54235127 53627553 52130485 51655042
 [9] 50774638 50430847

Smallest eigenvalues:
 [1]  0.52577290  0.44791593  0.44507264  0.42522652  0.40956918  0.32030244
 [7]  0.26905038  0.25116249  0.03949773 -3.55598146

Largest  eigenvalues:
 [1] 64028388 60494596 57305659 55457985 55421628 53789062 52142663 51644882
 [9] 51596122 50985361

Smallest eigenvalues:
 [1]  0.45927568  0.40792906  0.34647808  0.16756599  0.15008075  0.12221237
 [7]  0.02620009 -0.04167823 -1.70533891 -4.75844230

Largest  eigenvalues:
 [1] 63891147 60773041 57265620 55998321 55385328 53979768 52479540 52187052
 [9] 51922218 51246787

Smallest eigenvalues:
 [1]   0.3658060   0.3344778   0.2609219   0.2585509   0.2447063   0.2104382
 [7]   0.2077177  -0.7278696  -8.2276847 -15.0700102

Largest  eigenvalues:
 [1] 64483348 61333696 57914624 56963065 56347620 55238270 53095534 52650016
 [9] 52244831 51651957

Smallest eigenvalues:
 [1]  0.46336357  0.45592025  0.44394742  0.44011852  0.35075441  0.28089595
 [7]  0.21568867  0.19742019  0.05017135 -1.02496290

Largest  eigenvalues:
 [1] 65876945 59900772 57232945 57023840 54797503 53342754 52912172 52178580
 [9] 52044331 51544345

Smallest eigenvalues:
 [1]   0.09331526   0.08430914   0.07642639   0.06544419  -0.21492851
 [6]  -0.62237701  -1.94636125  -6.75770299 -16.21286283 -72.71620056

Largest  eigenvalues:
 [1] 63830985 59377991 56483001 54934838 54475152 52755719 51900839 51243473
 [9] 51228092 50973095

Smallest eigenvalues:
 [1]  0.5208337  0.5094838  0.4714323  0.4199900  0.4109660  0.3748212
 [7]  0.3635074  0.3141239  0.2957035 -0.5989800

Largest  eigenvalues:
 [1] 63946712 60834585 57532401 56271544 55842777 54105767 52252869 52181186
 [9] 52072040 51098075

Smallest eigenvalues:
 [1]  0.6228705  0.5367966  0.4539265  0.4428860  0.4382406  0.4312686
 [7]  0.3611855  0.2584860 -0.1526940 -0.1740106

Largest  eigenvalues:
 [1] 64778376 60168439 57600582 56058337 55245881 53448519 52497551 52228099
 [9] 51788225 51390955

Smallest eigenvalues:
 [1]  0.5623987  0.5508477  0.4884565  0.4715541  0.3372215  0.3332619
 [7]  0.3248973  0.3136648  0.2342237 -0.2901622

Largest  eigenvalues:
 [1] 63353098 59648912 57169215 55339317 55195617 53672384 52006946 51659559
 [9] 51238630 50802159

Smallest eigenvalues:
 [1]  0.46199620  0.41583094  0.40561975  0.37038139  0.34098673  0.24059476
 [7]  0.04359031 -0.01212928 -0.18812592 -5.40076580

Largest  eigenvalues:
 [1] 64392870 59572334 56665517 56002026 54296993 52655575 52049097 51588225
 [9] 51216224 50650935

Smallest eigenvalues:
 [1]  0.5687584  0.5231477  0.4547006  0.3911932  0.3620886  0.3549302
 [7]  0.2607110  0.1873131  0.1758160 -0.7588787

Largest  eigenvalues:
 [1] 65028383 60744558 57500351 56671285 55760286 53936361 52903403 52602091
 [9] 52441538 51759936

Smallest eigenvalues:
 [1]  0.52267425  0.50711209  0.48094858  0.43873683  0.41275434  0.32880348
 [7]  0.31814716  0.03158521 -0.17098228 -0.21816864

Largest  eigenvalues:
 [1] 62926712 59906413 56340071 54971011 54905555 52938512 51719281 50992644
 [9] 50757307 49981242

Smallest eigenvalues:
 [1]  0.42374613  0.42248700  0.37151878  0.36214386  0.34850539  0.15052846
 [7]  0.07696728 -0.07022859 -0.72900921 -6.81405877

Largest  eigenvalues:
 [1] 64254464 59554755 56592807 55576483 54581035 53001255 51558422 51530729
 [9] 51191222 50530038

Smallest eigenvalues:
 [1]  0.24794884  0.13277562 -0.02630301 -0.17926705 -0.23286774 -0.28406237
 [7] -0.99511794 -2.43292388 -4.52280031 -8.82809816

Largest  eigenvalues:
 [1] 64708373 60315898 57612249 55679761 55346327 53752051 52358657 51872342
 [9] 51833624 51473634

Smallest eigenvalues:
 [1]  0.44675367  0.41600358  0.38652505  0.35633222  0.30386080  0.26809874
 [7]  0.22320797  0.15526093  0.04887881 -0.67850821

Largest  eigenvalues:
 [1] 64594404 59987723 56882404 56124773 54869510 53163929 52241606 52149971
 [9] 51299313 51223473

Smallest eigenvalues:
 [1]  0.44595910  0.43518750  0.31623774  0.21598209  0.20568876  0.18448963
 [7]  0.12054535  0.09483435 -0.36964111 -3.93732128

Largest  eigenvalues:
 [1] 63992776 59493412 57027877 55678440 54762180 53168399 52077094 51677258
 [9] 51508350 51101213

Smallest eigenvalues:
 [1]  0.4433661  0.4014599  0.3651950  0.3537610  0.3323528  0.2566188
 [7]  0.2298878  0.1781846 -2.4815648 -2.9872113

Largest  eigenvalues:
 [1] 64679687 59815762 57286583 55912331 55251418 53980271 52433559 52007626
 [9] 51805514 51314304

Smallest eigenvalues:
 [1]  0.36158858  0.33892998  0.31593207  0.30452609  0.28671851  0.19124657
 [7]  0.18861537  0.14971534 -0.09705962 -0.87385158

Largest  eigenvalues:
 [1] 64307760 60416838 57698407 55724068 55691134 54063603 52475201 52232214
 [9] 51789200 51488869

Smallest eigenvalues:
 [1]  0.53126014  0.51489103  0.48549203  0.46373719  0.35405130  0.27781297
 [7]  0.14508453 -0.07970191 -0.54654659 -6.46910453

Largest  eigenvalues:
 [1] 63707636 60689355 57666806 55780426 55162932 53733317 52361452 52198383
 [9] 51797803 51368405

Smallest eigenvalues:
 [1]  0.4017686  0.3745679  0.3234126  0.2578434  0.2239854  0.1935594
 [7]  0.1371283 -0.3670697 -0.7660613 -2.0296918

Largest  eigenvalues:
 [1] 65996802 60318143 57872549 57238203 55491980 54033674 53088185 52840927
 [9] 52057273 51872540

Smallest eigenvalues:
 [1]  0.5547056  0.4959835  0.3297929  0.3145666  0.2944331  0.2922839
 [7]  0.2079433  0.1309476  0.1106708 -0.4161479

Largest  eigenvalues:
 [1] 63735679 60454604 58026319 55444767 55236716 53957950 52067604 51925232
 [9] 51732964 51076455

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	7.596198	0.8863222	15.4405	0	2.693242	7.028819

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

HR ~ alt + n + body_temp + PM25

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- HR_fd
covariates <- list(altitude = altitude_fd, 
                   noise = noise_fd,
                   temp_body = body_temperature_ENT_fd,
                   pollution = pollution25_fd)
path_plot <- 'figures/model_HR_alt_noise_tempBody_PM25_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     noise = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     temp_body = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     pollution = list(nbetabasis = 80, norder = 4, lambda = 1e3))

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, 
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 17.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 470 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	7.254627	0.7154126	15.03311	0.18	3.3453	2.466049

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

HR ~ alt + n + body_temp + PM1

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- HR_fd
covariates <- list(altitude = altitude_fd, 
                   noise = noise_fd,
                   temp_body = body_temperature_ENT_fd,
                   pollution = pollution1_fd)
path_plot <- 'figures/model_HR_alt_noise_tempBody_PM1_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     noise = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     temp_body = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     pollution = list(nbetabasis = 80, norder = 4, lambda = 1e3))

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, 
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 17.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 512 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	7.20459	0.705722	15.50223	0.195	3.365779	2.358078

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

HR ~ alt + speed + PM25

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- HR_fd
covariates <- list(altitude = altitude_fd, 
                   speed = speed_fd,
                   pollution = pollution25_fd)
path_plot <- 'figures/model_HR_alt_speed_PM25_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     speed = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     pollution = list(nbetabasis = 80, norder = 4, lambda = 1e3))

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, 
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 31.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Warning message in `^.fd`((outcome - yhatfd), 2):
"The maximum error exceeds the tolerance level."
Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 444 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Smallest eigenvalues:
 [1]  0.80303814  0.80025109  0.79591494  0.64395486  0.59275608  0.58180483
 [7]  0.47461210  0.44006250  0.34035829 -0.02212782

Largest  eigenvalues:
 [1] 101924604  95288625  89618154  86660808  85727800  83149890  80240426
 [8]  80142577  79455565  78144599

Smallest eigenvalues:
 [1]  0.9578227  0.7410638  0.7232372  0.6978029  0.6309295  0.6026807
 [7]  0.5930601  0.5169529  0.3603450 -0.7130933

Largest  eigenvalues:
 [1] 101739685  92685832  88014231  87914286  83967919  81932192  81595175
 [8]  79054347  78612758  77164595

Smallest eigenvalues:
 [1]  0.9789891  0.9146893  0.8308172  0.6046982  0.5388086  0.5082604
 [7]  0.4216574  0.4142075  0.3684576 -0.1526504

Largest  eigenvalues:
 [1] 101015488  94216616  90057330  87230836  84933726  82715870  80995867
 [8]  80268289  80101947  78403674

Smallest eigenvalues:
 [1]  0.98402389  0.92100906  0.85619242  0.81291225  0.79520223  0.69935647
 [7]  0.68744471  0.60844435  0.51309756 -0.06082258

Largest  eigenvalues:
 [1] 99098417 93385940 88509441 85265431 85006681 82624519 79627062 79069120
 [9] 78228723 77260272

Smallest eigenvalues:
 [1]  1.0219525  0.9121243  0.7413772  0.6185044  0.5769625  0.4986761
 [7]  0.4089405  0.2998299  0.2311689 -0.3125157

Largest  eigenvalues:
 [1] 99253715 93353157 88677563 85552467 85268485 82678163 79741463 79410642
 [9] 79197370 78193297

Smallest eigenvalues:
 [1]  0.96930984  0.95682727  0.84599942  0.78937414  0.70668587  0.70375146
 [7]  0.67732389  0.60460004  0.54501371 -0.06140711

Largest  eigenvalues:
 [1] 97027351 93029697 88456584 84692185 84532852 82618340 79643389 78309987
 [9] 77451747 77079216

Smallest eigenvalues:
 [1]  0.9698603  0.9496725  0.9316423  0.6769017  0.6135550  0.5708756
 [7]  0.4787908  0.4324105  0.3385942 -0.3027704

Largest  eigenvalues:
 [1] 100418218  93281929  89215548  86443519  84800221  82796726  80270559
 [8]  79803163  78443356  77452695

Smallest eigenvalues:
 [1]  1.35369662  1.11824226  0.90193982  0.85442737  0.83203937  0.80403034
 [7]  0.72417644  0.63737172  0.63107180 -0.03517777

Largest  eigenvalues:
 [1] 100476629  93473726  89775456  85868387  85258064  82804953  80078686
 [8]  79809708  78851635  77698123

Smallest eigenvalues:
 [1]  0.9862023  0.8662345  0.7504058  0.7418887  0.7007132  0.6331729
 [7]  0.5113809  0.5082773  0.4772174 -0.4453628

Largest  eigenvalues:
 [1] 100702100  93523633  88470423  86747570  84859260  82684536  80569575
 [8]  79654342  78835411  77259522

Smallest eigenvalues:
 [1]  0.9096825  0.8947335  0.8697531  0.7794065  0.5993544  0.5626623
 [7]  0.4826807  0.4633000  0.4112802 -1.0857081

Largest  eigenvalues:
 [1] 102825723  94258075  89559298  87285590  85681733  83570033  81122697
 [8]  80517920  80288640  78198329

Smallest eigenvalues:
 [1]  0.7815919  0.7730961  0.7114449  0.7093999  0.6317899  0.5733451
 [7]  0.4059138  0.1777360 -1.0121216 -1.0774387

Largest  eigenvalues:
 [1] 100936581  94870795  89571318  86782403  86181366  83519669  80544192
 [8]  80453638  80432924  78188289

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	7.603597	0.7075871	12.76307	0.005	1.156436	2.205751

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

HR ~ alt + speed + PM1

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- HR_fd
covariates <- list(altitude = altitude_fd, 
                   speed = speed_fd,
                   pollution = pollution1_fd)
path_plot <- 'figures/model_HR_alt_speed_PM1_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     speed = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     pollution = list(nbetabasis = 80, norder = 4, lambda = 1e3))

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, 
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 31.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Warning message in `^.fd`((outcome - yhatfd), 2):
"The maximum error exceeds the tolerance level."
Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 452 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Smallest eigenvalues:
 [1]  0.81341976  0.80172464  0.78888646  0.65938550  0.59360590  0.58544932
 [7]  0.48074686  0.45257201  0.34079378 -0.02648318

Largest  eigenvalues:
 [1] 101848469  95212834  89540876  86599612  85633747  83078531  80164168
 [8]  80091089  79393813  78090666

Smallest eigenvalues:
 [1]  0.9626420  0.7400741  0.7113889  0.6939494  0.6297731  0.5992602
 [7]  0.5832355  0.5091785  0.3567443 -0.7105975

Largest  eigenvalues:
 [1] 101720930  92662552  87993495  87898086  83947287  81914646  81581069
 [8]  79034719  78592107  77151650

Smallest eigenvalues:
 [1]  0.9759312  0.8108620  0.8058702  0.5727452  0.5137479  0.5012124
 [7]  0.4061430  0.3929668  0.3534176 -0.1714933

Largest  eigenvalues:
 [1] 101002744  94200865  90044311  87219536  84918050  82701173  80986323
 [8]  80251575  80089101  78393514

Smallest eigenvalues:
 [1]  0.98945178  0.91681273  0.84700046  0.81576046  0.80986661  0.70199243
 [7]  0.68019397  0.60888265  0.50172875 -0.08501274

Largest  eigenvalues:
 [1] 99051298 93338595 88465229 85224800 84961377 82579081 79586680 79032279
 [9] 78186227 77223388

Smallest eigenvalues:
 [1]  1.0201935  0.9174463  0.7411120  0.6203104  0.5746062  0.4972004
 [7]  0.4050046  0.2961912  0.2332851 -0.3167967

Largest  eigenvalues:
 [1] 99189840 93272691 88593098 85500394 85174855 82579593 79654700 79347582
 [9] 79150041 78130970

Smallest eigenvalues:
 [1]  0.9734237  0.9491729  0.8432285  0.8000740  0.7078493  0.7023319
 [7]  0.6831534  0.5964720  0.5467915 -0.1156481

Largest  eigenvalues:
 [1] 97002366 92998779 88428839 84660081 84508673 82591729 79618163 78290109
 [9] 77428565 77056219

Smallest eigenvalues:
 [1]  0.9455775  0.9362206  0.9263068  0.6732952  0.5812299  0.5738530
 [7]  0.4704938  0.4256222  0.3417548 -0.3249727

Largest  eigenvalues:
 [1] 100400027  93251194  89186516  86427240  84765523  82759705  80256381
 [8]  79773610  78421058  77426583

Smallest eigenvalues:
 [1]  1.35888213  1.11908321  0.90181129  0.85292339  0.83395623  0.80395421
 [7]  0.72471701  0.63104400  0.62312820 -0.03696274

Largest  eigenvalues:
 [1] 100423882  93403387  89709104  85823519  85179311  82733631  80008810
 [8]  79770023  78802586  77635956

Smallest eigenvalues:
 [1]  0.9885411  0.8621542  0.7441775  0.7432723  0.7014195  0.6321689
 [7]  0.5089159  0.5069203  0.4678219 -0.4565331

Largest  eigenvalues:
 [1] 100660985  93468141  88417837  86711619  84803599  82633414  80537742
 [8]  79605314  78792290  77220776

Smallest eigenvalues:
 [1]  0.9192864  0.8946082  0.8634820  0.7793226  0.5909177  0.5566973
 [7]  0.4801440  0.4525031  0.4110680 -1.1381125

Largest  eigenvalues:
 [1] 102796141  94222866  89527909  87259821  85648090  83540458  81100540
 [8]  80488034  80260930  78174195

Smallest eigenvalues:
 [1]  0.7846323  0.7734625  0.7171531  0.7088025  0.6327957  0.5715181
 [7]  0.4087505  0.1771194 -1.0470611 -1.1330396

Largest  eigenvalues:
 [1] 100881447  94798889  89506914  86736755  86111989  83461934  80504123
 [8]  80400141  80379770  78140037

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	7.608386	0.7074309	12.73253	0.005	1.186233	2.19348

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

Model comparison

Finally, we compare fitted functional models based on various criteria.

# Specify the models folders
models_path <- list.dirs(path = "figures/") |>
  (\(x) x[grepl("^figures/model_HR.*_N200$", x)])() |>
  sub("^figures/", "", x = _)

# Create a data frame where the characteristics will be stored
model_comparison <- data.frame(model = NA, N = NA, RMSE = NA, maxR2 = NA, integratedR2 = NA, 
                               pval = NA, qval = NA, Fobs = NA)

# Load all models 
for (model_path in models_path) {
    load(file = paste0("figures/", model_path, "/model.RData"), verbose = FALSE)
    model_comparison <- rbind(
        model_comparison, 
        c(substr(model_path, 7, nchar(model_path) - 5), 
          length(model_1$common_IDs), 
          unlist(as.vector(model_2$df_res_metrics))))
}

model_comparison <- model_comparison[-1, ] |> 
    mutate(N = as.numeric(N),
           RMSE = round(as.numeric(RMSE), 6),
           maxR2 = round(as.numeric(maxR2), 6),
           integratedR2 = as.numeric(integratedR2),
           pval = as.numeric(pval),
           qval = round(as.numeric(qval), 4),
           Fobs = round(as.numeric(Fobs), 4))
model_comparison[rev(order(model_comparison$maxR2)), ]

A data.frame: 32 × 8

	model	N	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<chr>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
16	HR_alt_noise_steps_PM1	19	7.596198	0.886322	15.440500	0.000	2.6932	7.0288
17	HR_alt_noise_steps_PM25	19	7.595585	0.882461	15.194607	0.000	2.7384	6.7673
14	HR_alt_noise_speed_PM25	23	7.246352	0.850977	16.165170	0.000	2.0549	4.4484
13	HR_alt_noise_speed_PM1	23	7.229381	0.846894	16.343329	0.000	2.0670	4.2697
12	HR_alt_noise_speed	39	8.373718	0.760873	12.628704	0.000	0.8301	2.4966
21	HR_alt_noise_temp_speed	33	8.263548	0.757306	14.611970	0.000	1.0788	2.8659
22	HR_alt_noise_temp_steps	32	8.262888	0.736877	13.816507	0.000	1.1071	2.3669
15	HR_alt_noise_steps	32	8.555006	0.718060	11.376717	0.000	0.9352	2.0435
24	HR_alt_noise_tempBody_PM25	17	7.254627	0.715413	15.033106	0.180	3.3453	2.4660
30	HR_alt_steps_Sex	39	8.308018	0.710620	11.956099	0.000	0.7517	2.1195
28	HR_alt_speed_PM25	31	7.603597	0.707587	12.763065	0.005	1.1564	2.2058
27	HR_alt_speed_PM1	31	7.608386	0.707431	12.732527	0.005	1.1862	2.1935
23	HR_alt_noise_tempBody_PM1	17	7.204590	0.705722	15.502226	0.195	3.3658	2.3581
29	HR_alt_speed_Sex	47	8.265521	0.680346	12.408756	0.000	0.7131	1.8909
19	HR_alt_noise_temp_body_acc	22	19.509485	0.673596	1821.111769	0.050	2.2815	2.3260
6	HR_alt_noise_acc_PM25	19	7.557765	0.667754	15.215718	0.375	2.8854	1.5566
26	HR_alt_noise_tempEntrant	24	8.332604	0.656385	15.753599	0.040	1.3316	1.4692
5	HR_alt_noise_acc_PM1	19	7.531307	0.651828	15.359033	0.465	2.6927	1.4462
18	HR_alt_noise_temp_acc	32	8.334506	0.557506	12.402946	0.145	1.0109	0.8306
7	HR_alt_noise_acc_Sex	31	8.668593	0.554813	12.215680	0.195	1.2572	1.0712
4	HR_alt_noise_acc	32	8.588232	0.539411	9.702973	0.115	0.8661	0.6865
20	HR_alt_noise_temp_body_ENT	28	8.399143	0.533202	11.206135	0.045	0.9175	0.9335
31	HR_alt_temp_body_ENT	34	8.464485	0.478750	8.416988	0.005	0.6000	0.7784
9	HR_alt_noise_pollution1	23	7.666164	0.450873	9.603953	0.625	1.4022	0.7105
10	HR_alt_noise_pollution25	23	7.685670	0.449567	9.376699	0.645	1.4781	0.6998
3	HR_airpress_noise_temp	25	8.724708	0.440012	9.678972	0.210	1.1793	0.9077
25	HR_alt_noise_tempEmpatica	33	8.567088	0.429390	9.358159	0.085	0.7230	0.6613
8	HR_alt_noise	39	8.736482	0.411138	6.871452	0.010	0.4733	0.6125
2	HR_airpress_noise	30	8.784591	0.401951	6.733928	0.040	0.6637	0.6927
33	HR_alt_temp_pollution25	27	7.684850	0.393268	9.166168	0.430	1.0992	0.6483
32	HR_alt_temp_pollution1	27	7.685915	0.393187	9.208156	0.445	1.1403	0.6482
11	HR_alt_noise_Sex_Bspl	38	8.518559	0.379981	9.999879	0.035	0.5320	0.5998

write.csv(model_comparison[rev(order(model_comparison$maxR2)), ], 
          file = "model_comparison_HR.csv")

MODELS for EDA

Now, we want to model EDA on other covariates. We use the functions defined above. For new model, we only change the first cell below and the second cell then computes everything for us. Especially, we have to specify:

• outcome ... fd object
• covariates ... named list of the covariates
• path_plot ... path where to save the figures
• basis_params ... list of the parameters used for defining B-spline basis for each covariate and intercept
• N_repeats ... number of bootstrapped sampled used to construct pointwise CI's, it should be at least 1000
• nperm ... number of permutations for permutation $F$-test, it should be at least 200
• nsim ... number of simulations for calculating Global Envelope Test, it should be at least 2499

# Set the numbers for all models
N_repeats <- 101#1001
nperm <- 200
nsim <- 2499
# Length of vector of time points
lenght_tt <- 501
# Specify that the outcome is EDA, not HR
HR <- FALSE

EDA ~ alt + noise

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- EDA_fd
covariates <- list(altitude = altitude_fd, 
                   noise = noise_fd)
path_plot <- 'figures/model_EDA_alt_noise_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 90, norder = 4, lambda = 1e2),
                     noise = list(nbetabasis = 90, norder = 4, lambda = 1e2))

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, HR = HR, 
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 32.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 178 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	1.026654	0.3563771	6.133042	0.265	0.6648075	0.4472435

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 8, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

EDA ~ alt + noise + Sex (B-spline for sex)

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

NOTE: If we define also some scalar variable, we have to specify the basis parameters for corresponding parametric function. It is done by `basis_params`.

- If we specify for the name of the factor corresponding list of parameters, then the <b>B-splines</b> of specified order will be created
- Otherwise (if we do not specify the basis parameters for factor), the <b>constant basis</b> will be used for this parametric function.

• Be careful, the code is slightly different for cases with factors.

outcome <- EDA_fd
covariates <- list(altitude = altitude_fd, 
                   noise = noise_fd)
path_plot <- 'figures/model_EDA_alt_noise_Sex_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e6),
                     altitude = list(nbetabasis = 90, norder = 4, lambda = 1e2),
                     noise = list(nbetabasis = 90, norder = 4, lambda = 1e2),
                     Sex = list(nbetabasis = 90, norder = 4, lambda = 1e2))

factors <- list(Sex = participant_info$Sex |> as.factor())

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params,
                            factors = factors)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}
for (fact in names(factors)) {
    assign(fact, factors[[fact]][participant_info$ID %in% (model_1$common_IDs |> 
                                                           substr(4, 9))] |> as.numeric())
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, HR = HR,
                            basis_params = basis_params, nperm = nperm, factors = factors, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        if(!is.na(factors[1])) {for (fact in names(factors)) {
            assign(paste0(fact, '_BS'), 
                   factors[[fact]][participant_info$ID %in% (model_1$common_IDs |> substr(4, 9))][BS_sample] |> 
                   as.numeric())}}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS'))
        if(!is.na(factors[1])) {for(nam in names(factors)) {formula_BS <- paste0(formula_BS, '+', nam, '_BS')}}
        formula_BS <- as.formula(formula_BS)
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 31.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 342 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	1.021243	0.3608707	8.206033	0.33	0.7591384	0.489331

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, sex = FALSE, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

GET_res <- GET_function(J = j+1, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, sex = TRUE, lenght_tt = lenght_tt)
GET_results[[j+1]] <- GET_res

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
            (GET_results[[3]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

EDA ~ alt + noise + temp (Empatica)

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- EDA_fd
covariates <- list(altitude = altitude_fd, 
                   noise = noise_fd,
                   temperature = temperature_fd)
path_plot <- 'figures/model_EDA_alt_noise_tempEmpatica_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 90, norder = 4, lambda = 1e2),
                     noise = list(nbetabasis = 90, norder = 4, lambda = 1e2),
                     temperature = list(nbetabasis = 90, norder = 4, lambda = 1e2))

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, HR = HR,
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 32.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 844 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	0.9806856	0.5026002	11.13673	0.01	0.8105395	0.953169

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

EDA ~ alt + noise + temp (Entrant)

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- EDA_fd
covariates <- list(altitude = altitude_fd, 
                   noise = noise_fd,
                   temperature = air_temperature_ENT_fd)
path_plot <- 'figures/model_EDA_alt_noise_tempEntrant_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 90, norder = 4, lambda = 1e2),
                     noise = list(nbetabasis = 90, norder = 4, lambda = 1e2),
                     temperature = list(nbetabasis = 90, norder = 4, lambda = 1e2))

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, HR = HR,
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 19.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Warning message in `^.fd`((outcome - yhatfd), 2):
"The maximum error exceeds the tolerance level."
Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 1022 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Smallest eigenvalues:
 [1]  0.4747687  0.4574177  0.4257354  0.3680904  0.3096263  0.2376351
 [7]  0.2306224  0.1742160  0.1632070 -0.4374138

Largest  eigenvalues:
 [1] 57010815 54102242 51503062 50768795 49258917 47733267 47425762 46522527
 [9] 46340117 45844167

Smallest eigenvalues:
 [1]  0.4460772  0.4393647  0.3974302  0.3715897  0.2670383  0.2617466
 [7]  0.2282979  0.1408668 -0.1643602 -1.2597654

Largest  eigenvalues:
 [1] 57549532 54616092 51430193 50857337 49448282 48124440 47929747 47216213
 [9] 46775471 46197597

Smallest eigenvalues:
 [1]  0.6450638  0.6167103  0.5900787  0.5547841  0.5233902  0.4371264
 [7]  0.3835381  0.3237964  0.2595001 -1.6535915

Largest  eigenvalues:
 [1] 57147373 53829059 51058383 50235017 48863331 47705179 47306491 46115412
 [9] 46031724 45086121

Smallest eigenvalues:
 [1]  0.6182247  0.5909644  0.4716211  0.4552177  0.4454533  0.4228770
 [7]  0.4076849  0.3296401  0.3102789 -0.2962637

Largest  eigenvalues:
 [1] 57342325 53508083 50484868 49809124 48948458 47528254 47362086 45707269
 [9] 45667467 44818068

Smallest eigenvalues:
 [1]  0.48188152  0.46267268  0.46059733  0.41401408  0.40938763  0.31256848
 [7]  0.25681985  0.24910818  0.04919699 -3.77451313

Largest  eigenvalues:
 [1] 57120570 53913226 51269742 50101393 48670730 47796932 47241527 46534055
 [9] 46239842 45476534

Smallest eigenvalues:
 [1]  0.72402544  0.68438971  0.62110388  0.61853327  0.57479976  0.53536928
 [7]  0.37270196  0.22364597  0.15110019 -0.09406395

Largest  eigenvalues:
 [1] 56216438 54452903 50773788 50461334 49648383 48115585 47215797 47160305
 [9] 46198353 45883265

Smallest eigenvalues:
 [1]  0.5549913  0.5019532  0.4317150  0.4065969  0.3835204  0.3355137
 [7]  0.3346319  0.2205805  0.1478164 -0.4294444

Largest  eigenvalues:
 [1] 58339225 54418258 51633050 51435862 49740254 48545961 47588584 46951519
 [9] 46861206 46054341

Smallest eigenvalues:
 [1]  0.4791537  0.4751458  0.4451501  0.4295989  0.3990474  0.3015072
 [7]  0.2609971  0.2010509  0.2008824 -0.4835392

Largest  eigenvalues:
 [1] 57771136 54076342 51713407 51331619 49227746 48262636 47458069 46490010
 [9] 46102273 45473600

Smallest eigenvalues:
 [1]  0.39566999  0.35852395  0.31737142  0.29458972  0.27060302  0.19524266
 [7]  0.18250898  0.14147331  0.12899834 -0.05520984

Largest  eigenvalues:
 [1] 57686111 53311657 52301038 51105859 49054844 48104058 46968092 46048924
 [9] 46042289 45139979

Smallest eigenvalues:
 [1]  0.5845770  0.5538007  0.4682918  0.4601395  0.4442040  0.3169237
 [7]  0.3066175  0.2725544  0.1815992 -0.1595323

Largest  eigenvalues:
 [1] 58130534 54482869 52588102 51297152 49290799 49118980 47381065 46405338
 [9] 46340560 45479447

Smallest eigenvalues:
 [1]  0.5517688  0.5305087  0.5243246  0.4645273  0.3579128  0.3305835
 [7]  0.3084425  0.2457567  0.1358420 -2.3636817

Largest  eigenvalues:
 [1] 58312246 55221952 52243045 50907878 50080027 48956934 48208910 47403952
 [9] 46774211 46091862

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	0.9711039	0.6344874	14.23971	0.095	1.889565	1.676169

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

EDA ~ alt + n + t + acc

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- EDA_fd
covariates <- list(altitude = altitude_fd, 
                   noise = noise_fd,
                   temperature = temperature_fd,
                   acceleration = acceleration_fd)
path_plot <- 'figures/model_EDA_alt_noise_temp_acc_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     noise = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     temperature = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     acceleration = list(nbetabasis = 80, norder = 4, lambda = 1e3))

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, HR = HR,
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 31.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 478 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Smallest eigenvalues:
 [1]  0.71529531  0.65715715  0.64792174  0.64748316  0.62485081  0.61437600
 [7]  0.45717784  0.24001428 -0.05688383 -0.05864894

Largest  eigenvalues:
 [1] 104336178 101120577  94713204  92244050  91553646  88936312  86838039
 [8]  86126116  85194082  84610587

Smallest eigenvalues:
 [1]  1.05996704  0.93413211  0.93328033  0.92355319  0.80464017  0.64028175
 [7]  0.60194751  0.49722662  0.48281740 -0.02751828

Largest  eigenvalues:
 [1] 104491813  99173309  93577024  91724163  90765912  88060081  85401110
 [8]  85207132  84878235  83691649

Smallest eigenvalues:
 [1]  0.80458985  0.79608720  0.65299851  0.64806186  0.59300681  0.51281124
 [7]  0.46586174  0.15709994 -0.04152955 -1.44037925

Largest  eigenvalues:
 [1] 105591704  98871068  94179382  92455192  90107299  87560926  85805339
 [8]  85750439  85532052  84426281

Smallest eigenvalues:
 [1]  0.9157942  0.8713203  0.7643244  0.6796424  0.5759326  0.5408278
 [7]  0.5040664  0.3814823 -0.3521426 -0.7787503

Largest  eigenvalues:
 [1] 102848533  99177367  93214441  91293211  90298242  88095052  85578931
 [8]  84805975  83830870  83381463

Smallest eigenvalues:
 [1]  0.9819799  0.9504422  0.8845354  0.8211504  0.6299600  0.5931640
 [7]  0.5768839  0.5288442  0.3028801 -0.1473391

Largest  eigenvalues:
 [1] 105848228 100098178  93833409  92920639  91359789  88284660  86240055
 [8]  86068079  85968122  84383682

Smallest eigenvalues:
 [1]  0.8805152  0.7861475  0.7819451  0.7410960  0.7368880  0.6239228
 [7]  0.6217446  0.5700907  0.1062220 -0.6778086

Largest  eigenvalues:
 [1] 106849408 100196431  94731283  92475308  91125728  88419248  86374542
 [8]  85553904  85519077  83790875

Smallest eigenvalues:
 [1]  0.7900502  0.7809359  0.7402488  0.7329204  0.7259472  0.6505090
 [7]  0.5576750  0.5567297  0.5446177 -1.0804488

Largest  eigenvalues:
 [1] 103168843  99611748  94595090  91792239  90226060  89049471  86157465
 [8]  85679277  84000705  83736233

Smallest eigenvalues:
 [1]  0.7999668  0.7761854  0.7142653  0.7101801  0.6072047  0.5046810
 [7]  0.4640279  0.4621066  0.4588508 -0.6873907

Largest  eigenvalues:
 [1] 103317462 100380249  94576920  91722525  91067107  88681455  86507927
 [8]  85727214  84845521  84145253

Smallest eigenvalues:
 [1]  0.7114285  0.6018538  0.5828802  0.5329441  0.4852198  0.3981705
 [7]  0.3755107  0.3632016  0.2399731 -1.5730160

Largest  eigenvalues:
 [1] 103020179  99309423  94129407  90768249  90632376  88367993  86251060
 [8]  84972859  83791509  83628049

Smallest eigenvalues:
 [1]  0.8294642  0.7889080  0.7717433  0.5074243  0.4982853  0.4728394
 [7]  0.4637711 -0.2213382 -0.2777116 -0.8022646

Largest  eigenvalues:
 [1] 104963540  99928983  93571404  93366686  90611711  88162341  86125702
 [8]  85307762  85263255  83938231

Smallest eigenvalues:
 [1]  0.9403842  0.8138846  0.7939806  0.7466947  0.6186996  0.5924597
 [7]  0.5364208  0.5078007  0.3342102 -1.4993228

Largest  eigenvalues:
 [1] 104684972  99943249  94581898  91739359  91588733  88989798  86368165
 [8]  85544457  85013414  84153078

Smallest eigenvalues:
 [1]  0.8190458  0.7958099  0.7926415  0.7522592  0.7090974  0.6802037
 [7]  0.6410282  0.5262110  0.2806294 -0.1501503

Largest  eigenvalues:
 [1] 104155092  99779755  93805648  91870485  91160199  88258315  85899377
 [8]  85343072  84896099  84333207

Smallest eigenvalues:
 [1]  0.7942810  0.6982561  0.6779712  0.5945609  0.5787978  0.4573007
 [7]  0.4423982  0.3486892 -0.2641523 -1.5036612

Largest  eigenvalues:
 [1] 106201317  99779614  94307338  92276543  91215981  88398643  86111612
 [8]  85948271  85468081  84590541

Smallest eigenvalues:
 [1]  1.0076487  0.9291392  0.9141106  0.7938150  0.7459482  0.7162959
 [7]  0.7044750  0.5951691  0.5790196 -0.1838981

Largest  eigenvalues:
 [1] 102980588  99444049  93384377  90939729  90706886  88151266  86176533
 [8]  84878758  84063841  83550233

Smallest eigenvalues:
 [1]  0.6503689  0.6381602  0.6305463  0.6007480  0.5727479  0.5191914
 [7]  0.5031690  0.3865452 -0.3486639 -1.2112455

Largest  eigenvalues:
 [1] 104773776  99849573  94584854  91894754  91370287  88889426  86444614
 [8]  85368920  85282628  83987064

Smallest eigenvalues:
 [1]  0.8508928  0.8154733  0.7889989  0.7198550  0.5797130  0.5455997
 [7]  0.4576095  0.3295522  0.1648467 -1.7417164

Largest  eigenvalues:
 [1] 103542247  99805340  94576022  91849347  90926886  89538569  87402549
 [8]  84955212  84132453  83981741

Smallest eigenvalues:
 [1]  0.86434892  0.71191472  0.66773084  0.58820570  0.53176765  0.47241539
 [7]  0.04233538  0.02190882 -0.34846668 -0.87841904

Largest  eigenvalues:
 [1] 104459768 100643354  94752165  92096529  91614355  88910129  87173560
 [8]  85829817  85074408  84343865

Smallest eigenvalues:
 [1]  0.8456069  0.7465641  0.6288245  0.6052800  0.5810443  0.4979016
 [7]  0.4551947  0.3455334  0.3185152 -0.2205209

Largest  eigenvalues:
 [1] 105520051 100528497  93908994  93039696  91392066  88305435  86448802
 [8]  86326636  85895573  84744166

Smallest eigenvalues:
 [1]  0.8905142  0.8355155  0.6761222  0.6481694  0.5863778  0.4744086
 [7]  0.4650638  0.4621487  0.2364487 -4.5114150

Largest  eigenvalues:
 [1] 104776967  98847672  94354523  91447097  90695750  88580676  86278035
 [8]  85667063  84677331  84181983

Smallest eigenvalues:
 [1]  0.87598298  0.86113938  0.78975814  0.76686869  0.51371504  0.50805878
 [7]  0.34464378  0.34192928 -0.01327554 -0.19392059

Largest  eigenvalues:
 [1] 103066549  98874815  93334518  91184491  91152863  87988784  85720183
 [8]  84820579  84447319  83239556

Smallest eigenvalues:
 [1]  0.90708637  0.85489073  0.85148793  0.81152331  0.80868881  0.59858548
 [7]  0.55842709  0.53160979  0.37886523 -0.08591264

Largest  eigenvalues:
 [1] 105773731 101401800  94411704  92418693  91337633  88776590  86580064
 [8]  86162368  85527183  84647787

Smallest eigenvalues:
 [1]  0.96105320  0.93672019  0.89052396  0.88373194  0.56469670  0.47863259
 [7]  0.36120183  0.26395063 -0.09439721 -0.11575120

Largest  eigenvalues:
 [1] 103100151  98765653  92943726  90904040  89520099  87279334  85711730
 [8]  84640981  84010872  83447623

Smallest eigenvalues:
 [1]  1.07154982  0.98145244  0.87116725  0.83750530  0.72760255  0.64643464
 [7]  0.53692575  0.30055805 -0.02088184 -0.42137468

Largest  eigenvalues:
 [1] 103891658 100420734  94380565  92156702  91572140  89020489  86098254
 [8]  85751893  85012058  84233866

Smallest eigenvalues:
 [1]  0.8226975  0.8034129  0.7898369  0.6697591  0.5698265  0.4855859
 [7]  0.4276710  0.4091999 -0.1209642 -0.4437921

Largest  eigenvalues:
 [1] 106444015 100954276  95040224  92825220  92092041  88885875  86892238
 [8]  86326281  86132898  85379433

Smallest eigenvalues:
 [1]  0.73580674  0.71547592  0.60374002  0.52317564  0.49379349  0.47035492
 [7]  0.37569714  0.23896398  0.22458028 -0.02580594

Largest  eigenvalues:
 [1] 104020137  99291632  93508859  91233784  90028942  87323463  85152296
 [8]  84733830  84465737  83669395

Smallest eigenvalues:
 [1]  0.8796374  0.8780907  0.8239308  0.7721236  0.6873911  0.5056303
 [7]  0.4310891  0.3015257  0.3003582 -1.1422438

Largest  eigenvalues:
 [1] 103441122  99497873  93672338  91520965  90831344  88363939  86813799
 [8]  84515813  84444951  83357443

Smallest eigenvalues:
 [1]  0.8430146  0.7198505  0.7074024  0.6814185  0.6114685  0.4335933
 [7]  0.3977367  0.3593130 -0.1388345 -1.2327597

Largest  eigenvalues:
 [1] 105419334  99220768  93792330  91777138  90574755  87521985  85933188
 [8]  85051824  84687125  84528451

Smallest eigenvalues:
 [1]  0.8386778  0.6537879  0.6139774  0.6053720  0.4878238  0.3639670
 [7]  0.2237071  0.2179899 -0.2629713 -0.3340416

Largest  eigenvalues:
 [1] 104480729 100634781  95153742  92243208  91833613  89287421  86854880
 [8]  85735046  85610349  84328154

Smallest eigenvalues:
 [1]  0.8078024  0.7688366  0.7194096  0.5690648  0.5450135  0.5320275
 [7]  0.5283654  0.4889537  0.3320814 -1.0096363

Largest  eigenvalues:
 [1] 103033470 101166628  94232638  91458910  90492742  88571155  86301064
 [8]  85201635  84038568  83816212

Smallest eigenvalues:
 [1]  0.8745098  0.7681173  0.6969455  0.6246933  0.5833410  0.4730661
 [7]  0.4679226  0.4368091  0.4263006 -0.5865654

Largest  eigenvalues:
 [1] 104457878  99493157  94089804  91604090  91442603  88408573  86248229
 [8]  85531261  84818903  84407265

Smallest eigenvalues:
 [1]  0.8443338  0.7737227  0.6052366  0.6008664  0.5938124  0.5510738
 [7]  0.4600482  0.4215770  0.4113577 -3.4367402

Largest  eigenvalues:
 [1] 104664629  98951527  93578715  91175207  90339225  88014608  85712003
 [8]  84760915  84327760  83408653

Smallest eigenvalues:
 [1]  0.7484673  0.7389982  0.7377629  0.7334076  0.6834172  0.4626127
 [7]  0.4398324  0.3862404  0.0976895 -0.4748319

Largest  eigenvalues:
 [1] 103589017  99355433  94281765  91905985  89815812  87630224  85962524
 [8]  85568067  85073011  83737772

Smallest eigenvalues:
 [1]  0.7962071  0.7603090  0.7441163  0.7179555  0.6518519  0.5803225
 [7]  0.5381808  0.4985848  0.1036667 -0.6044022

Largest  eigenvalues:
 [1] 106511086  99822911  94183537  92557121  91971214  88969313  86987832
 [8]  86362954  85763231  85025331

Smallest eigenvalues:
 [1]  0.7398333  0.7215139  0.6606134  0.6514172  0.4553336  0.4525559
 [7]  0.3587850  0.2997641 -0.1003223 -0.7904825

Largest  eigenvalues:
 [1] 106573775  99317610  94143514  92185752  90717909  88360388  85494394
 [8]  85269182  85045181  84056108

Smallest eigenvalues:
 [1]  0.75839038  0.68246347  0.67902311  0.58827083  0.57354438  0.35780311
 [7]  0.32803338  0.06960289 -0.60924555 -1.13343261

Largest  eigenvalues:
 [1] 105990378  99922272  95365582  93472732  91159553  88774143  86934004
 [8]  86604410  86035443  84923748

Smallest eigenvalues:
 [1]  0.8513186  0.7775980  0.6818863  0.6469987  0.6344979  0.4935909
 [7]  0.4866547  0.4711691  0.3208297 -0.8497610

Largest  eigenvalues:
 [1] 106237500  99380784  94301203  92931660  89998447  87636401  85859848
 [8]  85541906  85473706  84047218

Smallest eigenvalues:
 [1]  0.9301248  0.8724659  0.7922428  0.7597574  0.5496032  0.5211803
 [7]  0.4750837  0.4008746  0.2013147 -1.8428235

Largest  eigenvalues:
 [1] 101964176  98878306  93509471  90671658  89639588  87948768  85562454
 [8]  84501003  83441040  83102113

Smallest eigenvalues:
 [1]  0.8899350  0.8408969  0.7448646  0.6898572  0.6489925  0.5524051
 [7]  0.4621801  0.2817378 -0.3614150 -1.0933649

Largest  eigenvalues:
 [1] 104501304  99316054  93745896  91416986  91029807  88233722  85895607
 [8]  85094520  84681101  83418420

Smallest eigenvalues:
 [1]  0.9381133  0.9188096  0.9144229  0.8822154  0.8179349  0.6496309
 [7]  0.5982140  0.5957501  0.1731166 -0.7899581

Largest  eigenvalues:
 [1] 107565574  99125609  94278013  93234682  91098156  88330081  86333100
 [8]  85874402  85386024  84547408

Smallest eigenvalues:
 [1]  1.0529908  0.9049032  0.8427068  0.8127357  0.7828059  0.7689413
 [7]  0.6174655  0.5710951  0.4215169 -2.4973977

Largest  eigenvalues:
 [1] 103983159  97894163  93037265  90218028  90035822  87507968  85643115
 [8]  84513599  83495773  82937669

Smallest eigenvalues:
 [1]  0.9654332  0.7821536  0.7798522  0.7454313  0.7134808  0.6406593
 [7]  0.4728133  0.4152741  0.3649767 -1.1618239

Largest  eigenvalues:
 [1] 104435978  99618955  94649326  91774154  91516095  88652488  86022406
 [8]  85930882  85140459  84272633

Smallest eigenvalues:
 [1]  0.81773819  0.76909417  0.75269308  0.65035879  0.64022264  0.55498111
 [7]  0.50953342  0.38756285 -0.03974764 -0.35407391

Largest  eigenvalues:
 [1] 107464723 100622442  94435724  93748127  91142713  88333133  86928636
 [8]  86234540  85197728  84442451

Smallest eigenvalues:
 [1]  0.8338658  0.6746731  0.6720420  0.6097554  0.5970376  0.5804414
 [7]  0.5191579  0.3620539  0.0871708 -0.1099318

Largest  eigenvalues:
 [1] 104519191  98642669  93223873  91073463  90385336  87586545  85561498
 [8]  84782366  84473843  83725855

Smallest eigenvalues:
 [1]  0.8929311  0.7681394  0.7202351  0.6178122  0.5983453  0.4603386
 [7]  0.4575106  0.3056823  0.1611379 -0.1974608

Largest  eigenvalues:
 [1] 107049180  99163516  94538436  92471350  90419111  87550636  86516913
 [8]  85717507  85693305  85194228

Smallest eigenvalues:
 [1]  0.8884553  0.8856775  0.7539470  0.6684768  0.6381232  0.5383722
 [7]  0.4811965  0.4713399  0.4618388 -1.4110076

Largest  eigenvalues:
 [1] 105351341  99369216  94995891  92067154  90930699  88565758  86285411
 [8]  86119722  85237043  84405728

Smallest eigenvalues:
 [1]  0.9444013  0.9291426  0.8721264  0.8178605  0.7025553  0.6955132
 [7]  0.5807001  0.3640566  0.3285204 -0.1308723

Largest  eigenvalues:
 [1] 105194494  99065122  93528396  92444499  90539326  87822564  85476731
 [8]  85365552  85326097  83816116

Smallest eigenvalues:
 [1]  0.97658559  0.97030419  0.90009971  0.88867702  0.74304795  0.63847534
 [7]  0.59479255  0.53679144  0.43830732 -0.08021742

Largest  eigenvalues:
 [1] 104157755  99208721  93401377  91929848  90497511  87865684  85867312
 [8]  85192659  84793520  83665107

Smallest eigenvalues:
 [1]  0.8337573  0.7065419  0.6640999  0.5800426  0.5671935  0.5499698
 [7]  0.5411207  0.4208867 -0.2280637 -1.0622205

Largest  eigenvalues:
 [1] 106895212 100788329  95188750  94292247  91474874  89019523  87212633
 [8]  86391092  86283859  84818930

Smallest eigenvalues:
 [1]  0.6967824  0.6442530  0.6012996  0.5768479  0.5731350  0.5432930
 [7]  0.4675510  0.1281104 -0.2418260 -4.3489789

Largest  eigenvalues:
 [1] 107029422 101080114  95287564  93335628  91290638  88506810  86690936
 [8]  86493074  86090580  84705949

Smallest eigenvalues:
 [1]  0.8826730  0.8740377  0.8002370  0.6500185  0.6322033  0.5040362
 [7]  0.4095338  0.2205173  0.1726404 -0.2255056

Largest  eigenvalues:
 [1] 106829970  99643395  94867180  93677242  90688011  87930635  86656704
 [8]  86255637  85632896  84605822

Smallest eigenvalues:
 [1]  0.8725536  0.8400439  0.8093211  0.7755989  0.7688947  0.5537328
 [7]  0.4316948  0.2899139 -0.2391339 -0.7682721

Largest  eigenvalues:
 [1] 105716612  99623780  93737216  92349414  91267469  88348283  85952927
 [8]  85524296  84844391  83686582

Smallest eigenvalues:
 [1]  0.8818685  0.8740855  0.7737895  0.7466789  0.6284974  0.6185893
 [7]  0.6122184  0.4828108 -0.2181644 -0.5219358

Largest  eigenvalues:
 [1] 104649231  98541945  92933258  92135779  90135506  87524211  85568500
 [8]  85388438  85089879  83935824

Smallest eigenvalues:
 [1]  0.99169984  0.85595259  0.84428134  0.78240254  0.77751121  0.59920223
 [7]  0.58984954  0.54566010  0.06978536 -1.50926647

Largest  eigenvalues:
 [1] 103872021  98527270  92934053  90787094  90177712  87041550  85297734
 [8]  85153949  84146545  83875504

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	0.9597557	0.5332638	14.44874	0.09	1.106629	1.014447

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

EDA ~ alt + n + t + speed

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- EDA_fd
covariates <- list(altitude = altitude_fd, 
                   noise = noise_fd,
                   temperature = temperature_fd,
                   speed = speed_fd)
path_plot <- 'figures/model_EDA_alt_noise_temp_speed_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 100, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 90, norder = 4, lambda = 1e4),
                     noise = list(nbetabasis = 90, norder = 4, lambda = 1e4),
                     temperature = list(nbetabasis = 90, norder = 4, lambda = 1e4),
                     speed = list(nbetabasis = 90, norder = 4, lambda = 1e4))

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, HR = HR,
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 32.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 516 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Smallest eigenvalues:
 [1]  0.8023326  0.7306568  0.5930300  0.5784356  0.5660754  0.4486113
 [7]  0.3847868  0.3455271  0.2515624 -0.1991579

Largest  eigenvalues:
 [1] 96292771 92110720 86573470 85574960 84154838 81990063 80539458 79906470
 [9] 77883632 77852314

Smallest eigenvalues:
 [1]  0.8130933  0.7657174  0.5990278  0.5959814  0.5311977  0.5213477
 [7]  0.4962745  0.4469545  0.3857830 -0.3024419

Largest  eigenvalues:
 [1] 95439344 92509953 87820472 85515156 84490174 82535084 80704250 79423703
 [9] 79156954 78221011

Smallest eigenvalues:
 [1]  0.95360030  0.79554248  0.61498527  0.58710836  0.52652436  0.52243351
 [7]  0.46332465  0.46239561  0.30109619 -0.02969841

Largest  eigenvalues:
 [1] 96212271 92761282 86850468 86579804 83896613 81797478 80613539 79757593
 [9] 78658487 77189551

Smallest eigenvalues:
 [1]  0.8667990  0.8625264  0.8457241  0.7588064  0.6484854  0.4891209
 [7]  0.4686352  0.4625845  0.4112604 -0.1139496

Largest  eigenvalues:
 [1] 96959878 92131671 86847039 86503916 84168532 81750369 80524947 79666280
 [9] 78566937 77587356

Smallest eigenvalues:
 [1]  0.8507446  0.7772218  0.7363910  0.5669263  0.5406401  0.5272125
 [7]  0.5089937  0.3605121  0.1736629 -0.5250817

Largest  eigenvalues:
 [1] 96380906 92161514 86998980 85897990 84433475 82271723 80466092 79994440
 [9] 78583933 77450409

Smallest eigenvalues:
 [1]  0.7879745  0.7184224  0.7100303  0.5989931  0.5827538  0.4897499
 [7]  0.4790893  0.3112615  0.1526596 -0.2378991

Largest  eigenvalues:
 [1] 96662563 91922391 86690050 86162257 84537752 82340003 80593058 80203277
 [9] 78235319 77938036

Smallest eigenvalues:
 [1]  0.8270973  0.7748892  0.7664919  0.5443116  0.4468675  0.4406728
 [7]  0.3466308  0.3176865  0.1447340 -0.0493373

Largest  eigenvalues:
 [1] 96009923 91358284 86925984 85656715 84628297 82716677 80726114 80144369
 [9] 78450400 78011592

Smallest eigenvalues:
 [1]  0.84749171  0.83644010  0.82322868  0.74751525  0.67307654  0.65059059
 [7]  0.62256924  0.43098287  0.36947403 -0.01827428

Largest  eigenvalues:
 [1] 95646294 92317290 86694244 85852548 84543185 82205788 80084197 79576240
 [9] 78523879 77159717

Smallest eigenvalues:
 [1]  0.86009285  0.74860994  0.60229623  0.57807967  0.54081888  0.48055032
 [7]  0.45924758  0.27363625  0.04797604 -0.05643324

Largest  eigenvalues:
 [1] 95420026 91237449 85675088 85555028 84625624 81873091 79626472 79139858
 [9] 77351183 77287963

Smallest eigenvalues:
 [1]  0.6988804  0.5381416  0.5169461  0.4440645  0.4429098  0.4199216
 [7]  0.3539133  0.3491382  0.1359943 -0.8780256

Largest  eigenvalues:
 [1] 96158590 91992731 87360328 86192567 83887723 82376332 80507375 80127623
 [9] 78245467 77606244

Smallest eigenvalues:
 [1]  0.7524768  0.7486927  0.7354138  0.7008322  0.6579877  0.4992293
 [7]  0.4714912  0.4055988  0.3710590 -0.2093639

Largest  eigenvalues:
 [1] 96399156 91800480 85763194 85593892 83807080 81850976 80573383 79140318
 [9] 78672889 77419405

Smallest eigenvalues:
 [1]  0.93209776  0.83536702  0.79677212  0.77498429  0.71394999  0.67694649
 [7]  0.54520265  0.51255610  0.41150507 -0.01113285

Largest  eigenvalues:
 [1] 96307042 91968831 86429401 86123562 84108121 82028702 80839774 79515824
 [9] 77920666 77460336

Smallest eigenvalues:
 [1]  0.7830629  0.7070390  0.5885160  0.5747904  0.5672663  0.5430718
 [7]  0.5361667  0.4649680  0.4065079 -0.2506416

Largest  eigenvalues:
 [1] 98264475 92236769 87741807 87075538 84374336 81968609 81449334 79553376
 [9] 78688667 77292962

Smallest eigenvalues:
 [1]  0.70546259  0.62760187  0.59316086  0.43921190  0.37966541  0.36184532
 [7]  0.34035727  0.26602798  0.07259927 -0.09715703

Largest  eigenvalues:
 [1] 98310919 92355241 87754627 87450377 84484656 82738596 81544582 80057618
 [9] 78498418 77744690

Smallest eigenvalues:
 [1]  0.899030852  0.855844796  0.847746166  0.764017142  0.727826265
 [6]  0.612152923  0.431827418  0.125784886  0.125488792 -0.008586478

Largest  eigenvalues:
 [1] 98330573 91523235 86904072 86787261 84092398 82109556 81350341 79835873
 [9] 78794387 77912923

Smallest eigenvalues:
 [1]  0.9244387  0.8599096  0.8284976  0.7885026  0.7461661  0.7182859
 [7]  0.6504258  0.5253792  0.4368723 -2.5996317

Largest  eigenvalues:
 [1] 97613423 91648543 86518457 86016073 83905756 82140003 79976457 78699033
 [9] 78464549 77379351

Smallest eigenvalues:
 [1]  0.7623535  0.7039853  0.6698169  0.6052488  0.5885044  0.5183588
 [7]  0.4401257  0.4322316  0.3472072 -0.8608683

Largest  eigenvalues:
 [1] 95896130 90483110 85963577 85662653 83441379 81488409 79712679 79107844
 [9] 77935794 77050543

Smallest eigenvalues:
 [1]  1.0010092  0.8616235  0.8329634  0.7870186  0.5835864  0.5060907
 [7]  0.5003330  0.2902580  0.2091715 -0.3220562

Largest  eigenvalues:
 [1] 96803606 91917252 86851218 86080707 84108338 82355907 80011399 79071608
 [9] 78933428 77287942

Smallest eigenvalues:
 [1]  0.8238099  0.7815312  0.7652700  0.6555720  0.5812882  0.5733222
 [7]  0.5531999  0.4326715  0.4127030 -0.3300745

Largest  eigenvalues:
 [1] 94808210 90846892 86139300 84846745 83557223 81815506 79210424 78782066
 [9] 77306270 77189146

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	0.9784529	0.4986595	25.74513	0.765	1.321357	0.9232714

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

EDA ~ alt + n + t + steps

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- EDA_fd
covariates <- list(altitude = altitude_fd, 
                   noise = noise_fd,
                   temperature = temperature_fd,
                   steps = steps_fd)
path_plot <- 'figures/model_EDA_alt_noise_temp_steps_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 80, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     noise = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     temperature = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     steps = list(nbetabasis = 80, norder = 4, lambda = 1e3))

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, HR = HR,
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 31.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 448 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Smallest eigenvalues:
 [1]  0.8196595  0.8044466  0.6853499  0.6840547  0.6416641  0.5000847
 [7]  0.4919223  0.4162059  0.3512690 -1.6095933

Largest  eigenvalues:
 [1] 106261679  99644644  93848745  92985924  91207569  88436906  86003831
 [8]  85722197  85399404  83821687

Smallest eigenvalues:
 [1]   1.0243802   1.0042661   0.9074820   0.8848076   0.6822417   0.6656719
 [7]   0.6595394   0.5936150   0.5464485 -16.8462585

Largest  eigenvalues:
 [1] 102952997  99264758  93314383  91395716  90396182  88191151  85656243
 [8]  84903734  83921335  83480049

Smallest eigenvalues:
 [1]  0.93474535  0.88953946  0.86492019  0.79618887  0.77567234  0.64266068
 [7]  0.47448650  0.45876537  0.39235486 -0.06361396

Largest  eigenvalues:
 [1] 103835118 100126938  93913753  92095472  90603400  88014380  86347171
 [8]  86104552  84947737  84571274

Smallest eigenvalues:
 [1]  0.6424902  0.5804021  0.4430021  0.4208843  0.3595852  0.2851461
 [7]  0.1373264 -0.1128517 -0.2345978 -0.7043995

Largest  eigenvalues:
 [1] 105952490 100186330  93940728  93017042  91460258  88381820  86342228
 [8]  86161250  86049650  84483471

Smallest eigenvalues:
 [1]  1.0173485  0.8549337  0.8174713  0.8062163  0.7948853  0.5978083
 [7]  0.5920966  0.4753799  0.3281027 -0.5971899

Largest  eigenvalues:
 [1] 106954903 100284820  94840793  92571347  91224212  88516510  86456406
 [8]  85652975  85611368  83890024

Smallest eigenvalues:
 [1]  0.38422372  0.22671987  0.19928928  0.12576788  0.10996263  0.09690684
 [7]  0.03039322 -0.16705310 -1.02607067 -1.94259144

Largest  eigenvalues:
 [1] 103125424  99395034  94232529  90868430  90728629  88465616  86332812
 [8]  85072625  83886235  83723967

Smallest eigenvalues:
 [1]   0.94683153   0.82727887   0.77773333   0.66781492   0.52404798
 [6]   0.49053237   0.30285488   0.08017989  -0.18854318 -37.14900405

Largest  eigenvalues:
 [1] 105586688 100156622  94368592  93050418  91410704  88542240  86248204
 [8]  86058775  85764301  83966875

Smallest eigenvalues:
 [1]  0.87129084  0.85692784  0.82183477  0.69695934  0.68216177  0.67006993
 [7]  0.65826422  0.47638148  0.45361357 -0.08585576

Largest  eigenvalues:
 [1] 104370583 100528836  94865266  92133549  91601193  89208480  86503024
 [8]  85696452  85020705  84096407

Smallest eigenvalues:
 [1]   0.250108494   0.242523990   0.087507796   0.070919500  -0.001204408
 [6]  -0.016844338  -0.826135206  -1.704947970  -6.974567217 -24.603975432

Largest  eigenvalues:
 [1] 101771717  99312013  93142237  91557752  89371803  88137168  85952737
 [8]  83864954  82729797  82655034

Smallest eigenvalues:
 [1]   0.8387625   0.8273547   0.7879769   0.6854452   0.5280797   0.4976924
 [7]   0.3818900   0.3189906   0.2045337 -12.2193458

Largest  eigenvalues:
 [1] 103646808  99891303  94680836  91952032  91022791  89632045  87481257
 [8]  85056756  84223969  84069409

Smallest eigenvalues:
 [1]  1.01442807  0.97275961  0.95795650  0.88684745  0.87107463  0.74558370
 [7]  0.57022466  0.46913488  0.14578255 -0.03876611

Largest  eigenvalues:
 [1] 104357352  98982818  93077712  91895437  90508861  87748742  85329004
 [8]  85202504  84904788  83383727

Smallest eigenvalues:
 [1]  1.1049448  1.0592071  1.0523930  0.9276761  0.9232503  0.7781647
 [7]  0.6550936  0.4882699  0.4236503 -0.6533081

Largest  eigenvalues:
 [1] 104496448  99139433  93680086  92434623  90622925  87894492  85576715
 [8]  85200908  85172017  83861451

Smallest eigenvalues:
 [1]  0.9249614  0.8820767  0.8196297  0.7358541  0.6754209  0.4264131
 [7]  0.4047466  0.3883430  0.3849609 -0.6345571

Largest  eigenvalues:
 [1] 107262331 100406807  94959708  93604209  91327790  88359696  86755444
 [8]  86072587  85991151  84674536

Smallest eigenvalues:
 [1]  0.8951750  0.8094381  0.7268142  0.7030697  0.6052475  0.4918147
 [7]  0.4310893  0.3931693  0.3801434 -0.4329674

Largest  eigenvalues:
 [1] 103978975  99287902  93424526  91901233  91661691  88249710  85472008
 [8]  84794646  84555675  83159828

Smallest eigenvalues:
 [1]  0.9290823  0.9074280  0.8649258  0.7850286  0.7024474  0.6751984
 [7]  0.5240887  0.4496939  0.4027126 -2.6934274

Largest  eigenvalues:
 [1] 104884607  98936568  94464302  91547350  90799037  88679521  86360307
 [8]  85769972  84772520  84281823

Smallest eigenvalues:
 [1]  0.7836526  0.7320805  0.5906383  0.5859380  0.4428995  0.4386205
 [7]  0.4302052  0.3978384  0.2668234 -0.3212869

Largest  eigenvalues:
 [1] 105187183 100942427  95413563  92903751  91862136  89370885  86956994
 [8]  86675299  86057980  85016786

Smallest eigenvalues:
 [1]  0.8909155  0.8746383  0.8343011  0.7560164  0.6183052  0.6158490
 [7]  0.4889652  0.3491698  0.2147309 -0.9447103

Largest  eigenvalues:
 [1] 105878929 101491096  94518007  92516120  91437295  88875704  86671164
 [8]  86241685  85619389  84745437

Smallest eigenvalues:
 [1]   0.5343448   0.5238116   0.5219636   0.4860134   0.2741081   0.2480360
 [7]   0.2248062  -0.5623572  -1.5396562 -86.9791467

Largest  eigenvalues:
 [1] 103206512  98845791  93049584  91002514  89618385  87368941  85792539
 [8]  84742558  84105268  83547035

Smallest eigenvalues:
 [1]  0.9263446  0.8719181  0.7827959  0.7564749  0.7333258  0.6480056
 [7]  0.5060685  0.4596948  0.4303588 -0.2420529

Largest  eigenvalues:
 [1] 107981945 101329640  95564272  94383361  91725065  88763531  87560757
 [8]  86919555  86831387  85120954

Smallest eigenvalues:
 [1]  1.0616214  0.9766720  0.9277764  0.9209410  0.7994646  0.7586696
 [7]  0.5606442  0.4983990  0.4796401 -0.4711130

Largest  eigenvalues:
 [1] 107344634 100818994  94125231  94068780  91886672  88884787  86981669
 [8]  86112649  85910283  84366288

Smallest eigenvalues:
 [1]  0.87925742  0.85964046  0.73783219  0.71225394  0.61185693  0.45277877
 [7]  0.35651200  0.32761879 -0.01542535 -0.91171730

Largest  eigenvalues:
 [1] 105919357  98244322  93468363  92715722  89673270  86899232  85840512
 [8]  84658237  84198951  83292554

Smallest eigenvalues:
 [1]  0.7494719  0.6579574  0.6324924  0.5690456  0.4733595  0.4669362
 [7]  0.4581893  0.3612288  0.2915466 -0.2245592

Largest  eigenvalues:
 [1] 102584868  99856527  94257667  91367664  90696731  88090486  86189476
 [8]  85849059  84649432  84000760

Smallest eigenvalues:
 [1]    0.6938824    0.6844554    0.6772146    0.6605042    0.5666201
 [6]    0.3192113    0.1544394    0.1214697    0.1172577 -111.2578620

Largest  eigenvalues:
 [1] 105526798  99310442  93896206  91877853  90676258  87622033  86036043
 [8]  85136935  84786774  84627351

Smallest eigenvalues:
 [1]  0.7839034  0.6677506  0.6483113  0.5470486  0.5081555  0.5029692
 [7]  0.3993546  0.3190194  0.3120477 -0.2696197

Largest  eigenvalues:
 [1] 105722127 100225546  94675091  93133449  91003530  88503737  86238636
 [8]  85716527  85281569  83878103

Smallest eigenvalues:
 [1]  0.52142718  0.43728438  0.41453525  0.37892685  0.21906974  0.11353888
 [7] -0.01496437 -0.09717759 -0.26969856 -0.54465620

Largest  eigenvalues:
 [1] 104587298 100724335  95256757  92341962  91938056  89387340  86938856
 [8]  85839867  85703828  84419337

Smallest eigenvalues:
 [1]  0.62727973  0.53182308  0.42810272  0.22792692  0.12242602  0.02302653
 [7] -0.01326906 -0.16570588 -0.31323935 -1.32354506

Largest  eigenvalues:
 [1] 104561932  99589333  94193032  91699365  91543678  88508858  86344031
 [8]  85616290  84911910  84504424

Smallest eigenvalues:
 [1]  0.8908322  0.8851475  0.8446448  0.7755036  0.7660910  0.7456906
 [7]  0.6363262  0.5030096  0.4544611 -4.3796006

Largest  eigenvalues:
 [1] 104776347  99044022  93688384  91276687  90445616  88117132  85795209
 [8]  84868271  84424471  83512079

Smallest eigenvalues:
 [1]  0.7806053  0.6809623  0.5683034  0.5269032  0.4690017  0.4515576
 [7]  0.4404079  0.4269714  0.3618563 -0.6147707

Largest  eigenvalues:
 [1] 106156485 100463913  95033229  92896246  92455854  89619792  86715285
 [8]  86335632  85981407  84446956

Smallest eigenvalues:
 [1]  1.0038761  0.9135669  0.8347945  0.7240845  0.7147767  0.6517433
 [7]  0.4985436  0.4861040  0.4254801 -0.4997422

Largest  eigenvalues:
 [1] 106615719  99917535  94287427  92652684  92074892  89065256  87085112
 [8]  86444184  85854364  85125296

Smallest eigenvalues:
 [1]  0.85802596  0.74570393  0.72215775  0.67460185  0.52876759  0.52765608
 [7]  0.52489237  0.49958474  0.25989217 -0.03833498

Largest  eigenvalues:
 [1] 105638709 100052414  94421267  92418535  91023732  88806392  86437826
 [8]  85707399  85096092  84626840

Smallest eigenvalues:
 [1]  0.8426319  0.7629597  0.7627586  0.7535063  0.7045397  0.5384999
 [7]  0.4363654  0.3660655  0.3585452 -0.3635503

Largest  eigenvalues:
 [1] 105198558  99906862  94095225  92670188  90842280  88408363  86361106
 [8]  86346150  85707331  84334146

Smallest eigenvalues:
 [1]   1.07301313   1.05007555   0.83878861   0.72550068   0.67434711
 [6]   0.61661829   0.41223986   0.26342700   0.09501782 -29.09794935

Largest  eigenvalues:
 [1] 105255090 100751804  94957016  92072793  91743890  88976092  86563261
 [8]  86451486  85333163  84575312

Smallest eigenvalues:
 [1]  0.84649187  0.78203849  0.68553864  0.61112767  0.52192843  0.47494514
 [7]  0.42719277  0.11098407 -0.02413549 -0.04802989

Largest  eigenvalues:
 [1] 106098181 100015601  95470295  93573147  91261909  88876826  87031679
 [8]  86698456  86121176  85025885

Smallest eigenvalues:
 [1]  0.80418551  0.78367278  0.70880372  0.68984633  0.59806619  0.51986245
 [7]  0.51612547  0.51123790  0.40000075 -0.05287891

Largest  eigenvalues:
 [1] 105329211 100537758  94783997  92726337  91850141  89244364  86788607
 [8]  86089671  85271433  84401052

Smallest eigenvalues:
 [1]  0.7590050  0.7055272  0.5921747  0.5320261  0.5276959  0.5030242
 [7]  0.4891627  0.3555474  0.3303684 -0.1386635

Largest  eigenvalues:
 [1] 105664425 100415948  94901863  93474657  91864342  89276718  86763490
 [8]  86517450  86351623  84792522

Smallest eigenvalues:
 [1]  0.38939703  0.26811735 -0.03329406 -0.20080089 -0.27962565 -0.32020108
 [7] -0.64573332 -0.74294933 -1.13191880 -2.78097339

Largest  eigenvalues:
 [1] 104607323  99401924  93844078  91514007  91129372  88330448  85976032
 [8]  85200270  84774891  83517741

Smallest eigenvalues:
 [1]  0.8701757  0.8359618  0.7756885  0.7173479  0.6313990  0.6008591
 [7]  0.4155364  0.3360510  0.2319035 -0.7099531

Largest  eigenvalues:
 [1] 108506838 100921191  94756896  93703607  91512905  88786914  87010038
 [8]  86106737  85779851  84459959

Smallest eigenvalues:
 [1]  0.8660840  0.8379707  0.8032716  0.6981793  0.6283414  0.5457798
 [7]  0.4662889  0.3442181  0.3039907 -0.1382705

Largest  eigenvalues:
 [1] 105140831 100226140  93976177  92974535  91679707  88867396  86445388
 [8]  85586439  85252980  83484128

Smallest eigenvalues:
 [1]  0.8878128  0.8856357  0.8721985  0.8001869  0.7693452  0.6224080
 [7]  0.6169580  0.4386508  0.2647493 -0.2861727

Largest  eigenvalues:
 [1] 104731022 100852422  94413882  91971036  91820171  89045923  86743214
 [8]  85507572  85186965  83933670

Smallest eigenvalues:
 [1]  1.0520046  0.9636423  0.7910852  0.7746524  0.6950678  0.6746206
 [7]  0.6241497  0.4532057  0.4249675 -0.4286315

Largest  eigenvalues:
 [1] 106716597  99369237  94061588  93306600  90650691  87662102  86232573
 [8]  85421768  85093904  83853578

Smallest eigenvalues:
 [1]  0.9912773  0.9767569  0.7615214  0.6283479  0.5598192  0.5424520
 [7]  0.4858531  0.3630912  0.2837625 -1.0471986

Largest  eigenvalues:
 [1] 106934487  99728605  94974389  93772034  90783787  88029905  86746371
 [8]  86348266  85712694  84702566

Smallest eigenvalues:
 [1]  0.9179462  0.7996117  0.7907295  0.7574301  0.6766746  0.6585297
 [7]  0.6142183  0.4744912  0.4020389 -0.5154558

Largest  eigenvalues:
 [1] 105810535 100331874  94151115  92777331  91019076  88135876  86245923
 [8]  85832870  85614005  84462328

Smallest eigenvalues:
 [1]  0.9301329  0.8944272  0.7914852  0.7887828  0.7134680  0.7065633
 [7]  0.5760252  0.4407584  0.2610854 -0.3981682

Largest  eigenvalues:
 [1] 102109375 100130698  93718856  91627563  90453132  88835254  86895765
 [8]  85780179  84056712  83758460

Smallest eigenvalues:
 [1]  0.9077808  0.8981995  0.8582748  0.7888569  0.7596013  0.5052185
 [7]  0.4777994  0.4397059  0.3007343 -0.6416396

Largest  eigenvalues:
 [1] 105819126  99710026  93836059  92443282  91365638  88441599  86029217
 [8]  85612459  84942220  83783311

Smallest eigenvalues:
 [1]  0.92405633  0.72106321  0.55220536  0.54775112  0.41949204  0.33623383
 [7]  0.32327985  0.25608123  0.04364464 -1.72722280

Largest  eigenvalues:
 [1] 106689852 100269518  94799029  93003180  91247418  88727221  86998260
 [8]  86736684  86318851  85138976

Smallest eigenvalues:
 [1]  0.8247083  0.8111348  0.8019690  0.7584728  0.6976873  0.5529231
 [7]  0.5424216  0.4783611  0.4535837 -2.2503883

Largest  eigenvalues:
 [1] 107865231 101197175  95176002  94334583  91551338  88900760  87293079
 [8]  86146705  85561124  83927520

Smallest eigenvalues:
 [1]  1.08318561  0.89952892  0.78688449  0.74957939  0.69768806  0.65558491
 [7]  0.57659461  0.48818150  0.41798730 -0.01727594

Largest  eigenvalues:
 [1] 104745840 100437166  94869555  91705325  91527211  89085504  86579797
 [8]  85985856  84978659  84212738

Smallest eigenvalues:
 [1]  1.0352508  0.9897234  0.8236016  0.7787709  0.7295700  0.6998424
 [7]  0.6357687  0.4797202  0.4550250 -0.1599307

Largest  eigenvalues:
 [1] 105176363  99465392  94681385  92005338  90229470  87925164  85572072
 [8]  85247392  85187900  83431362

Smallest eigenvalues:
 [1]  0.8995431  0.7500717  0.7238995  0.6673440  0.6138038  0.4698957
 [7]  0.4247194  0.3684657  0.3247149 -2.6122985

Largest  eigenvalues:
 [1] 104754790  98630815  93038068  92231986  90236935  87618670  85642257
 [8]  85478656  85180050  84033121

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	0.9677958	0.4842474	13.27987	0.26	1.347121	0.9114945

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

EDA ~ alt + body_temp

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- EDA_fd
covariates <- list(altitude = altitude_fd, 
                   temp_body = body_temperature_ENT_fd
                  )
path_plot <- 'figures/model_EDA_alt_temp_body_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 90, norder = 4, lambda = 1e2),
                     temp_body = list(nbetabasis = 90, norder = 4, lambda = 1e2)
                    )

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, HR = HR,
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 28.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 126 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	1.017492	0.337989	6.511186	0.19	0.8152904	0.5145628

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

EDA ~ alt + noise + body_temp

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- EDA_fd
covariates <- list(altitude = altitude_fd, 
                   noise = noise_fd,
                   temp_body = body_temperature_ENT_fd
                  )
path_plot <- 'figures/model_EDA_alt_noise_temp_body_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 90, norder = 4, lambda = 1e2),
                     noise = list(nbetabasis = 90, norder = 4, lambda = 1e2),
                     temp_body = list(nbetabasis = 90, norder = 4, lambda = 1e2)
                    )

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, HR = HR, 
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 23.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 194 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Smallest eigenvalues:
 [1]  0.5580166  0.5558347  0.5381929  0.4805582  0.4721537  0.4282874
 [7]  0.4069764  0.3271206  0.1738422 -0.7051061

Largest  eigenvalues:
 [1] 71914345 66588453 63903546 63076720 60598711 59944374 58587721 57366838
 [9] 57243487 56153851

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	1.015597	0.4567955	13.11223	0.285	1.362067	0.8815355

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

EDA ~ alt + noise + PM25

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- EDA_fd
covariates <- list(altitude = altitude_fd, 
                   noise = noise_fd,
                   pollution = pollution25_fd
                  )
path_plot <- 'figures/model_EDA_alt_noise_pollution25_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 90, norder = 4, lambda = 1e2),
                     noise = list(nbetabasis = 90, norder = 4, lambda = 1e2),
                     pollution = list(nbetabasis = 90, norder = 4, lambda = 1e2)
                    )

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, HR = HR,
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 20.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 344 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Smallest eigenvalues:
 [1]  0.59766275  0.57714156  0.56519578  0.45717817  0.45280857  0.44303853
 [7]  0.39168946  0.28010084  0.23224744 -0.03949094

Largest  eigenvalues:
 [1] 60608346 56039797 53525623 53019615 51347891 50471481 49458177 48511765
 [9] 48467796 47643946

Smallest eigenvalues:
 [1]  0.5927592  0.5540943  0.5127549  0.4704407  0.4596631  0.4098020
 [7]  0.3718021  0.3348278  0.3105294 -0.2917947

Largest  eigenvalues:
 [1] 61425982 56508413 53716581 53207965 52258415 50853010 50558159 48816562
 [9] 48582404 47848773

Smallest eigenvalues:
 [1]  0.5730787  0.5173521  0.5096257  0.5091916  0.4746070  0.3652126
 [7]  0.3363023  0.3275646  0.2563110 -0.3730923

Largest  eigenvalues:
 [1] 59908270 56625609 53949224 52994040 52315184 51341582 49777845 49711054
 [9] 48563635 48177646

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	3.432118	0.675262	12.74966	0.015	1.683717	1.945614

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

EDA ~ alt + temp + PM25

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- EDA_fd
covariates <- list(altitude = altitude_fd, 
                   temperature = temperature_fd,
                   pollution = pollution25_fd
                  )
path_plot <- 'figures/model_EDA_alt_temp_pollution25_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 90, norder = 4, lambda = 1e2),
                     temperature = list(nbetabasis = 90, norder = 4, lambda = 1e2),
                     pollution = list(nbetabasis = 90, norder = 4, lambda = 1e2)
                    )

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, HR = HR, 
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 27.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 386 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	3.322605	0.4649318	16.2151	0.1	0.9856302	0.7987283

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

EDA ~ alt + noise + PM1

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- EDA_fd
covariates <- list(altitude = altitude_fd, 
                   noise = noise_fd,
                   pollution = pollution1_fd
                  )
path_plot <- 'figures/model_EDA_alt_noise_pollution1_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 90, norder = 4, lambda = 1e2),
                     noise = list(nbetabasis = 90, norder = 4, lambda = 1e2),
                     pollution = list(nbetabasis = 90, norder = 4, lambda = 1e2)
                    )

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, HR = HR, 
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 20.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 372 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Smallest eigenvalues:
 [1]  0.5949359  0.5729446  0.5629381  0.4542439  0.4484370  0.4316471
 [7]  0.3782772  0.2833228  0.2319732 -0.1124750

Largest  eigenvalues:
 [1] 60587206 56007235 53505086 52989592 51315156 50451702 49419279 48480162
 [9] 48438864 47619347

Smallest eigenvalues:
 [1]  0.5868226  0.5502143  0.5128114  0.4662680  0.4585074  0.4105382
 [7]  0.3670269  0.3342109  0.3075513 -0.3539924

Largest  eigenvalues:
 [1] 61415394 56493900 53707209 53194862 52245944 50844328 50543316 48803149
 [9] 48570224 47836208

Smallest eigenvalues:
 [1]  0.5721323  0.5098603  0.5072900  0.5028651  0.4633471  0.3730525
 [7]  0.3281127  0.3159918  0.2619605 -0.3615199

Largest  eigenvalues:
 [1] 59901588 56618855 53945196 52989338 52307992 51334661 49775093 49706916
 [9] 48560502 48173137

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	3.426543	0.6791619	13.04562	0.025	1.719113	1.946984

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

EDA ~ alt + temp + PM1

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- EDA_fd
covariates <- list(altitude = altitude_fd, 
                   temperature = temperature_fd,
                   pollution = pollution1_fd
                  )
path_plot <- 'figures/model_EDA_alt_temp_pollution1_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 90, norder = 4, lambda = 1e2),
                     temperature = list(nbetabasis = 90, norder = 4, lambda = 1e2),
                     pollution = list(nbetabasis = 90, norder = 4, lambda = 1e2)
                    )

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, HR = HR, 
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 27.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 378 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	3.312653	0.4661084	16.47744	0.12	0.9843847	0.7875081

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

EDA ~ air pressure + noise

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- EDA_fd
covariates <- list(air_pressure = airpressure_fd, 
                   noise = noise_fd
                  )
path_plot <- 'figures/model_EDA_airpress_noise_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
                     air_pressure = list(nbetabasis = 90, norder = 4, lambda = 1e2),
                     noise = list(nbetabasis = 90, norder = 4, lambda = 1e2)
                    )

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, HR = HR, 
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 25.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 184 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Smallest eigenvalues:
 [1]  0.10647289  0.10546970  0.10475571  0.10441301  0.10334892  0.10153813
 [7]  0.10098287  0.05533742  0.05212848 -0.23792976

Largest  eigenvalues:
 [1] 15507332 15386060 15270604 15101780 14931862 14711134 14664505 14499720
 [9] 14418718 14366087

Smallest eigenvalues:
 [1]  0.11399720  0.11343162  0.11061244  0.10857894  0.10817622  0.10097086
 [7]  0.10022515  0.06204365  0.05630579 -0.75793805

Largest  eigenvalues:
 [1] 15497329 15265435 15165329 15030179 14975714 14825577 14725503 14685036
 [9] 14564747 14448756

Smallest eigenvalues:
 [1]  0.13951882  0.13885938  0.13738446  0.13606086  0.13534702  0.13369462
 [7]  0.12628514  0.07203423  0.07043961 -0.13303745

Largest  eigenvalues:
 [1] 15388617 15292917 15149733 15100482 14945311 14782932 14683466 14598492
 [9] 14495046 14409507

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	3.576449	0.3785018	8.174668	0.405	1.040496	0.4829507

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

EDA ~ air pressure + noise + air temp

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- EDA_fd
covariates <- list(air_pressure = airpressure_fd, 
                   noise = noise_fd,
                   temperature = temperature_fd
                  )
path_plot <- 'figures/model_EDA_airpress_noise_temp_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
                     air_pressure = list(nbetabasis = 90, norder = 4, lambda = 1e2),
                     noise = list(nbetabasis = 90, norder = 4, lambda = 1e2),
                     temperature = list(nbetabasis = 90, norder = 4, lambda = 1e2)
                    )

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, HR = HR, 
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 25.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 322 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Smallest eigenvalues:
 [1]  0.10049050  0.09870038  0.09683498  0.09604983  0.09565113  0.09325221
 [7]  0.09139448  0.05526609  0.04407148 -0.32047288

Largest  eigenvalues:
 [1] 16355053 16198674 16132178 15903323 15792269 15611790 15471286 15345177
 [9] 15263289 15199542

Smallest eigenvalues:
 [1]  0.10760275  0.10682632  0.10317115  0.10090800  0.09703859  0.09303815
 [7]  0.08418235  0.06159548  0.04931716 -1.22004555

Largest  eigenvalues:
 [1] 16361221 16100095 15977299 15853573 15809618 15699875 15574450 15511030
 [9] 15414523 15261930

Smallest eigenvalues:
 [1]  0.13587619  0.13276008  0.13207705  0.12912577  0.12441757  0.12243005
 [7]  0.09461737  0.07095360  0.06942470 -0.22605266

Largest  eigenvalues:
 [1] 16254373 16132921 16014237 15926807 15820685 15699559 15536213 15475377
 [9] 15326802 15241950

Smallest eigenvalues:
 [1]  0.082537385  0.081961386  0.079301818  0.078346931  0.076345831
 [6]  0.073700496  0.068863082  0.043700523  0.031455814 -0.009860154

Largest  eigenvalues:
 [1] 16404595 16215084 16190676 15860716 15797660 15695601 15490967 15395130
 [9] 15287997 15235032

Smallest eigenvalues:
 [1]  0.0579022118  0.0560362018  0.0546029674  0.0532622023  0.0514941030
 [6]  0.0510026453  0.0487051856  0.0471930905  0.0278328470 -0.0001433643

Largest  eigenvalues:
 [1] 16432027 16160121 16156371 15928699 15903793 15677388 15561430 15426807
 [9] 15346551 15292998

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	3.313302	0.5794782	16.32764	0.04	1.152863	1.382889

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
            (GET_results[[3]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

EDA ~ alt + n + acc

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- EDA_fd
covariates <- list(altitude = altitude_fd, 
                   noise = noise_fd,
                   acceleration = acceleration_fd)
path_plot <- 'figures/model_EDA_alt_noise_acc_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     noise = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     acceleration = list(nbetabasis = 80, norder = 4, lambda = 1e3))

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, HR = HR, 
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 32.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 450 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Smallest eigenvalues:
 [1]  0.9739181  0.9070555  0.9044741  0.8227855  0.7871775  0.5797282
 [7]  0.5447441  0.5304211  0.1462120 -0.3233728

Largest  eigenvalues:
 [1] 107757898 102082451  95875388  93692545  92991159  90103538  87300144
 [8]  87123994  86805321  85850434

Smallest eigenvalues:
 [1]  0.9600672  0.7639749  0.7222864  0.6831188  0.5820995  0.4457554
 [7]  0.4429751  0.4157449  0.3607366 -0.3871306

Largest  eigenvalues:
 [1] 106461459 102714673  96523396  93752390  93550486  90720069  87770294
 [8]  87276932  86752277  85605894

Smallest eigenvalues:
 [1]  1.12144307  1.06242080  0.87649874  0.79347665  0.74439217  0.66350438
 [7]  0.60190233  0.55378957  0.51711597 -0.02045023

Largest  eigenvalues:
 [1] 105829349 103394034  97749405  93653001  93095508  91441423  88374627
 [8]  88050165  86682215  86102144

Smallest eigenvalues:
 [1]  0.9973730  0.8630682  0.8204420  0.7664982  0.7029154  0.5189685
 [7]  0.5145405  0.5063051  0.2355076 -1.1446937

Largest  eigenvalues:
 [1] 106262500 101803413  96408942  93325711  93038505  90436544  88368260
 [8]  87122424  86188854  85614843

Smallest eigenvalues:
 [1]  0.9380506  0.9057991  0.7974583  0.7854969  0.7488043  0.6271615
 [7]  0.6157394  0.5951337  0.4298249 -0.1027140

Largest  eigenvalues:
 [1] 105888788 103182592  97000905  93468480  93316605  91022840  88196838
 [8]  87249699  86366499  85750471

Smallest eigenvalues:
 [1]  0.9959630  0.9587178  0.8511334  0.7057276  0.6709490  0.6441068
 [7]  0.5804226  0.5782194  0.2786083 -1.2692560

Largest  eigenvalues:
 [1] 108097038 101658959  96210444  93879148  92044067  89873924  87499400
 [8]  87105833  86999861  85447673

Smallest eigenvalues:
 [1]  1.0602412  0.9374022  0.9279722  0.8926586  0.7895102  0.7717937
 [7]  0.7001134  0.5497410  0.4865444 -0.6337533

Largest  eigenvalues:
 [1] 105569136 102515039  96393532  93228582  92611669  90551635  87551044
 [8]  87399116  85880860  85533123

Smallest eigenvalues:
 [1]  1.0522998  0.9887746  0.9156795  0.8701023  0.8261606  0.7990901
 [7]  0.7593079  0.7167662  0.3340540 -0.5894481

Largest  eigenvalues:
 [1] 107082135 102200653  96209165  93509252  92524823  90588967  87853406
 [8]  87276167  86071986  85207164

Smallest eigenvalues:
 [1]  0.9342266  0.9163383  0.7692761  0.6682715  0.6471987  0.5963400
 [7]  0.5617708  0.4187039  0.1625168 -0.2475219

Largest  eigenvalues:
 [1] 106501411 101930061  95686593  93077685  92859929  90129501  87533204
 [8]  86946163  85672585  85317158

Smallest eigenvalues:
 [1]  0.9954587  0.9656373  0.8385163  0.8183769  0.7468686  0.6036963
 [7]  0.5662285  0.4359675  0.4074427 -0.1552247

Largest  eigenvalues:
 [1] 107088196  99984352  95383721  92982159  91605599  89076474  86263273
 [8]  86181958  85876111  84957046

Smallest eigenvalues:
 [1]  0.7824925  0.7510949  0.6095060  0.5779382  0.5731246  0.5522463
 [7]  0.4849424  0.4824695  0.1987788 -0.6091327

Largest  eigenvalues:
 [1] 106546940 102558831  96903721  93204445  92896778  90696179  88422239
 [8]  87555852  86250195  85709403

Smallest eigenvalues:
 [1]  0.93256259  0.78722467  0.74130118  0.73611676  0.69867149  0.58071432
 [7]  0.58037770  0.33130211  0.27698438 -0.08817705

Largest  eigenvalues:
 [1] 105273231 101492058  96093008  93039779  92595070  90284383  87895010
 [8]  87259920  86134106  85754897

Smallest eigenvalues:
 [1]  1.0254990  0.9100123  0.8884040  0.8660469  0.8539111  0.6463336
 [7]  0.5813533  0.4988011  0.2079018 -1.3079552

Largest  eigenvalues:
 [1] 107247314 101561558  96239419  93415521  92490345  90227034  87886485
 [8]  86957699  86542579  85578622

Smallest eigenvalues:
 [1]  0.8154282  0.7877572  0.6802313  0.6671185  0.5109802  0.4850972
 [7]  0.4836900  0.4629582  0.3260486 -0.7163060

Largest  eigenvalues:
 [1] 108469806 103343989  96547874  94687313  93766980  90407563  87987230
 [8]  87847784  87623981  86167216

Smallest eigenvalues:
 [1]  0.9456455  0.8984036  0.8866654  0.8832891  0.6631040  0.6600169
 [7]  0.5796109  0.5008270  0.2935479 -0.6530128

Largest  eigenvalues:
 [1] 109676154 102844716  96957559  94695928  93532279  90818974  88235819
 [8]  87967576  87890004  86409684

Smallest eigenvalues:
 [1]  1.0483063  0.8318142  0.8043516  0.7301932  0.7110074  0.6254776
 [7]  0.5638472  0.3718597  0.3240146 -0.1978363

Largest  eigenvalues:
 [1] 105316952 102459779  96476288  92681962  92509315  90220461  87594586
 [8]  86441673  85771783  84897398

Smallest eigenvalues:
 [1]  1.09141225  1.07669232  1.01665677  0.95552947  0.88231725  0.87835712
 [7]  0.67359767  0.63757596  0.60719812 -0.01507027

Largest  eigenvalues:
 [1] 106739727 102068652  96163577  93570663  92969149  90671731  87256747
 [8]  87163185  86163665  85607077

Smallest eigenvalues:
 [1]  1.1193088  1.1184372  1.0164019  0.8572574  0.8291404  0.7187604
 [7]  0.6574832  0.6528185  0.5952092 -0.4579073

Largest  eigenvalues:
 [1] 106539673 102642731  96460135  93646440  93437770  90865029  87464845
 [8]  87428334  86687024  85779571

Smallest eigenvalues:
 [1]  1.0188610  0.7415235  0.7170481  0.6089356  0.5346981  0.4727927
 [7]  0.3380275  0.2920763 -0.1335225 -0.8869777

Largest  eigenvalues:
 [1] 106558703 100221025  95320206  92834115  91450142  88326528  87130785
 [8]  86452796  86020181  85313657

Smallest eigenvalues:
 [1]  1.1361328  1.0545885  0.9298457  0.8439620  0.6850588  0.6830385
 [7]  0.5856037  0.5693867  0.4086119 -0.5385280

Largest  eigenvalues:
 [1] 107256592 101498566  96535298  94008026  92603884  90202423  87387895
 [8]  87069620  86620373  85870043

Smallest eigenvalues:
 [1]  0.6890101  0.6524320  0.6485062  0.5782830  0.5497101  0.3645368
 [7]  0.3133968  0.2086596 -0.2817090 -1.9828159

Largest  eigenvalues:
 [1] 108480312 100853582  96589590  93113610  92255329  89341376  87134928
 [8]  86562125  86355509  85727803

Smallest eigenvalues:
 [1]  1.0955902  1.0409376  0.9183825  0.8478418  0.7498295  0.6879591
 [7]  0.5251165  0.5117385  0.3928066 -0.2432927

Largest  eigenvalues:
 [1] 105371754 100416913  95027949  92137122  92118418  89287405  86990511
 [8]  86118875  85278386  84780001

Smallest eigenvalues:
 [1]  0.8654643  0.8501803  0.6557305  0.5953598  0.5876937  0.5624438
 [7]  0.3403873  0.3399493  0.2272461 -0.2142548

Largest  eigenvalues:
 [1] 108756210 102682611  97522858  95741999  93430264  90957393  88257961
 [8]  88173520  87932791  86326087

Smallest eigenvalues:
 [1]  0.9306975  0.8753051  0.7986481  0.7878632  0.7436808  0.5883950
 [7]  0.5191112  0.2534280  0.1071440 -0.2756760

Largest  eigenvalues:
 [1] 108704297 103010102  97278702  95999986  93890698  91396459  88522334
 [8]  88095321  87615291  86411240

Smallest eigenvalues:
 [1]  1.0399542  0.9155670  0.8671659  0.8337449  0.7370843  0.6036512
 [7]  0.5964418  0.5219686  0.2235807 -0.3133140

Largest  eigenvalues:
 [1] 106550292 101841994  96294820  93131214  92786668  90355335  88269321
 [8]  86948202  86243817  85548646

Smallest eigenvalues:
 [1]  1.1321073  1.0896680  1.0208217  0.9838445  0.8353567  0.8005417
 [7]  0.7259968  0.6940746  0.5083624 -0.6082429

Largest  eigenvalues:
 [1] 108733158 101307471  96119582  93759244  92736810  89999366  87644581
 [8]  87069819  86996291  86205278

Smallest eigenvalues:
 [1]  0.8549064  0.7923236  0.7761904  0.7292166  0.6752019  0.6499100
 [7]  0.5727572  0.5258840 -0.2340326 -0.6195309

Largest  eigenvalues:
 [1] 107800389 102038357  97031044  94184788  92623989  90196274  88117397
 [8]  87752913  87406320  86562664

Smallest eigenvalues:
 [1]  0.84665529  0.79642648  0.66157459  0.59468960  0.59095047  0.44760698
 [7]  0.43947429  0.41525945  0.29558469 -0.07780902

Largest  eigenvalues:
 [1] 107486780 102397613  96246139  94955101  92493242  90317269  87811284
 [8]  87600492  87218129  85772277

Smallest eigenvalues:
 [1]  1.0399587  1.0004180  0.7030955  0.6702356  0.6508857  0.6409989
 [7]  0.5537590  0.5534124  0.4161613 -0.9415906

Largest  eigenvalues:
 [1] 105226174 101384146  96207126  92667623  91916540  90129115  87578087
 [8]  86834390  85760947  85265229

Smallest eigenvalues:
 [1]  1.0740236  0.9699365  0.9257382  0.8976239  0.8814413  0.8189048
 [7]  0.7087698  0.5209375  0.4943526 -0.6475468

Largest  eigenvalues:
 [1] 105432599 101961961  96632200  93200940  92903891  90942382  88527626
 [8]  86921735  85813932  85438444

Smallest eigenvalues:
 [1]  0.9613563  0.8535764  0.8520412  0.8291887  0.7795163  0.6968560
 [7]  0.5084520  0.4892364  0.3059006 -0.0407415

Largest  eigenvalues:
 [1] 108389100 101563713  96232884  94956012  92782694  90057687  87408472
 [8]  87205428  86912569  85714317

Smallest eigenvalues:
 [1]  0.9539057  0.9133985  0.8185856  0.6942262  0.6925654  0.4889985
 [7]  0.4595531  0.4110463  0.1071997 -0.1582165

Largest  eigenvalues:
 [1] 109272464 102640614  96526103  95468141  93805268  90601919  88419732
 [8]  88145744  87126209  86505585

Smallest eigenvalues:
 [1]  0.8484347  0.6440976  0.6061702  0.5426354  0.5336470  0.4505841
 [7]  0.4443875  0.2906917 -0.3276361 -1.4825787

Largest  eigenvalues:
 [1] 108071369 102573761  96562558  94781465  92606132  90093096  87891813
 [8]  87851695  86869427  85747906

Smallest eigenvalues:
 [1]  1.02355361  0.96973626  0.90924679  0.89008064  0.83161944  0.72567351
 [7]  0.58141891  0.58048383  0.44611625 -0.08229867

Largest  eigenvalues:
 [1] 106467640 100899267  95673039  93050578  92103650  89236240  87316141
 [8]  87098983  86233727  85986087

Smallest eigenvalues:
 [1]  0.7859443  0.7827471  0.7658371  0.6862303  0.6082995  0.5313227
 [7]  0.5001402  0.4797584  0.4562193 -0.8163203

Largest  eigenvalues:
 [1] 106338183 101741941  96582443  92904785  92145666  90014135  86924138
 [8]  86333393  86194225  84856749

Smallest eigenvalues:
 [1]  1.070407878  0.933948588  0.898295072  0.860893853  0.810180977
 [6]  0.655686908  0.562261570  0.557175728  0.550095770 -0.001107183

Largest  eigenvalues:
 [1] 106724776 101722385  96206922  93328293  93124718  90456090  87294056
 [8]  86751106  86173386  85034085

Smallest eigenvalues:
 [1]  0.8775099  0.8684947  0.7630967  0.6250612  0.5756749  0.5541340
 [7]  0.3185507  0.3141688  0.1140295 -1.1804514

Largest  eigenvalues:
 [1] 105311288  99680273  94926540  91728595  90973605  88726663  86707190
 [8]  86238942  85344718  85008989

Smallest eigenvalues:
 [1]  1.0698727  0.9825964  0.9636048  0.7260857  0.6620844  0.6241240
 [7]  0.4912535  0.4525449  0.3955901 -2.3864842

Largest  eigenvalues:
 [1] 105085125 100817852  95057283  92591380  92386877  89547713  87597386
 [8]  85899385  85526899  84540699

Smallest eigenvalues:
 [1]  1.0582997  1.0423215  0.9252621  0.9156458  0.8376192  0.8134114
 [7]  0.7389213  0.6342170  0.5806265 -0.6904383

Largest  eigenvalues:
 [1] 106831057 102251934  96516194  93007097  92784583  90216579  87734029
 [8]  86941752  86198545  85166290

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	3.239632	0.3421001	7.981684	0.295	0.8108634	0.5254974

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

EDA ~ alt + n + speed

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- EDA_fd
covariates <- list(altitude = altitude_fd, 
                   noise = noise_fd,
                   speed = speed_fd)
path_plot <- 'figures/model_EDA_alt_noise_speed_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 90, norder = 4, lambda = 1e4),
                     noise = list(nbetabasis = 90, norder = 4, lambda = 1e4),
                     speed = list(nbetabasis = 90, norder = 4, lambda = 1e4))

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, HR = HR, 
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 33.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 500 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Smallest eigenvalues:
 [1]  1.0965649  0.9741293  0.8189636  0.7045693  0.7012212  0.5996803
 [7]  0.5656703  0.4772370  0.1095383 -1.7848981

Largest  eigenvalues:
 [1] 98898182 93456398 88382267 87668332 85531624 83157159 82223612 81011797
 [9] 80468305 78952990

Smallest eigenvalues:
 [1]  0.9213638  0.8376573  0.7542189  0.5963766  0.5003226  0.4665080
 [7]  0.4563031  0.4402115  0.3712504 -1.9122791

Largest  eigenvalues:
 [1] 99393129 93910459 88950787 88387511 86025266 83910127 82495443 81740389
 [9] 80018970 79344358

Smallest eigenvalues:
 [1]  0.9037080  0.8090196  0.7764319  0.7730590  0.7506336  0.6406840
 [7]  0.5591572  0.4885665  0.3182691 -0.7492455

Largest  eigenvalues:
 [1] 98403892 92293795 87502464 87150079 84972043 82927066 80737437 79964849
 [9] 79734995 78733767

Smallest eigenvalues:
 [1]  0.6510428  0.5934467  0.5194604  0.4265543  0.3529960  0.2930514
 [7]  0.2189307 -0.1254805 -0.5687495 -2.5864173

Largest  eigenvalues:
 [1] 98398602 93636609 88724524 88060260 85706731 84110648 82311189 81217383
 [9] 79553930 78954059

Smallest eigenvalues:
 [1]  1.0785916  1.0618919  0.9747039  0.8367183  0.7119334  0.5965782
 [7]  0.5815541  0.5390983  0.2694387 -0.1762636

Largest  eigenvalues:
 [1] 97748068 93706598 88815917 87783974 86247562 84620180 81602774 81515880
 [9] 79921630 79235465

Smallest eigenvalues:
 [1]  0.9826523  0.8172134  0.7969923  0.6510303  0.5502280  0.5270022
 [7]  0.4419622  0.3566591 -0.1429335 -0.9232720

Largest  eigenvalues:
 [1] 99794340 93669350 88589699 88036751 85521394 83841655 81744408 81606651
 [9] 79569340 79059377

Smallest eigenvalues:
 [1]  0.9728999  0.9379950  0.8394080  0.6392351  0.6201838  0.5692414
 [7]  0.4984737  0.4181252  0.3358790 -0.4244707

Largest  eigenvalues:
 [1] 98590909 94757458 89501604 87997138 86730883 85053656 82423267 81980215
 [9] 80212216 79870142

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	3.224626	0.3320367	11.06011	0.71	1.207222	0.6771296

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

EDA ~ alt + n + steps

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- EDA_fd
covariates <- list(altitude = altitude_fd, 
                   noise = noise_fd,
                   steps = steps_fd)
path_plot <- 'figures/model_EDA_alt_noise_steps_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 90, norder = 4, lambda = 1e3),
                     noise = list(nbetabasis = 90, norder = 4, lambda = 1e3),
                     steps = list(nbetabasis = 90, norder = 4, lambda = 1e3))

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, HR = HR, 
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 32.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 444 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Smallest eigenvalues:
 [1]  1.1183631  1.0176210  0.9297772  0.8452723  0.7416317  0.7239285
 [7]  0.6755437  0.6392289  0.4596060 -7.0519949

Largest  eigenvalues:
 [1] 97342625 89767749 85927968 85393823 82761422 80416058 79617758 77874284
 [9] 77830476 76648885

Smallest eigenvalues:
 [1]  0.8210996  0.7967740  0.7775604  0.6622976  0.5964201  0.4700285
 [7]  0.3924557  0.3526923  0.2299710 -1.9672223

Largest  eigenvalues:
 [1] 97687654 91789160 86679747 86363060 83441144 81363035 81221010 79222884
 [9] 77766615 76801490

Smallest eigenvalues:
 [1]  0.7809085  0.7613850  0.7280797  0.6448397  0.6044466  0.5885938
 [7]  0.3637156 -0.3397471 -0.4689503 -0.9617772

Largest  eigenvalues:
 [1] 94616108 92014319 87189576 84496714 83900342 82116066 79681349 78839727
 [9] 78226421 77210041

Smallest eigenvalues:
 [1]   0.8790409   0.8762651   0.8668854   0.8083423   0.6172791   0.4986781
 [7]   0.4639298   0.4487909   0.3879823 -83.8401403

Largest  eigenvalues:
 [1] 95013428 90569749 85918908 84249953 83632789 81235229 79313667 79022815
 [9] 77538099 77432421

Smallest eigenvalues:
 [1]  0.8182690  0.6401740  0.5501843  0.5120892  0.4566674  0.4324881
 [7]  0.3822173  0.3785554  0.3085159 -0.2504592

Largest  eigenvalues:
 [1] 96966908 91255816 86770080 85821377 83067470 81559868 80487231 78717159
 [9] 77957178 76823548

Smallest eigenvalues:
 [1]  0.8443321452  0.7014341727  0.5375279694  0.4550888811  0.4201822598
 [6]  0.4051580069  0.3375296354  0.1761667111  0.0007127554 -0.0165973187

Largest  eigenvalues:
 [1] 96806438 91300290 86815235 86162579 83218191 81217851 80537921 78963757
 [9] 78268287 77282901

Smallest eigenvalues:
 [1]  0.9823531  0.8947998  0.8728813  0.8447557  0.8135737  0.6899906
 [7]  0.6732836  0.5242621  0.4675930 -1.3404609

Largest  eigenvalues:
 [1] 95451019 91570758 86104006 85195379 83155760 80992776 79440481 78670863
 [9] 78018942 76633417

Smallest eigenvalues:
 [1]   1.0390931   0.9529703   0.9339237   0.8237270   0.7792322   0.7282763
 [7]   0.6451593   0.5112481   0.3376959 -28.3220241

Largest  eigenvalues:
 [1] 95834393 90947640 85769393 83874098 83688641 81565216 78836824 78824626
 [9] 77592514 76924571

Smallest eigenvalues:
 [1]  1.0335811  0.9599569  0.8353745  0.7895177  0.7619191  0.6985246
 [7]  0.6390835  0.5487342  0.3134193 -0.1837513

Largest  eigenvalues:
 [1] 96205870 90409373 85933555 85664122 83076060 80855113 80097453 78266143
 [9] 77974082 76646107

Smallest eigenvalues:
 [1]  0.8848091  0.8357054  0.8175768  0.6723973  0.6027441  0.5282721
 [7]  0.4208806  0.3864270 -0.5034857 -1.3005486

Largest  eigenvalues:
 [1] 96600178 90314570 84956974 84778438 83021410 81098185 79706643 77985859
 [9] 77523600 76252610

Smallest eigenvalues:
 [1]  0.9727185  0.8713698  0.8211615  0.8076140  0.7866359  0.5450408
 [7]  0.4848952  0.3819790  0.3526645 -0.6073986

Largest  eigenvalues:
 [1] 98159840 91550927 86406960 85948383 83750655 81535491 80511086 79445043
 [9] 78057025 76963392

Smallest eigenvalues:
 [1]  0.7994454  0.7980990  0.7727976  0.7306752  0.6654204  0.5804071
 [7]  0.4938032  0.4620601  0.3854601 -5.2689323

Largest  eigenvalues:
 [1] 96236424 89930310 85186737 85037654 82927329 80801786 79964170 78108661
 [9] 76365710 75632436

Smallest eigenvalues:
 [1]   0.9987405   0.8282154   0.7820841   0.7083499   0.7068107   0.6720074
 [7]   0.6550574   0.5963241   0.3904962 -26.0125030

Largest  eigenvalues:
 [1] 95897137 90277161 86094230 85415539 83015600 80970027 79298922 78717499
 [9] 77342657 76535222

Smallest eigenvalues:
 [1]  0.9106482  0.8725599  0.8068087  0.7525102  0.6446547  0.5736019
 [7]  0.5572219  0.4385993  0.3041376 -0.1036589

Largest  eigenvalues:
 [1] 94785674 89700105 84956515 84689601 81917125 80247314 79217789 77990231
 [9] 76801161 76283336

Smallest eigenvalues:
 [1]  0.8493593  0.7656852  0.7633727  0.6794515  0.6147809  0.5883757
 [7]  0.4586596  0.4099439  0.2995486 -0.2556937

Largest  eigenvalues:
 [1] 94698839 89899913 85030277 83892467 82941184 80746361 78672462 77918520
 [9] 77092099 76206674

Smallest eigenvalues:
 [1]  0.7597501  0.7359965  0.6113205  0.5533182  0.4643636  0.4331087
 [7]  0.4169669  0.2676231 -1.2904106 -7.4245328

Largest  eigenvalues:
 [1] 96694596 90550331 85791487 85504495 83231538 81174834 80138656 78776778
 [9] 77743858 76746502

Smallest eigenvalues:
 [1]  0.8096768  0.8080229  0.6192397  0.5808576  0.5696829  0.5216424
 [7]  0.4242342  0.3107008  0.2545836 -4.0480507

Largest  eigenvalues:
 [1] 97234301 91336989 87023326 86981303 83801467 81663531 80789482 79297968
 [9] 78308457 76932022

Smallest eigenvalues:
 [1]  0.8345835  0.7678830  0.7280397  0.6273266  0.6126059  0.5681748
 [7]  0.4992526  0.4169739  0.2130704 -1.1686863

Largest  eigenvalues:
 [1] 97173752 91673607 87080868 86734701 84034652 82325471 81185718 79060794
 [9] 78263298 76991975

Smallest eigenvalues:
 [1]  0.70745480  0.63708534  0.62267342  0.52474762  0.49496496  0.41734368
 [7]  0.40898477  0.32801835  0.09583426 -2.29334387

Largest  eigenvalues:
 [1] 92521415 89854653 85216031 82706697 82653520 81250894 78875544 76959270
 [9] 76841184 76474316

Smallest eigenvalues:
 [1]  0.9656954  0.9408413  0.8876182  0.7705218  0.7403162  0.6023363
 [7]  0.5968584  0.2868750  0.2190016 -0.2576864

Largest  eigenvalues:
 [1] 97038967 89604736 85449932 85242478 82450162 79980244 79463271 78075041
 [9] 76964527 76154970

Smallest eigenvalues:
 [1]  0.8880987  0.8879066  0.8675313  0.7690868  0.6384597  0.5964105
 [7]  0.5667384  0.4505765  0.4454542 -6.3000596

Largest  eigenvalues:
 [1] 97086238 90234362 85995703 85770637 83112879 81081677 81039049 78791957
 [9] 77757862 76853844

Smallest eigenvalues:
 [1]  0.8777975  0.8357658  0.7048800  0.6263099  0.5689071  0.5550204
 [7]  0.4405208  0.4316264  0.4193840 -0.1576789

Largest  eigenvalues:
 [1] 96700338 92147228 86839380 86180997 83471622 81246164 80646263 79252846
 [9] 78243911 77133471

Smallest eigenvalues:
 [1]  0.7569901  0.6930407  0.6167104  0.5166723  0.4608167  0.3336871
 [7]  0.2862939  0.1773101 -0.2638416 -1.8712947

Largest  eigenvalues:
 [1] 97862004 91019788 86122981 85669038 83412634 81367364 80406622 78584223
 [9] 78086890 76877454

Smallest eigenvalues:
 [1]  1.006842016  0.803337527  0.760850995  0.742796120  0.711957733
 [6]  0.682263884  0.532263495  0.398594162  0.001300631 -0.056494873

Largest  eigenvalues:
 [1] 93189303 91116267 85755306 83621079 82556698 81711333 78863027 77549826
 [9] 77484557 76886579

Smallest eigenvalues:
 [1]   0.9254361   0.8677790   0.6952662   0.6213181   0.5171152   0.4233124
 [7]   0.4127589   0.3896964   0.3616560 -20.0647939

Largest  eigenvalues:
 [1] 97517421 90887275 86741133 86308801 83738187 81727076 80767522 79247290
 [9] 78308366 77071954

Smallest eigenvalues:
 [1]  0.9221112  0.6273579  0.6017540  0.5419971  0.4840735  0.3566440
 [7]  0.3321478  0.3161846  0.2590900 -5.8431321

Largest  eigenvalues:
 [1] 98336627 90609523 86826911 86802791 83156548 80831082 80515045 78748336
 [9] 77845632 76744263

Smallest eigenvalues:
 [1]  1.0152904  0.9485014  0.8074888  0.7356652  0.7132664  0.5698418
 [7]  0.5522237  0.5110457  0.3421706 -1.6223099

Largest  eigenvalues:
 [1] 96436714 90775402 86565474 85370198 83043566 80878595 80146647 79007926
 [9] 78213492 77122380

Smallest eigenvalues:
 [1]  0.6262398  0.6030298  0.5897837  0.5417284  0.4639333  0.4227664
 [7]  0.3858953  0.1800709  0.1686028 -0.1691043

Largest  eigenvalues:
 [1] 96109951 91196818 85990241 85785450 82846540 81125703 80281543 78891487
 [9] 77473128 76810432

Smallest eigenvalues:
 [1]  0.9225509  0.9007225  0.8430807  0.7667531  0.7384909  0.6761920
 [7]  0.6278637  0.4378571  0.4051111 -0.4958256

Largest  eigenvalues:
 [1] 94926675 90415114 85419204 84769461 82684548 80510406 79162966 78518963
 [9] 77207221 76592112

Smallest eigenvalues:
 [1]  0.89785602  0.79423905  0.65984252  0.64846354  0.59898882  0.51796339
 [7]  0.44763014  0.32853625  0.23615514 -0.09008767

Largest  eigenvalues:
 [1] 96760475 91025403 85965696 85347750 83328351 81417932 80083727 78734951
 [9] 76977323 76886583

Smallest eigenvalues:
 [1]   0.8579348   0.8448779   0.7492269   0.6510432   0.5938614   0.5244255
 [7]   0.4847245   0.4549396   0.2810066 -10.8838739

Largest  eigenvalues:
 [1] 96582844 91841933 86374739 85300909 83113508 81140530 79398771 78749502
 [9] 77522302 76396169

Smallest eigenvalues:
 [1]  0.9813092  0.8430597  0.6818274  0.5987037  0.5922118  0.5200347
 [7]  0.4079037  0.3899331  0.3627472 -0.1262698

Largest  eigenvalues:
 [1] 94178693 88700630 84615615 83088373 81502142 79580880 77815670 77771354
 [9] 76629914 75973029

Smallest eigenvalues:
 [1]  0.8986536  0.8660044  0.7985145  0.7141116  0.6439741  0.5981077
 [7]  0.4698929  0.4130062  0.1723396 -0.4823159

Largest  eigenvalues:
 [1] 94888908 91178708 85724452 84807081 83789787 81504809 79743807 79626801
 [9] 77364800 77146917

Smallest eigenvalues:
 [1]   0.8245662   0.8212721   0.7058040   0.5876186   0.5287688   0.4516459
 [7]   0.3917832   0.3289544   0.3176127 -54.4242583

Largest  eigenvalues:
 [1] 95537133 88814399 84941291 83430609 82419458 80144807 77745157 77230520
 [9] 77136002 76392147

Smallest eigenvalues:
 [1]  0.7935410  0.7711320  0.7223435  0.5948197  0.5520337  0.5169339
 [7]  0.5151069  0.3901845  0.3163592 -3.5536421

Largest  eigenvalues:
 [1] 94931478 91268911 85460407 85458955 83142289 81245998 79212731 78801384
 [9] 77537339 77066987

Smallest eigenvalues:
 [1]  0.738303921  0.718467994  0.696675291  0.657685616  0.563580808
 [6]  0.449522496  0.374952228  0.258969352  0.186110053 -0.004662431

Largest  eigenvalues:
 [1] 95568795 92218054 87347682 85337592 84414188 82440341 80068791 79232920
 [9] 78757811 77819859

Smallest eigenvalues:
 [1]  0.83487953  0.80007875  0.65175969  0.61502176  0.58914868  0.54243355
 [7]  0.50488690  0.22633978  0.16764347 -0.01283282

Largest  eigenvalues:
 [1] 97871149 90012619 86656062 85658486 82504679 80649890 80352807 78139276
 [9] 77199974 76007852

Smallest eigenvalues:
 [1]   0.9063662   0.8437767   0.6882514   0.6507760   0.5958862   0.4931903
 [7]   0.4465234   0.4002606   0.2787049 -11.0352552

Largest  eigenvalues:
 [1] 95831899 91329581 86490907 85397769 83382993 81706383 80070057 79095968
 [9] 77735560 76838843

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	3.237065	0.3534545	8.077096	0.52	1.100534	0.5554857

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

EDA ~ alt + n + acc + PM25

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- EDA_fd
covariates <- list(altitude = altitude_fd, 
                   noise = noise_fd,
                   acceleration = acceleration_fd,
                   pollution = pollution25_fd)
path_plot <- 'figures/model_EDA_alt_noise_acc_PM25_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 80, norder = 4, lambda = 1e4),
                     noise = list(nbetabasis = 80, norder = 4, lambda = 1e4),
                     acceleration = list(nbetabasis = 80, norder = 4, lambda = 1e4),
                     pollution = list(nbetabasis = 80, norder = 4, lambda = 1e4))

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, HR = HR,
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 19.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 604 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Smallest eigenvalues:
 [1]  0.3572400  0.3241591  0.3175724  0.2539564  0.2211844  0.1429275
 [7]  0.1386985 -0.1192288 -0.1583929 -4.0563352

Largest  eigenvalues:
 [1] 64057025 60144807 57579659 55680452 55075247 53420479 52147618 51727274
 [9] 51700094 51150786

Smallest eigenvalues:
 [1]  0.20815480  0.19527708  0.13001476  0.07394004  0.05268478 -0.02520543
 [7] -0.03022643 -0.04639147 -0.18712336 -2.86933727

Largest  eigenvalues:
 [1] 63362686 61063658 57705778 55877424 55340792 53945203 52744004 52432708
 [9] 51874744 51619834

Smallest eigenvalues:
 [1]  0.320485037  0.308484457  0.294083995  0.287061731  0.236586395
 [6]  0.161861584  0.032725122 -0.005492232 -0.144953778 -0.522917077

Largest  eigenvalues:
 [1] 64171547 61147712 58395964 55891118 55767221 54364253 53237999 52349784
 [9] 52116894 51922555

Smallest eigenvalues:
 [1]  0.4918629799  0.4834773366  0.4230672504  0.3498649743  0.3391757226
 [6]  0.2622011103  0.2493391868  0.0006027109 -0.0047136550 -0.0656738895

Largest  eigenvalues:
 [1] 61992275 60517246 57617107 55854646 54975045 54089904 52470477 52433817
 [9] 51229294 51014200

Smallest eigenvalues:
 [1]  0.3364004  0.3289831  0.2962855  0.2262138  0.2071379  0.1997672
 [7]  0.1718978  0.1221774 -0.3798499 -2.5629421

Largest  eigenvalues:
 [1] 65213933 59900563 57366967 56070586 54801621 53236418 52165572 52027160
 [9] 51510823 51178965

Smallest eigenvalues:
 [1]  0.43960886  0.40739004  0.38036940  0.29119135  0.28331892  0.15010614
 [7]  0.04677086 -0.03605983 -0.10474583 -0.32354130

Largest  eigenvalues:
 [1] 64395757 60692182 57313959 56079725 55705692 53907634 52786711 52051200
 [9] 51774711 51464929

Smallest eigenvalues:
 [1]  0.2763762  0.2154392  0.1824499  0.1802923  0.1437914  0.1125075
 [7] -0.2037908 -0.2308594 -0.3786692 -0.4594503

Largest  eigenvalues:
 [1] 65043228 61026199 57678547 56174052 55510518 53897637 52985881 52156865
 [9] 52064095 51786866

Smallest eigenvalues:
 [1]  0.35130208  0.32195043  0.25929832  0.21560677  0.19993165 -0.06684521
 [7] -0.12772567 -0.30386030 -0.42230894 -0.56429931

Largest  eigenvalues:
 [1] 64887832 59884269 56538136 56494640 54526093 52725113 52491518 52190857
 [9] 51718398 51256374

Smallest eigenvalues:
 [1]  0.50100352  0.43554188  0.41233819  0.30676249  0.28168009  0.23034198
 [7]  0.20108541  0.07812386 -0.00289683 -0.14461111

Largest  eigenvalues:
 [1] 63905801 59824571 57232425 55822166 54696749 53191030 52245752 51787068
 [9] 51659209 51048402

Smallest eigenvalues:
 [1]  0.38226613  0.36936228  0.36840363  0.34104063  0.22871764  0.22722070
 [7]  0.21700001  0.13023772  0.07185889 -0.01500420

Largest  eigenvalues:
 [1] 64551889 60467163 58052828 55668533 55378222 54135552 52760185 52159002
 [9] 51911737 51745547

Smallest eigenvalues:
 [1]  0.44454890  0.39600696  0.35937368  0.33392174  0.20398786  0.06862949
 [7] -0.43067560 -0.45885425 -1.07110227 -3.59165125

Largest  eigenvalues:
 [1] 64721302 60074629 57264269 55818235 55237105 53021585 52213272 51976403
 [9] 51734457 51260959

Smallest eigenvalues:
 [1]  0.36073040  0.32762768  0.32553822  0.28244905  0.27152783  0.17385777
 [7]  0.12877348  0.02402656 -0.26864776 -1.67871407

Largest  eigenvalues:
 [1] 63336801 59899788 57139555 55231761 54844198 53644892 52169184 52061273
 [9] 51363479 51023299

Smallest eigenvalues:
 [1]  0.38919150  0.38198269  0.35993389  0.27814312  0.27361771  0.21880853
 [7]  0.21064366 -0.04733215 -0.22615366 -1.18213899

Largest  eigenvalues:
 [1] 64876586 59738225 57167871 56545952 54793387 53322920 52552913 52191143
 [9] 51496041 50778932

Smallest eigenvalues:
 [1]  0.56599589  0.51522001  0.49716308  0.42173562  0.37622006  0.37414837
 [7]  0.26249298  0.21907298  0.15529848 -0.01614275

Largest  eigenvalues:
 [1] 65044260 59528686 56804412 55982911 54935764 53289992 52171507 51972175
 [9] 51898375 51231592

Smallest eigenvalues:
 [1]  0.48076328  0.38622990  0.37523225  0.32448140  0.23316474  0.21960765
 [7]  0.14829284  0.09201754 -0.09826087 -0.11605853

Largest  eigenvalues:
 [1] 66301320 59326859 57246433 56655941 54051276 53267548 52561339 51334121
 [9] 51137182 50525665

Smallest eigenvalues:
 [1]  0.5181210  0.5010810  0.4883916  0.4406659  0.4190410  0.3673086
 [7]  0.2696495  0.1548473 -0.1228540 -0.2300485

Largest  eigenvalues:
 [1] 63366952 60111230 56810156 55261569 55002375 53483030 52025304 51386874
 [9] 50856721 50536505

Smallest eigenvalues:
 [1]  0.3934942  0.2690784  0.2653280  0.2518613  0.2162878  0.1790993
 [7]  0.1593644  0.1175771 -0.1392969 -0.5375719

Largest  eigenvalues:
 [1] 66530749 60558415 57877572 57276985 55065660 53399490 53207130 52953137
 [9] 51671805 51516286

Smallest eigenvalues:
 [1]  0.47095992  0.41151151  0.39009730  0.23555497  0.22889025  0.12739543
 [7]  0.11521296  0.08318608  0.06435559 -0.78822906

Largest  eigenvalues:
 [1] 65784661 60536220 56993951 56779371 55145628 53496493 52748314 52261602
 [9] 52051702 51288186

Smallest eigenvalues:
 [1]  0.49795664  0.49293705  0.46341960  0.39675058  0.34727816  0.27428560
 [7]  0.16133323  0.02520763 -0.08061078 -0.67548394

Largest  eigenvalues:
 [1] 63446078 59919192 57098632 55394866 54909682 53829454 52461465 51827299
 [9] 51013573 50912857

Smallest eigenvalues:
 [1]  0.4059169  0.3553364  0.3515291  0.3078905  0.2967307  0.2566029
 [7]  0.2360790  0.1652289  0.1104114 -0.0558672

Largest  eigenvalues:
 [1] 64299467 61503460 58102473 56629090 55669088 54037930 52798274 52541105
 [9] 52485403 51789855

Smallest eigenvalues:
 [1]  0.4460437  0.4370955  0.3816666  0.3473450  0.3281377  0.3055509
 [7]  0.2611311  0.2450317  0.1088500 -0.1154320

Largest  eigenvalues:
 [1] 64841249 61117481 58031276 56429263 56429118 54727577 53077512 52603011
 [9] 52328076 51720325

Smallest eigenvalues:
 [1]  0.29172716  0.26705452  0.16475462  0.11652670  0.09431992  0.01559144
 [7] -0.10874491 -0.10925043 -0.44551949 -1.44650426

Largest  eigenvalues:
 [1] 64767110 60244226 57025007 55944094 54913161 53357316 52009406 51944806
 [9] 51579422 50906645

Smallest eigenvalues:
 [1]  0.36347944  0.29839340  0.29050353  0.27232831  0.27195074  0.24277733
 [7]  0.19766683  0.09278354 -0.46095206 -0.47329183

Largest  eigenvalues:
 [1] 63926626 59805241 57282049 55213482 54470430 53013311 51953515 51381162
 [9] 51152429 51105799

Smallest eigenvalues:
 [1]  0.33389114  0.28761147  0.25725293  0.24741809  0.23223098  0.21213310
 [7]  0.20080965  0.08105087 -0.15044906 -0.24208737

Largest  eigenvalues:
 [1] 65795003 60475623 57891783 56764538 55158152 53459724 53025740 52786711
 [9] 52031389 51942040

Smallest eigenvalues:
 [1]  0.4327472  0.3712711  0.3592195  0.3255310  0.2916081  0.2505628
 [7]  0.1975630  0.1294015  0.1226310 -1.0956320

Largest  eigenvalues:
 [1] 65018324 59900371 57227164 56061496 55095751 53287288 52129538 52095714
 [9] 51571133 51184690

Smallest eigenvalues:
 [1]  0.49976091  0.44936337  0.35862225  0.35276438  0.34221020  0.29944621
 [7]  0.27312165  0.15231482 -0.06882362 -0.99085301

Largest  eigenvalues:
 [1] 63552092 59153520 57013572 55547625 54473665 52932118 51610368 51507431
 [9] 51463963 50580109

Smallest eigenvalues:
 [1]  0.44000755  0.39221958  0.32075230  0.31369847  0.26194793  0.21126722
 [7] -0.04150861 -0.04166315 -0.04180957 -0.26528260

Largest  eigenvalues:
 [1] 61138081 59059968 56149375 54859398 54134902 52952757 51834903 50853739
 [9] 50135535 49964435

Smallest eigenvalues:
 [1] -0.2384820 -0.3236995 -0.3343005 -0.3601049 -0.4290560 -0.5295021
 [7] -0.5546944 -0.9277185 -1.1302971 -1.2198926

Largest  eigenvalues:
 [1] 64898588 61095112 58239056 55669635 55579062 54249523 52480127 52006758
 [9] 51696025 51445370

Smallest eigenvalues:
 [1]  0.284032075  0.269374108  0.243847802  0.228442778  0.185862668
 [6]  0.037836381  0.008364788 -0.257175665 -0.420003497 -0.881523873

Largest  eigenvalues:
 [1] 64854170 61072067 57743302 56639843 55610572 54015814 52784207 52606800
 [9] 52385667 51809985

Smallest eigenvalues:
 [1]  0.39745675  0.30378715  0.28698407  0.26038800  0.21561967  0.12034930
 [7]  0.09870136 -0.08735814 -1.11663102 -1.26942154

Largest  eigenvalues:
 [1] 64523575 60174634 56672842 56286533 55328894 53334607 52575618 52264961
 [9] 52213394 51231045

Smallest eigenvalues:
 [1]  0.465164853  0.381467739  0.338419493  0.285814524  0.255618713
 [6]  0.189508223  0.141939371 -0.007267245 -0.668396315 -1.002118380

Largest  eigenvalues:
 [1] 64041823 58837004 56494584 55832043 54013667 52296979 51760999 51300462
 [9] 51038577 49991980

Smallest eigenvalues:
 [1]  0.42135977  0.33064526  0.24581927  0.22783270  0.22315299  0.19639218
 [7]  0.17289158  0.12267540  0.04686315 -5.31312804

Largest  eigenvalues:
 [1] 61838534 59832243 56893230 55076043 54672635 53480740 52126963 51470915
 [9] 50730290 50528299

Smallest eigenvalues:
 [1]  0.28167814  0.22157573  0.21288895  0.19779428  0.07514761  0.05132728
 [7] -0.11726279 -0.18719471 -1.32155859 -2.87728671

Largest  eigenvalues:
 [1] 66521296 60602632 57417818 56450468 55360607 53713243 52566459 52437993
 [9] 51819287 51677782

Smallest eigenvalues:
 [1]  0.43084282  0.36104450  0.34359855  0.34209815  0.26088381  0.24825747
 [7]  0.22729943  0.19323460  0.06281628 -0.05721952

Largest  eigenvalues:
 [1] 64606593 60791818 58246345 55827890 55634400 54284458 52799172 52472818
 [9] 51810122 51555398

Smallest eigenvalues:
 [1]  0.31737948  0.29517252  0.28227197  0.22005093  0.21848316  0.17054747
 [7]  0.09857276 -0.16891386 -0.20307817 -2.19901137

Largest  eigenvalues:
 [1] 65092502 60587247 57765907 55910841 55845101 54172541 52449565 52256703
 [9] 52217606 51368550

Smallest eigenvalues:
 [1]  0.38163167  0.37451189  0.29926363  0.28470765  0.20351932  0.09792982
 [7]  0.04525726 -0.12321008 -0.19859943 -1.45050876

Largest  eigenvalues:
 [1] 63906345 59932378 57057508 55237595 55061015 53491821 52205040 51514534
 [9] 51373076 51216214

Smallest eigenvalues:
 [1]  0.46659129  0.38597616  0.35789100  0.32751038  0.32706560  0.31221075
 [7]  0.25349908  0.01068126 -0.01013948 -0.07940873

Largest  eigenvalues:
 [1] 65265428 60401834 57500936 56436683 54876402 53095347 52565577 52149870
 [9] 51327532 50910693

Smallest eigenvalues:
 [1]  0.37669338  0.36404481  0.34189170  0.26190141  0.24874713  0.20737541
 [7]  0.05400449 -0.02976017 -0.09473307 -2.55934522

Largest  eigenvalues:
 [1] 63181444 59833074 56975787 55162188 55000313 53385834 51720296 51676789
 [9] 51154527 50900452

Smallest eigenvalues:
 [1]  0.49248639  0.40960297  0.38621108  0.36023736  0.25673056  0.21464356
 [7]  0.19234884  0.12075105  0.04248594 -0.74549449

Largest  eigenvalues:
 [1] 65248302 59959049 57181583 57138421 54533561 53101756 52865862 52025574
 [9] 51921307 51080228

Smallest eigenvalues:
 [1]  0.39334122  0.33047064  0.32629501  0.19379635  0.16812416  0.13090414
 [7] -0.05477706 -0.18408445 -0.58098414 -0.73843717

Largest  eigenvalues:
 [1] 65099505 61015316 58085042 56802595 55375841 53431849 53031496 52679607
 [9] 51855798 51724354

Smallest eigenvalues:
 [1]  0.30548339  0.24554368  0.23642478  0.15987535  0.12703925  0.09378831
 [7] -0.01922214 -0.04353630 -0.76229442 -0.80612734

Largest  eigenvalues:
 [1] 64876948 60619630 58099614 56431443 55108354 53540208 52736423 52490566
 [9] 52120586 51811918

Smallest eigenvalues:
 [1]  0.32426554  0.28197256  0.27470200  0.22563615  0.14239162  0.02433923
 [7] -0.10797768 -0.37291393 -0.37486837 -1.13147897

Largest  eigenvalues:
 [1] 64183660 59619217 56887479 54899471 54800085 53098550 51321536 51264428
 [9] 51136247 50515792

Smallest eigenvalues:
 [1]  0.40126316  0.25364061  0.22030842  0.21609708  0.17124851 -0.02436149
 [7] -0.03301147 -0.03839447 -0.14124017 -1.71023636

Largest  eigenvalues:
 [1] 63345061 59846669 56972690 55212679 54762249 53165915 51686538 51499515
 [9] 51314190 50892958

Smallest eigenvalues:
 [1]  0.5420560  0.5337247  0.4513997  0.4431111  0.4387204  0.3984351
 [7]  0.3288936  0.3042720  0.2969365 -0.1362922

Largest  eigenvalues:
 [1] 64190092 60453721 57603505 55851775 55388324 53681934 51747159 51708031
 [9] 51587499 50661375

Smallest eigenvalues:
 [1]  0.55073374  0.54297222  0.51082963  0.41523274  0.37805263  0.34798850
 [7]  0.21287291  0.10695564  0.02502659 -0.30731463

Largest  eigenvalues:
 [1] 62155485 59563751 56678418 55281099 54357100 53446897 51731277 51612997
 [9] 50474959 50330190

Smallest eigenvalues:
 [1]  0.45152808  0.34221015  0.30429844  0.20070174  0.14375819  0.13941621
 [7]  0.08835044  0.07877502 -0.05718764 -1.53016412

Largest  eigenvalues:
 [1] 63522551 59582375 56789777 55303776 55069116 53402280 52399364 51864767
 [9] 51457574 51231107

Smallest eigenvalues:
 [1]  0.5290067  0.5073476  0.4420684  0.3898846  0.3662684  0.3397274
 [7]  0.3302179  0.2940417  0.2693324 -0.3899703

Largest  eigenvalues:
 [1] 63840064 59665589 57254705 55531452 54728658 52972436 51716648 51544130
 [9] 51094943 50413086

Smallest eigenvalues:
 [1]  0.38186404  0.31882138  0.28269268  0.26221908  0.20873195  0.15620325
 [7] -0.02502617 -0.30825898 -0.31270897 -1.12140298

Largest  eigenvalues:
 [1] 64256357 60086955 57105046 56034737 55098977 53576186 52434184 51980495
 [9] 51940992 51457099

Smallest eigenvalues:
 [1]  0.39110953  0.34511263  0.31179453  0.27568164  0.22779465  0.19631693
 [7]  0.19355203  0.04445829 -0.11891403 -0.22965545

Largest  eigenvalues:
 [1] 64839947 61068909 58364751 56124469 55809464 54409762 52478759 52320824
 [9] 52033838 51550025

Smallest eigenvalues:
 [1]  0.35694152  0.34963105  0.34781769  0.31988503  0.31902393  0.28779090
 [7]  0.22480478  0.01865781 -0.21348169 -0.30714021

Largest  eigenvalues:
 [1] 65504655 60510141 57714234 56596733 55246141 53717935 52512222 52195935
 [9] 52006730 51271604

Smallest eigenvalues:
 [1]  0.4909675452  0.4701221131  0.4694390051  0.3028352919  0.2452801542
 [6]  0.2434072671  0.2156807159  0.1587221503  0.1034061497 -0.0001388593

Largest  eigenvalues:
 [1] 62734711 59648912 56895573 55276388 54848491 53646421 52111196 52070200
 [9] 51026420 50847040

Smallest eigenvalues:
 [1]  0.48689541  0.48576490  0.42829449  0.42401995  0.34528136  0.34205796
 [7]  0.28160503  0.25025727  0.22272704 -0.02304821

Largest  eigenvalues:
 [1] 65413861 60757798 57982157 56637338 56053608 54461964 52624305 52393563
 [9] 52307239 51374075

Smallest eigenvalues:
 [1]  0.3527634  0.3377088  0.2587051  0.2288362  0.2127325  0.1806885
 [7]  0.1418255 -0.5672442 -0.7168194 -0.8473275

Largest  eigenvalues:
 [1] 66350945 60730408 57995685 57153080 55114805 53539171 53286408 52343010
 [9] 51910982 51533345

Smallest eigenvalues:
 [1]  0.339633151  0.310616532  0.291608181  0.277225532  0.252504765
 [6]  0.169082446  0.162774847  0.001912881 -0.319071006 -0.434709805

Largest  eigenvalues:
 [1] 63904353 60530472 57176519 55799468 55759682 54076998 52933246 52229310
 [9] 51972024 51712235

Smallest eigenvalues:
 [1]  0.46803290  0.40007338  0.39735059  0.38421421  0.28975389  0.25730761
 [7]  0.23455695  0.20195783  0.06326498 -0.10195046

Largest  eigenvalues:
 [1] 64926444 59584366 57024175 56457057 54213155 52691044 52451666 51421785
 [9] 51182888 50350749

Smallest eigenvalues:
 [1]  0.489624709  0.476595477  0.442252616  0.426693886  0.366338445
 [6]  0.304354167  0.286983162  0.071696970 -0.009922337 -0.447757310

Largest  eigenvalues:
 [1] 65282066 60214595 57649067 56349320 55503948 53486895 52614501 52116710
 [9] 51764200 51074615

Smallest eigenvalues:
 [1]  0.26667410  0.26436845  0.22151618  0.19676606  0.16215809  0.03159199
 [7] -0.14277823 -0.42581091 -0.60823173 -5.49263649

Largest  eigenvalues:
 [1] 66280509 60867634 57250468 57233839 55635451 53794764 53255816 52423911
 [9] 52234572 51477171

Smallest eigenvalues:
 [1]  0.28709078  0.20331330  0.20177601  0.12799313  0.07467996 -0.13078776
 [7] -0.28376289 -0.37779122 -1.02675664 -1.90156009

Largest  eigenvalues:
 [1] 64433506 60553778 57915879 56646316 55549939 53877112 52605303 52435448
 [9] 52267266 51276730

Smallest eigenvalues:
 [1]  0.16609193  0.09717454 -0.02646772 -0.07053619 -0.20321858 -0.27499109
 [7] -0.60901198 -1.23618886 -1.32677766 -1.47023854

Largest  eigenvalues:
 [1] 66253058 60130437 57946127 55909172 54888313 53086936 52370053 51736024
 [9] 51309271 50971911

Smallest eigenvalues:
 [1]  0.46975502  0.43519165  0.37942305  0.36708858  0.27975748  0.23585324
 [7]  0.19380726  0.15939322  0.05698807 -0.11427379

Largest  eigenvalues:
 [1] 65529438 61280097 58090169 56867114 55920524 54308978 53501979 52863928
 [9] 52407450 52105472

Smallest eigenvalues:
 [1]  0.30493520  0.30361421  0.25118172  0.23662969  0.18855208  0.13848131
 [7]  0.12401362  0.02835327 -0.79716026 -2.16432190

Largest  eigenvalues:
 [1] 63520605 59810322 56988333 55559966 54828332 53227450 51975931 51770147
 [9] 51535491 50967707

Smallest eigenvalues:
 [1]  0.30810328  0.29251766  0.28242599  0.25433050  0.24175884  0.21017416
 [7]  0.13656731  0.09620963 -0.05430687 -4.88009646

Largest  eigenvalues:
 [1] 63371756 60622385 57209715 55854883 54924041 53937623 51970148 51808118
 [9] 51042825 50743218

Smallest eigenvalues:
 [1]  0.32692241  0.29829005  0.27990019  0.20355077  0.17774474  0.12937465
 [7]  0.12499896  0.09147319 -0.02837267 -1.63256340

Largest  eigenvalues:
 [1] 65896751 60994812 58298313 56665523 55690281 54023518 53070445 52622140
 [9] 52504727 52218025

Smallest eigenvalues:
 [1]  0.29123360  0.25552098  0.24744107  0.18772308  0.14368051  0.13594990
 [7]  0.08102463 -0.01648910 -1.26516585 -1.66643920

Largest  eigenvalues:
 [1] 66363864 60452546 57785218 56830800 55104627 53950293 52662443 52521438
 [9] 52403732 51841080

Smallest eigenvalues:
 [1]  0.3176570  0.2599552  0.2206302  0.1857760  0.1767845  0.1608564
 [7] -0.1829376 -0.2739934 -0.3076590 -0.9759104

Largest  eigenvalues:
 [1] 66225723 59997228 57408594 56895546 54695757 53083737 52883697 52487458
 [9] 51680595 51629488

Smallest eigenvalues:
 [1]  0.28363349  0.21716033  0.17639894  0.14059422  0.08211850 -0.02726647
 [7] -0.07456445 -0.45684450 -0.46106893 -0.66625631

Largest  eigenvalues:
 [1] 63988847 60206749 57672892 55438938 54789217 53584650 51631636 51550552
 [9] 51538830 50952331

Smallest eigenvalues:
 [1]  0.42425696  0.38013073  0.37781261  0.32415938  0.23073376  0.22262037
 [7]  0.15176636  0.08159191  0.08022446 -0.18023148

Largest  eigenvalues:
 [1] 64625430 60376646 57509574 56341473 55326289 53849102 52404494 52394558
 [9] 52196673 51321110

Smallest eigenvalues:
 [1]  0.5191467  0.4686153  0.4516688  0.3730825  0.3441009  0.3229599
 [7]  0.3111210  0.1283469  0.1048464 -0.1217506

Largest  eigenvalues:
 [1] 64787356 59680482 57150602 55766186 54922128 53520921 51937823 51870435
 [9] 51333616 50441071

Smallest eigenvalues:
 [1]  0.37900607  0.37579912  0.27173130  0.21796658  0.19640719 -0.01881112
 [7] -0.02828844 -0.05670632 -0.06603805 -1.09931498

Largest  eigenvalues:
 [1] 64317344 60501775 57312053 55711535 55517062 53842750 52919276 52012859
 [9] 51925415 51669765

Smallest eigenvalues:
 [1]  0.50712127  0.48934228  0.45347655  0.41772840  0.31821041  0.31608375
 [7]  0.25888299  0.21728037  0.21681046 -0.05002221

Largest  eigenvalues:
 [1] 64251988 59601604 57278581 55460939 54652246 53099431 51707945 51415652
 [9] 51329183 50664169

Smallest eigenvalues:
 [1]  0.3815020  0.3807990  0.3111092  0.2517962  0.2453625  0.2000132
 [7]  0.1690091 -0.3948289 -0.6721841 -1.5067667

Largest  eigenvalues:
 [1] 62652338 59239403 56794264 55101152 54862422 53183050 51910360 51763619
 [9] 50959454 50629579

Smallest eigenvalues:
 [1]  0.60482897  0.59706653  0.55296030  0.44912071  0.40053895  0.35550987
 [7]  0.28081158  0.22796525  0.13531928 -0.01172452

Largest  eigenvalues:
 [1] 62827970 60198068 57100827 55800015 54823978 54143832 52473105 52220781
 [9] 51084783 50859672

Smallest eigenvalues:
 [1]  0.28537640  0.27041960  0.25421609  0.25285332  0.21962138  0.14971529
 [7]  0.04060564 -0.64100655 -0.89371618 -1.60482220

Largest  eigenvalues:
 [1] 64845499 60310134 57853417 56182016 55183337 53355559 52475901 52174561
 [9] 52123980 51625946

Smallest eigenvalues:
 [1]  0.4340012  0.3854872  0.3431338  0.3090682  0.2976295  0.1498647
 [7]  0.1238922  0.1113390 -0.1564700 -1.0322496

Largest  eigenvalues:
 [1] 65537564 60563339 57489206 56242934 55155758 53406753 52397355 52341330
 [9] 51946283 51357532

Smallest eigenvalues:
 [1]  0.05972360  0.05200599 -0.04472271 -0.16168531 -0.16186883 -0.24938951
 [7] -0.37060917 -0.50403192 -0.69908135 -1.45177859

Largest  eigenvalues:
 [1] 63057342 59950075 57158487 55183252 54773629 53154759 52203185 51393303
 [9] 51172907 50947017

Smallest eigenvalues:
 [1]  0.45780726  0.41737971  0.39189471  0.34565040  0.33201705  0.32925516
 [7]  0.27582942  0.26857818  0.22532502 -0.02481878

Largest  eigenvalues:
 [1] 61730421 59149979 56795635 54872641 54315883 53110801 51467664 51098763
 [9] 50403432 50107821

Smallest eigenvalues:
 [1]  0.3833729  0.2971821  0.2509440  0.2385454  0.2273118  0.1989267
 [7]  0.1780260  0.1460718 -0.1974149 -0.2472994

Largest  eigenvalues:
 [1] 64559982 60233243 57646543 56378330 54917363 53389939 52527544 51636354
 [9] 51499126 50476047

Smallest eigenvalues:
 [1]  0.3646963  0.3595078  0.3072282  0.2735260  0.2448138  0.2367198
 [7]  0.1456193  0.1061710 -0.4978399 -0.7282223

Largest  eigenvalues:
 [1] 65333194 60302100 58379970 55608168 55542254 54454931 52877525 52716338
 [9] 51870592 51565797

Smallest eigenvalues:
 [1]  0.39905585  0.34746703  0.33720530  0.29311411  0.22012125  0.16280442
 [7]  0.14794924  0.09903528 -0.24700643 -0.40767001

Largest  eigenvalues:
 [1] 63695027 59342693 57346795 55885049 54196878 52875004 51793667 51721753
 [9] 51423784 50701111

Smallest eigenvalues:
 [1]  0.434026699  0.420192491  0.371494212  0.358349883  0.347354950
 [6]  0.346054388  0.288792083  0.260117823 -0.003616318 -5.376752724

Largest  eigenvalues:
 [1] 64232300 60079341 57133128 55612150 55126506 53351497 52136211 51729628
 [9] 51640725 50865858

Smallest eigenvalues:
 [1]  0.4585522  0.3856040  0.3708957  0.3625370  0.3149726  0.2731110
 [7]  0.2052727  0.1783903  0.1507486 -0.1390350

Largest  eigenvalues:
 [1] 64071662 59743549 57114570 55988912 54757544 53261189 52106801 51859210
 [9] 51843735 50950023

Smallest eigenvalues:
 [1]  0.52550429  0.45846857  0.42359247  0.36130431  0.35432233  0.27856730
 [7]  0.25876853  0.17755187  0.04585812 -0.02392554

Largest  eigenvalues:
 [1] 61461227 59847398 56981738 56081301 54131884 53957016 52768555 51638564
 [9] 50771560 50680765

Smallest eigenvalues:
 [1]  0.50990672  0.46278808  0.41709809  0.35218117  0.32965894  0.31780317
 [7]  0.30296146  0.28301839  0.18501853 -0.00942292

Largest  eigenvalues:
 [1] 63736727 60732480 57344755 55938129 55842612 54144641 52561228 52046197
 [9] 51892779 51503323

Smallest eigenvalues:
 [1]  0.45191564  0.40166766  0.37066922  0.36635833  0.34610321  0.30301743
 [7]  0.26437871  0.22812645  0.08560410 -0.04506491

Largest  eigenvalues:
 [1] 61841680 60861022 57523438 55652906 55024490 53882842 52145718 52133906
 [9] 51249343 50993076

Smallest eigenvalues:
 [1]  0.35778838  0.32313732  0.28070710  0.23478564  0.18571347  0.17820559
 [7]  0.08602546 -0.09724300 -0.44512864 -0.61094981

Largest  eigenvalues:
 [1] 64625903 61385440 58300290 56597975 55845160 54012351 53779061 52835131
 [9] 52238935 52088055

Smallest eigenvalues:
 [1]  0.4258179  0.4123385  0.4066811  0.3173327  0.2935820  0.2873354
 [7]  0.2741114  0.2036702 -0.1543384 -3.3223935

Largest  eigenvalues:
 [1] 64939930 60522264 57799431 56325991 55224145 53740974 52412394 52134671
 [9] 52080729 51217120

Smallest eigenvalues:
 [1]  0.270139743  0.258125051  0.203855010  0.077238656 -0.001353699
 [6] -0.053471372 -0.118071092 -0.423497535 -0.585571198 -1.222890407

Largest  eigenvalues:
 [1] 64910131 59792874 56955673 55471984 54675711 53020805 51973689 51656018
 [9] 51318182 51136891

Smallest eigenvalues:
 [1]  0.39030630  0.36431513  0.36048649  0.33081098  0.32275195  0.30510288
 [7]  0.30134017  0.19091043  0.13860613 -0.08821795

Largest  eigenvalues:
 [1] 65305567 60809308 57448752 57138166 55260736 53667722 52883231 52679282
 [9] 52342210 51421750

Smallest eigenvalues:
 [1]  0.4336938  0.3811972  0.3025028  0.2152404  0.2143854  0.2104441
 [7]  0.1731974 -0.0584411 -0.5365725 -0.6975240

Largest  eigenvalues:
 [1] 65336805 61045320 57411766 56236779 56023012 54133555 53072179 52554321
 [9] 52224186 51677922

Smallest eigenvalues:
 [1]  0.5561153  0.4781759  0.4731293  0.4199611  0.3779361  0.3670875
 [7]  0.3379363  0.3342902  0.2321161 -0.1889379

Largest  eigenvalues:
 [1] 64128295 60229662 57354590 56035765 55393982 53533497 52070744 51986858
 [9] 51783110 50818410

Smallest eigenvalues:
 [1]  0.31847471  0.27490608  0.23103712  0.22072614  0.18654000  0.15055378
 [7]  0.13807697  0.05449083  0.04996715 -0.14503993

Largest  eigenvalues:
 [1] 62145682 58953799 56457959 54823954 54766718 53069711 52032662 51514143
 [9] 50725101 50484234

Smallest eigenvalues:
 [1]  0.54542371  0.54113868  0.48147653  0.43825609  0.40116155  0.39243073
 [7]  0.36925263  0.22188467  0.13469984 -0.06763395

Largest  eigenvalues:
 [1] 63989765 60064953 56688317 55432189 55317750 53611973 52250079 51468344
 [9] 51428732 50599410

Smallest eigenvalues:
 [1]  0.357807286  0.349088475  0.306174172  0.277724705  0.261292687
 [6]  0.173233031  0.162480802  0.025775202  0.003066232 -0.123847602

Largest  eigenvalues:
 [1] 64934958 59195924 56706974 56383183 54608310 53050491 52425423 51637283
 [9] 50773408 50214397

Smallest eigenvalues:
 [1]  0.38691058  0.37914400  0.33736700  0.31413882  0.29839175  0.22319961
 [7]  0.03296122 -0.21851472 -0.23160158 -2.89636509

Largest  eigenvalues:
 [1] 65486301 60407178 57524222 56061381 55528873 53988543 52680697 52180972
 [9] 52000827 51801406

Smallest eigenvalues:
 [1]  0.191085559  0.065989762  0.008864738 -0.183355908 -0.232380493
 [6] -0.334767617 -0.398897637 -0.657233726 -0.801103140 -4.031988330

Largest  eigenvalues:
 [1] 62467877 59642617 56815956 55395970 54469087 53479396 52096444 51827825
 [9] 51053428 50696642

Smallest eigenvalues:
 [1]  0.4398407  0.4306110  0.3948517  0.3484145  0.2794921  0.2648174
 [7]  0.1589810  0.1463925  0.1036701 -1.7050408

Largest  eigenvalues:
 [1] 63980535 60398989 57544343 55407189 55338956 53847128 52225912 52135617
 [9] 51542032 51339157

Smallest eigenvalues:
 [1]  0.4169138  0.3747850  0.3499980  0.3279687  0.2570091  0.2533887
 [7]  0.1829724  0.1039144 -0.3099311 -0.4348086

Largest  eigenvalues:
 [1] 63146644 60498559 56882123 55837653 54962582 53275487 52182459 51720406
 [9] 51549935 50745190

Smallest eigenvalues:
 [1]  0.3863383  0.3725693  0.3402612  0.3273823  0.2639087  0.2452811
 [7]  0.2289172  0.1238991 -0.1618517 -1.8142402

Largest  eigenvalues:
 [1] 61949083 59617663 56877805 54958154 54410347 53058589 51373009 51229911
 [9] 50626749 50419702

Smallest eigenvalues:
 [1]  0.46990848  0.40559481  0.35611387  0.34376946  0.32571544  0.30474885
 [7]  0.28793421  0.19319505  0.14470277 -0.02924618

Largest  eigenvalues:
 [1] 64953733 59868091 57465829 56072246 54744131 53119010 52212536 51873610
 [9] 51791675 51033031

Smallest eigenvalues:
 [1]  0.54957838  0.54463200  0.54083681  0.49891923  0.44485620  0.32740063
 [7]  0.19661494  0.12678108  0.06429228 -0.11750755

Largest  eigenvalues:
 [1] 63577287 60261787 57455345 55593772 55191894 53664021 52175088 51940753
 [9] 51687081 51055238

Smallest eigenvalues:
 [1]  0.4709673  0.4291171  0.4028882  0.3893349  0.3609741  0.1549805
 [7]  0.1294421  0.1147023 -0.2065128 -1.2897480

Largest  eigenvalues:
 [1] 64544441 59253113 56768190 54881410 54868360 53166589 52188223 51313191
 [9] 51236105 50625199

Smallest eigenvalues:
 [1]  0.45164240  0.44019667  0.40313259  0.37379501  0.29893470  0.17303321
 [7]  0.15966312  0.10582758  0.04361385 -1.57612389

Largest  eigenvalues:
 [1] 64465797 60173534 56910177 55991850 55341440 53346972 52389483 52067523
 [9] 51626043 51233134

Smallest eigenvalues:
 [1]  0.27477744  0.19467440  0.15954488  0.13991501  0.04603371  0.03438404
 [7] -0.14440284 -0.35007133 -0.71840349 -1.00148048

Largest  eigenvalues:
 [1] 64265707 60898864 57567800 55670013 55293760 53592729 52122966 51866676
 [9] 51558509 51228311

Smallest eigenvalues:
 [1]  0.4639443  0.3820820  0.3295740  0.3076395  0.2967086  0.2568272
 [7]  0.2402834  0.2292922 -0.1798325 -1.5247088

Largest  eigenvalues:
 [1] 63195149 60080687 57331128 55870705 54715203 53362558 52176900 51718922
 [9] 51652835 51199680

Smallest eigenvalues:
 [1]  0.39226084  0.37562998  0.29721386  0.25695495  0.22287605  0.21889827
 [7]  0.03522171 -0.01706078 -0.08423336 -4.77415802

Largest  eigenvalues:
 [1] 63384454 59723997 56753544 55135280 55009229 52935019 51489509 51476458
 [9] 51242597 50468580

Smallest eigenvalues:
 [1]  0.48214799  0.39204477  0.37424865  0.30111249  0.27718006  0.19968578
 [7]  0.19933059  0.17981972  0.04870542 -0.95063877

Largest  eigenvalues:
 [1] 64958122 59814991 57656939 55931689 54641361 53469264 52223894 51709642
 [9] 51491801 50804445

Smallest eigenvalues:
 [1]  0.34432973  0.33329624  0.26655716  0.25276806  0.21523261  0.21465369
 [7]  0.16558935  0.09561748 -0.20705440 -0.78292764

Largest  eigenvalues:
 [1] 62475151 60265280 57299132 55650530 55076418 53513444 52320094 52193170
 [9] 51463215 50825775

Smallest eigenvalues:
 [1]  0.22849935  0.18694592  0.18098389  0.16741839  0.07950545  0.06576836
 [7] -0.09110808 -0.30732187 -1.42761057 -1.49394263

Largest  eigenvalues:
 [1] 63628570 59499789 56996636 54843240 54713184 53246776 51625543 51142830
 [9] 51003266 50462528

Smallest eigenvalues:
 [1]  0.35787283  0.35011015  0.24563930  0.20501641  0.17293359  0.10539791
 [7]  0.02451984 -0.04600245 -0.27117584 -3.61089959

Largest  eigenvalues:
 [1] 64993769 59728540 56948551 56312540 54900219 53180784 52474433 52270809
 [9] 51783391 51276052

Smallest eigenvalues:
 [1]  0.31604271  0.19673866  0.15549241  0.13863547 -0.02487789 -0.06897950
 [7] -0.08343397 -0.21110623 -1.12848267 -2.62019299

Largest  eigenvalues:
 [1] 65900523 59804408 57078015 56628833 54590583 53078528 52673395 52198791
 [9] 51430489 51405360

Smallest eigenvalues:
 [1]  0.45523176  0.35999222  0.22123303  0.19836564  0.16940852  0.15057724
 [7]  0.12738629 -0.06692745 -0.36537776 -1.64320673

Largest  eigenvalues:
 [1] 63838185 59446151 56371291 55103399 54663391 52965884 51742312 51303359
 [9] 51148867 50390962

Smallest eigenvalues:
 [1]  0.39787487  0.35098284  0.25080461  0.21356840  0.06106247  0.02017161
 [7]  0.00824589 -0.05994448 -0.06769519 -0.61758956

Largest  eigenvalues:
 [1] 63377372 59462491 56783258 54808869 54550405 53042371 51706114 51281312
 [9] 51090453 50666183

Smallest eigenvalues:
 [1]  0.48339463  0.40487813  0.39380319  0.37767780  0.31110870  0.29576419
 [7]  0.28300147 -0.04288057 -0.04937407 -2.30489085

Largest  eigenvalues:
 [1] 64330203 60638336 57010518 55710863 55589969 53647643 52214285 52008904
 [9] 51837158 51149013

Smallest eigenvalues:
 [1]  0.255264366  0.254990769  0.217688954  0.035840286  0.004374647
 [6] -0.135924345 -0.439217037 -0.712485014 -1.004096669 -1.462425588

Largest  eigenvalues:
 [1] 65916877 59557708 56872477 56268542 54426004 53022054 52329167 51769053
 [9] 51385268 50961594

Smallest eigenvalues:
 [1]  0.31873412  0.31250610  0.21958598  0.19047078  0.12456352  0.04217012
 [7] -0.31752076 -0.84956313 -1.54931113 -1.85553762

Largest  eigenvalues:
 [1] 66480855 60451398 58477588 56962582 55166767 53218412 52907259 52235169
 [9] 51819266 51494708

Smallest eigenvalues:
 [1]  0.398368541  0.375293894  0.353760776  0.348714132  0.324237684
 [6]  0.297573747  0.259491607  0.190384594  0.188742215 -0.007200348

Largest  eigenvalues:
 [1] 64560412 60759659 58180807 55842189 55725554 54407633 52470706 52086613
 [9] 51948297 51214153

Smallest eigenvalues:
 [1]  0.09924339  0.09212016 -0.07674742 -0.11192897 -0.11770956 -0.30974467
 [7] -0.32442439 -0.41295500 -0.75624235 -1.25053246

Largest  eigenvalues:
 [1] 66174916 60425722 58000364 57270357 54879815 53398413 53127546 52816238
 [9] 51907206 51546062

Smallest eigenvalues:
 [1]  0.39169404  0.35807565  0.34137348  0.30946762  0.30397442  0.20935081
 [7]  0.10948453 -0.08906589 -0.16411154 -1.18168583

Largest  eigenvalues:
 [1] 63649704 60295657 57417707 56285869 55031440 53359681 52534598 52075870
 [9] 51845050 51345187

Smallest eigenvalues:
 [1]  0.49899881  0.44947993  0.44740584  0.41504017  0.32800306  0.28183749
 [7]  0.23949415  0.20376783  0.06009082 -0.05709857

Largest  eigenvalues:
 [1] 66277567 60079407 57790439 57107823 54888753 53599572 53206689 51950193
 [9] 51774331 51002716

Smallest eigenvalues:
 [1]  0.38366071  0.34406182  0.32912277  0.28789686  0.27037455  0.21597467
 [7]  0.19302749  0.06957620 -0.01169218 -0.39114228

Largest  eigenvalues:
 [1] 64975846 60161970 57064134 56596868 54936164 53341354 52572077 52522065
 [9] 52017910 51569705

Smallest eigenvalues:
 [1]  0.20658819  0.20612932  0.16018438  0.13353185 -0.08180843 -0.25074857
 [7] -0.49105292 -1.44979331 -1.64269705 -1.80304536

Largest  eigenvalues:
 [1] 65304738 60312398 57707210 56519668 54775305 53442200 52649438 52170833
 [9] 51628495 51359821

Smallest eigenvalues:
 [1]  0.5460028  0.5302948  0.5084107  0.4437580  0.3605250  0.3539121
 [7]  0.1820593  0.1637137  0.1177607 -0.2146693

Largest  eigenvalues:
 [1] 64230436 59313733 56643170 55582984 54401178 52349863 51640310 51166093
 [9] 51136973 50298500

Smallest eigenvalues:
 [1]  0.54698461  0.50663764  0.44033516  0.41707953  0.35626267  0.29646196
 [7]  0.26599981  0.04527109 -0.35341494 -4.01554427

Largest  eigenvalues:
 [1] 65509740 59852530 56857360 56455643 54578768 52577185 52279191 51489216
 [9] 51446201 50655796

Smallest eigenvalues:
 [1]  0.21512081  0.14906591  0.11011256 -0.02687004 -0.04432804 -0.11844368
 [7] -0.12821064 -0.75861408 -1.07331104 -1.88364080

Largest  eigenvalues:
 [1] 66346754 60430127 57394352 57201277 55015751 53289194 53142123 52837674
 [9] 51867902 51817783

Smallest eigenvalues:
 [1]  0.3710866  0.3508347  0.3330107  0.2301228  0.1937342  0.1514765
 [7]  0.1155636 -0.1839370 -0.3467024 -0.9801734

Largest  eigenvalues:
 [1] 64161091 59907824 56932779 55163755 54732640 53146760 51799713 51708517
 [9] 51315252 51075084

Smallest eigenvalues:
 [1]  0.40675491  0.39034868  0.37854384  0.31899379  0.24789933  0.21148566
 [7]  0.18662655  0.06834084  0.04751032 -1.39155705

Largest  eigenvalues:
 [1] 64636119 60346324 56880739 56056506 55420205 53660458 51922999 51808036
 [9] 51730717 50887629

Smallest eigenvalues:
 [1]  0.37560935  0.32417452  0.28600191  0.17181566  0.16361341  0.10896189
 [7]  0.07418611  0.04317457  0.01693225 -1.98185328

Largest  eigenvalues:
 [1] 64017903 60209294 57307816 55527122 55100499 53941130 52052588 51609549
 [9] 51137565 50816590

Smallest eigenvalues:
 [1]  0.23822468  0.15785225  0.07970109  0.03502709 -0.02867249 -0.03180909
 [7] -0.04859561 -0.14190216 -0.35951790 -0.80680108

Largest  eigenvalues:
 [1] 66185362 60797860 58203730 56379951 55293550 53795333 52608526 52301710
 [9] 51941995 51468308

Smallest eigenvalues:
 [1]  0.45419461  0.44368857  0.43370536  0.34804360  0.27836663  0.25406331
 [7]  0.05162261  0.03380550 -0.05274366 -2.24685353

Largest  eigenvalues:
 [1] 65335127 60115805 57124621 56485791 55228878 53740399 52397571 52154837
 [9] 51986445 51282511

Smallest eigenvalues:
 [1]  0.48826024  0.44528091  0.39528801  0.37821865  0.37242237  0.31592848
 [7]  0.29375195  0.18116860  0.12910893 -0.07278919

Largest  eigenvalues:
 [1] 64465138 59851261 56568612 55876383 54725508 53134958 51928974 51899398
 [9] 51459432 50812873

Smallest eigenvalues:
 [1]  0.34388338  0.31470295  0.28232951  0.22163303  0.21047650 -0.05258964
 [7] -0.09257466 -0.17995696 -0.55886801 -2.94081634

Largest  eigenvalues:
 [1] 65528265 60800537 57441141 55909013 55398441 53481114 52024662 51925550
 [9] 51660791 51175536

Smallest eigenvalues:
 [1]  0.42191337  0.40200855  0.38913334  0.34370348  0.31553045  0.31497820
 [7]  0.27415048  0.25952143  0.22060993 -0.07022526

Largest  eigenvalues:
 [1] 64195125 60152331 57304196 55463690 55434272 53799107 51926986 51583696
 [9] 51343087 50445553

Smallest eigenvalues:
 [1]  0.4103166  0.3596281  0.3257396  0.2889494  0.2519206  0.1794170
 [7]  0.1181834 -0.0274441 -0.1130602 -0.1458673

Largest  eigenvalues:
 [1] 65764229 60379872 57456948 56463180 55395999 53968774 52502043 52023538
 [9] 51853948 50636427

Smallest eigenvalues:
 [1]  0.30003658  0.27514071  0.17844680  0.15536466  0.12801314  0.11383686
 [7]  0.03036235 -0.76134313 -1.02306789 -1.02501568

Largest  eigenvalues:
 [1] 65345324 59863669 57682632 55964107 55052907 53777348 52565652 52048010
 [9] 52036139 51682016

Smallest eigenvalues:
 [1]  0.47415951  0.37584902  0.36955926  0.36509014  0.34253408  0.28984457
 [7]  0.26700710  0.23295508  0.17400323 -0.03047848

Largest  eigenvalues:
 [1] 65451957 60215216 57924912 56724194 54828496 53211681 52742956 52001688
 [9] 51813755 51223775

Smallest eigenvalues:
 [1]  0.142281911  0.101247008  0.058590347 -0.001330423 -0.018051874
 [6] -0.165937088 -0.235156334 -0.324502851 -0.873190654 -1.518822952

Largest  eigenvalues:
 [1] 63612917 60497610 57801040 55150393 54997608 53777524 51966738 51895853
 [9] 51181740 50962162

Smallest eigenvalues:
 [1]  0.44430905  0.42370743  0.39945639  0.38466041  0.31193506  0.28184779
 [7]  0.26945890  0.19909868  0.08485923 -0.02049831

Largest  eigenvalues:
 [1] 65151204 60334609 58049947 55760301 55419529 53694643 52455348 52100206
 [9] 51983032 51506661

Smallest eigenvalues:
 [1]  0.35826086  0.24687905  0.24497400  0.18758641  0.13949461  0.04921253
 [7]  0.02583006 -0.04954255 -0.18359965 -0.53091826

Largest  eigenvalues:
 [1] 66211298 60601066 57991016 56631218 55032931 53636523 52696588 52642256
 [9] 51961725 51793681

Smallest eigenvalues:
 [1]  0.36911374  0.36687346  0.35853611  0.27108959  0.23069233  0.16791281
 [7]  0.16721935  0.10432921  0.02927506 -0.42260927

Largest  eigenvalues:
 [1] 66573956 61037979 57893578 57292566 56070603 54380361 53325296 53235505
 [9] 52422433 52016380

Smallest eigenvalues:
 [1]  0.4190735  0.4070922  0.3405512  0.3072790  0.2964792  0.2503843
 [7]  0.1807682  0.1407221  0.1123483 -0.6553671

Largest  eigenvalues:
 [1] 65495821 59565246 57296642 56802713 54631670 53355384 52744751 51886134
 [9] 51510542 51004241

Smallest eigenvalues:
 [1]  0.56463874  0.48159187  0.47784485  0.41365549  0.37551443  0.26991481
 [7]  0.25479935  0.22357007 -0.07050388 -3.82438333

Largest  eigenvalues:
 [1] 64843447 60121967 57418202 56099220 55146568 53460555 52210715 51970094
 [9] 51943783 50976876

Smallest eigenvalues:
 [1]  0.45303443  0.44804797  0.41963693  0.39024844  0.34455935  0.25551341
 [7]  0.24148828  0.09942670  0.06185218 -3.53302476

Largest  eigenvalues:
 [1] 63805044 60644696 57912325 56030931 55706527 54414673 52713698 52670737
 [9] 51886899 51591819

Smallest eigenvalues:
 [1]  0.4578711  0.3773066  0.3653459  0.3542151  0.3523558  0.3166131
 [7]  0.2718408  0.2593948  0.1147047 -0.4169546

Largest  eigenvalues:
 [1] 64253743 60372200 57746910 55665604 55563209 54205803 52588849 52325706
 [9] 51650457 51142665

Smallest eigenvalues:
 [1]  0.44713283  0.42137137  0.38632405  0.29865266  0.20458295  0.18679541
 [7]  0.09734140  0.05745541  0.01992097 -1.39667907

Largest  eigenvalues:
 [1] 63035420 60100239 56982329 55403538 54676248 53660700 51811384 51729271
 [9] 50947612 50846655

Smallest eigenvalues:
 [1]  0.51203841  0.46721205  0.43036363  0.38347410  0.36912243  0.35571560
 [7]  0.34827207  0.14763799  0.10701455 -0.06605479

Largest  eigenvalues:
 [1] 65203605 61313877 57696881 56611895 56318921 54595251 53459840 52595437
 [9] 52313518 51842000

Smallest eigenvalues:
 [1]  0.44892974  0.42565504  0.38195828  0.37610479  0.33296835  0.28640749
 [7]  0.26135775 -0.03768478 -0.18366181 -0.77853612

Largest  eigenvalues:
 [1] 64156328 60460528 57654175 56136977 55415842 53872704 52373780 52179905
 [9] 51819921 51193054

Smallest eigenvalues:
 [1]   0.31731585   0.21097395   0.20436093   0.18989051   0.12797501
 [6]   0.08474374   0.02840311  -0.22049051  -0.29987531 -22.45608441

Largest  eigenvalues:
 [1] 65886530 59829752 57773321 56119051 54976959 53811668 52505007 52310217
 [9] 52004167 51444084

Smallest eigenvalues:
 [1]  0.4421756  0.4001940  0.3461679  0.2436915  0.2121544  0.1651616
 [7]  0.1135466 -0.2049093 -0.2953542 -0.7346995

Largest  eigenvalues:
 [1] 65775083 60449279 57675268 56924751 54877346 52924646 52865527 52450857
 [9] 51750396 51548305

Smallest eigenvalues:
 [1]  0.5660133  0.5591972  0.4488088  0.4276763  0.3074990  0.2735265
 [7]  0.2437631  0.2436161 -0.2092905 -0.2403396

Largest  eigenvalues:
 [1] 65518084 60770237 57694984 56663045 55505105 53769933 52798593 52618856
 [9] 51982966 51418190

Smallest eigenvalues:
 [1]  0.39201828  0.36607785  0.35204663  0.32680014  0.28956974  0.22437456
 [7]  0.14268699  0.12509449  0.03413339 -2.99073803

Largest  eigenvalues:
 [1] 63731433 59913220 57537649 55585139 54967054 53503923 51893813 51760078
 [9] 51578795 50913673

Smallest eigenvalues:
 [1]  0.34244869  0.24713111  0.22917031  0.21855827  0.12267815  0.02799559
 [7] -0.09435156 -0.25574024 -0.63660542 -1.31597273

Largest  eigenvalues:
 [1] 65188942 60609757 57885515 56226885 55318100 53900123 52354358 52096839
 [9] 51809490 51127977

Smallest eigenvalues:
 [1]  0.41227613  0.40870052  0.33616820  0.33362906  0.28079421  0.23104931
 [7]  0.19895556  0.12086652  0.05272953 -0.39137290

Largest  eigenvalues:
 [1] 65176525 60286508 57729669 56397156 55140153 53515113 53259637 52595000
 [9] 51885942 51641438

Smallest eigenvalues:
 [1]  0.5008149  0.4216607  0.3996957  0.3841024  0.3261405  0.3150002
 [7]  0.2412383  0.2055896 -0.1503619 -0.1628951

Largest  eigenvalues:
 [1] 64503744 60436940 57293888 55935278 55144083 53420476 51923137 51838316
 [9] 51810506 50910026

Smallest eigenvalues:
 [1]  0.6144951  0.5285018  0.5217817  0.5196151  0.4470148  0.3437827
 [7]  0.2999062  0.2523786  0.2484838 -0.6737067

Largest  eigenvalues:
 [1] 64546214 59863211 57068038 55710816 55048166 53609544 52170113 51846223
 [9] 51643171 50809190

Smallest eigenvalues:
 [1]  0.37222354  0.37165058  0.31668573  0.28685235  0.27794986  0.18920346
 [7]  0.18072816  0.17747899  0.13493871 -0.06034644

Largest  eigenvalues:
 [1] 65832347 60698452 58366800 56387753 55512010 53945062 52598967 52453114
 [9] 52357428 51818851

Smallest eigenvalues:
 [1]  0.35770525  0.33293579  0.32768492  0.30300358  0.25719724  0.20680826
 [7]  0.19959926  0.09582846 -0.49196518 -3.15240362

Largest  eigenvalues:
 [1] 65449561 59860469 57142189 56774543 54882509 52878486 52661818 52447356
 [9] 51871090 51498949

Smallest eigenvalues:
 [1]  0.4517968  0.4144365  0.3300266  0.3087105  0.2581300  0.2437867
 [7]  0.2334273  0.1675006  0.1075077 -0.5933252

Largest  eigenvalues:
 [1] 61990273 59495261 56169635 54830368 54810776 53084656 51980907 51963983
 [9] 50881904 50687090

Smallest eigenvalues:
 [1]  0.3506319230  0.2758619363  0.2657261017  0.2395028654  0.1649213441
 [6]  0.0811668969  0.0003459881 -0.1449473441 -0.5231058413 -0.8660665085

Largest  eigenvalues:
 [1] 65291053 61470136 58265204 57253097 55376675 53682057 53391601 52686558
 [9] 52297482 51450792

Smallest eigenvalues:
 [1]  0.4793136  0.4583449  0.4146647  0.3706613  0.3250721  0.2587679
 [7]  0.2264628  0.1974565  0.1659534 -0.5557488

Largest  eigenvalues:
 [1] 62927075 59428130 56917992 54832712 54746405 53274805 51958205 51216053
 [9] 50862840 50480673

Smallest eigenvalues:
 [1]  0.2412614  0.2390749  0.1992416  0.1908809  0.1331087  0.0116919
 [7] -0.1018362 -0.2505629 -0.3093319 -1.0932292

Largest  eigenvalues:
 [1] 64095374 59974165 57551797 55743796 54854443 53577597 51806523 51776650
 [9] 51717979 50834386

Smallest eigenvalues:
 [1]  0.41544694  0.37910818  0.23492621  0.07291494  0.07267453  0.04956870
 [7] -0.05042230 -0.06958034 -0.30108024 -2.05870162

Largest  eigenvalues:
 [1] 63849817 60299918 57457323 55643758 55519229 53803956 52656806 51852855
 [9] 51754879 51311383

Smallest eigenvalues:
 [1]  0.2246526516  0.1942011844  0.1937623025  0.1659102309  0.1623246554
 [6]  0.1610865035  0.0879658289 -0.0009876474 -0.2353104174 -0.3403656520

Largest  eigenvalues:
 [1] 63603903 59327103 56393229 55541008 54790499 53096645 51785774 51502903
 [9] 50837448 50204772

Smallest eigenvalues:
 [1]  0.50770215  0.39444190  0.37925689  0.37911256  0.33363794  0.29753137
 [7]  0.20674451  0.17236082 -0.08702109 -0.34161654

Largest  eigenvalues:
 [1] 64556946 60777383 57801352 55956468 55380047 53784533 52804492 52188723
 [9] 52119033 51895624

Smallest eigenvalues:
 [1]  0.3858945  0.3357381  0.3322148  0.2991350  0.2648856  0.2166075
 [7]  0.2097733  0.1959674 -0.1248980 -1.5621686

Largest  eigenvalues:
 [1] 64988000 60744097 58054952 55793758 55714057 54257483 52254240 52026348
 [9] 51952737 51354732

Smallest eigenvalues:
 [1]  0.22561415  0.16207596  0.15719959  0.07536898  0.03632150 -0.06279389
 [7] -0.35865122 -0.37470584 -1.38351044 -1.73710540

Largest  eigenvalues:
 [1] 64611910 59590608 56910221 55998848 54675695 53070642 52256865 52004935
 [9] 51630179 51039778

Smallest eigenvalues:
 [1]  0.44767823  0.40929841  0.31800547  0.29323309  0.24793446  0.23712671
 [7]  0.17928678  0.16993373 -0.04305723 -1.19057602

Largest  eigenvalues:
 [1] 64459967 60581001 57233205 56274291 55618530 53983003 52254222 52103640
 [9] 51949071 51065380

Smallest eigenvalues:
 [1]  0.29175891  0.23391803  0.17408246  0.15674499  0.13489617  0.03069871
 [7] -0.08542268 -0.29960155 -0.49240463 -1.15718716

Largest  eigenvalues:
 [1] 65011155 60446753 57391949 56561354 54868283 53567535 52497609 52424645
 [9] 51804319 51659271

Smallest eigenvalues:
 [1]  0.28625032  0.23514710  0.20044846  0.12233990  0.07800716 -0.17761160
 [7] -0.25776908 -0.35657178 -0.52667098 -1.41482632

Largest  eigenvalues:
 [1] 64139926 59265630 57053193 55480737 54299754 53206194 51861387 51672562
 [9] 51475812 50955437

Smallest eigenvalues:
 [1]  0.22936969  0.21020719  0.17412006  0.16857077  0.14773110 -0.04124600
 [7] -0.04524443 -0.13908801 -0.19386815 -1.60214300

Largest  eigenvalues:
 [1] 64827179 60849185 57772424 56091366 55686590 54345296 52699600 52619501
 [9] 52033152 51844209

Smallest eigenvalues:
 [1]   0.412687187   0.378728427   0.329309738   0.315846639   0.309482282
 [6]   0.260399031   0.258287998   0.004449181  -0.127375454 -10.241339447

Largest  eigenvalues:
 [1] 64424604 59948334 57293836 55663979 55086637 53523884 52232847 51767244
 [9] 51558272 50970216

Smallest eigenvalues:
 [1]  0.36599217  0.35035789  0.33298055  0.24896675  0.20065789  0.16959265
 [7]  0.13564926  0.13228616  0.07244268 -0.05980429

Largest  eigenvalues:
 [1] 62703934 60077912 57137338 55468784 55142718 53363255 52450982 52300059
 [9] 51319769 51097271

Smallest eigenvalues:
 [1]  0.3801999  0.3482936  0.2911245  0.2376649  0.2114886  0.2042119
 [7]  0.1396087 -0.1238492 -0.3356010 -1.5960486

Largest  eigenvalues:
 [1] 65509902 60152591 57115971 56687346 55225618 53671732 52595198 52389513
 [9] 52049240 51614870

Smallest eigenvalues:
 [1]  0.40036700  0.34391822  0.33329054  0.27999331  0.18251816  0.15645880
 [7]  0.04867742 -0.37491944 -0.43668209 -5.08273853

Largest  eigenvalues:
 [1] 65539086 60222540 57388358 56269213 55131641 53232074 52490064 52041479
 [9] 51631253 51249262

Smallest eigenvalues:
 [1]  0.1954337  0.1900241  0.1856947 -0.1009354 -0.1317049 -0.2657994
 [7] -0.3685551 -0.3867340 -0.4988534 -1.0059088

Largest  eigenvalues:
 [1] 65078229 61302853 57667033 56408164 56335387 54364814 53902332 52580335
 [9] 52210065 51853661

Smallest eigenvalues:
 [1]  0.4477225  0.3848476  0.3436877  0.3162659  0.2796636  0.2688860
 [7]  0.2687305  0.1863084 -0.1544271 -0.4701790

Largest  eigenvalues:
 [1] 64188783 60775878 58101977 56181014 55269762 53746974 52018781 51951917
 [9] 51867480 50942808

Smallest eigenvalues:
 [1]  0.29422165  0.19777063  0.10466091  0.09802734  0.08529111 -0.01484967
 [7] -0.03153301 -0.07522498 -0.08202590 -2.15647362

Largest  eigenvalues:
 [1] 65018490 59874004 57597808 56494080 55166656 53943434 52963395 52339654
 [9] 52293857 51909023

Smallest eigenvalues:
 [1]  0.4571294  0.4331764  0.3556075  0.3295324  0.3015585  0.2531303
 [7]  0.1890027 -0.0762550 -0.2423593 -2.0077737

Largest  eigenvalues:
 [1] 65594600 59761014 56750503 56303172 54397133 52641892 52325120 51402736
 [9] 51157988 50646589

Smallest eigenvalues:
 [1]  0.4646382  0.4500035  0.4326764  0.3553120  0.3421914  0.2759485
 [7]  0.2269887  0.1665191  0.1383409 -0.3495080

Largest  eigenvalues:
 [1] 64765642 59847766 57466185 55416579 55326091 53851506 51752952 51621365
 [9] 51513030 50756216

Smallest eigenvalues:
 [1]  0.54077236  0.45580438  0.39245221  0.36618302  0.32701812  0.25522995
 [7]  0.17374478  0.09220614  0.02697602 -0.18929149

Largest  eigenvalues:
 [1] 64297809 60192559 57326812 55886898 55741257 54169291 52391068 52339491
 [9] 51817913 51719604

Smallest eigenvalues:
 [1]   0.28795199   0.27277850   0.20074329   0.18314525   0.07810581
 [6]   0.07390435  -0.14078310  -0.23773276  -0.81091645 -19.99259512

Largest  eigenvalues:
 [1] 63386915 60157856 57630136 55396973 55059110 53740049 52612356 51764476
 [9] 51217132 50971375

Smallest eigenvalues:
 [1]  0.44495994  0.43756862  0.40479803  0.36700433  0.29030394  0.28358212
 [7]  0.20101780  0.16501665  0.06417002 -0.60855837

Largest  eigenvalues:
 [1] 65777865 59744112 57271941 56758633 54656306 53142956 52658067 52156304
 [9] 51650234 51153478

Smallest eigenvalues:
 [1]  0.5600320259  0.5197066362  0.4716906350  0.4274944451  0.3802579594
 [6]  0.3145297440  0.1539205452  0.0993539107  0.0449715190 -0.0008183772

Largest  eigenvalues:
 [1] 64622130 60260555 57568973 55499532 55270147 53859864 52528099 52187523
 [9] 51608209 51386552

Smallest eigenvalues:
 [1]  0.38680342  0.38043602  0.29153600  0.24563297  0.23429306  0.18889191
 [7]  0.01685479 -0.06894029 -0.25638247 -0.99896044

Largest  eigenvalues:
 [1] 64469025 59751953 56836436 56087082 54973882 53396839 52174809 52118878
 [9] 51635719 51052704

Smallest eigenvalues:
 [1]  0.46791424  0.42696534  0.40733922  0.29847974  0.27113267  0.26420213
 [7]  0.22380461  0.19868696  0.03986304 -1.18350445

Largest  eigenvalues:
 [1] 63467451 59614210 57326320 55294604 54774928 53569594 52225269 51868355
 [9] 51462107 51049675

Smallest eigenvalues:
 [1]  0.43702356  0.42604157  0.39079303  0.34412615  0.33467068  0.30929347
 [7]  0.21153955  0.05084477 -0.07964505 -0.36445304

Largest  eigenvalues:
 [1] 62826830 59678675 57072272 55577700 54873055 53217787 51617413 51517158
 [9] 51454822 50419893

Smallest eigenvalues:
 [1]  0.48176879  0.47590168  0.45135691  0.35256321  0.29979562  0.24374336
 [7]  0.18477920  0.15047625  0.04436969 -0.31178165

Largest  eigenvalues:
 [1] 64051732 60470592 57314570 55920693 55677193 53961064 52688454 52333781
 [9] 52084407 51491467

Smallest eigenvalues:
 [1]  0.5016051  0.4968539  0.4371616  0.3619396  0.2849206  0.2823763
 [7]  0.2764347  0.2168504 -0.4795734 -0.9207457

Largest  eigenvalues:
 [1] 63668237 59487438 56679394 55383196 54760833 52965982 52505702 51419262
 [9] 51258260 50827519

Smallest eigenvalues:
 [1]  0.41912095  0.41569188  0.38103989  0.35351037  0.32666803  0.15140703
 [7]  0.10824039  0.04329408  0.01489731 -0.63925734

Largest  eigenvalues:
 [1] 65886826 59762903 57373163 56081924 54784273 53253947 52266660 51992319
 [9] 51872940 50786459

Smallest eigenvalues:
 [1]  0.43595765  0.39682051  0.39075055  0.33381001  0.29843423  0.27807291
 [7]  0.08690499  0.06523444 -0.02987169 -0.15160563

Largest  eigenvalues:
 [1] 64742431 59808026 57082245 55931053 55223080 53601270 51979427 51713581
 [9] 51200746 50160068

Smallest eigenvalues:
 [1]  0.40488521  0.33661461  0.31488626  0.30953580  0.20523401  0.19087398
 [7]  0.12114293 -0.04880466 -0.21783977 -1.20261650

Largest  eigenvalues:
 [1] 63223035 60261246 57197895 55536047 54634545 53602041 51867519 51650129
 [9] 51020678 50782355

Smallest eigenvalues:
 [1]  0.4849433275  0.4841665497  0.3777428439  0.3416971499  0.2464414420
 [6]  0.1714379744  0.1662778665  0.1268239945  0.0005470483 -0.7292119221

Largest  eigenvalues:
 [1] 62227487 59472121 56301950 54810892 54627139 52990412 51981668 51350084
 [9] 50758495 50592550

Smallest eigenvalues:
 [1]  0.56944125  0.56092355  0.53088372  0.38999585  0.37768531  0.33125085
 [7]  0.14577636  0.07204877 -0.01303944 -0.08134181

Largest  eigenvalues:
 [1] 65509212 59707801 56930931 56801415 54693907 52846224 52825664 51613132
 [9] 51241242 50563950

Smallest eigenvalues:
 [1]  0.45139495  0.33014890  0.32141809  0.24491037  0.20517283  0.06123890
 [7]  0.05308619 -0.11056516 -0.41556868 -1.78319977

Largest  eigenvalues:
 [1] 65090916 61286284 57576899 57017512 56036583 54061194 53642363 52598580
 [9] 52562384 52037266

Smallest eigenvalues:
 [1]  0.37826796  0.26562021  0.22840776  0.21147742  0.10750055  0.08870933
 [7] -0.07661383 -0.57303159 -0.72562523 -1.43752797

Largest  eigenvalues:
 [1] 66099606 59632397 56959965 56639559 54271809 52790293 52774600 51948815
 [9] 51194509 51138006

Smallest eigenvalues:
 [1]  0.49795328  0.48946833  0.37090172  0.34569614  0.34364666  0.24733095
 [7]  0.23063347  0.03688379 -0.06018632 -0.07092340

Largest  eigenvalues:
 [1] 64304716 59211940 56646151 55378824 54553727 52950678 51749212 51337080
 [9] 51010538 50350073

Smallest eigenvalues:
 [1]  0.57828218  0.43946131  0.43929519  0.43191753  0.32229192  0.26328218
 [7]  0.25870389  0.15465279 -0.01163865 -0.17573346

Largest  eigenvalues:
 [1] 63856256 59434670 56599109 55565201 54294527 52741153 51592902 51416187
 [9] 50854223 49980333

Smallest eigenvalues:
 [1]  0.32262618  0.28155888  0.26583075  0.25263305  0.18970866  0.18448297
 [7]  0.14260862  0.06096392  0.02455327 -0.61564965

Largest  eigenvalues:
 [1] 65520186 60717282 58313241 56814197 55276033 54077777 52758127 52422198
 [9] 52209834 51323013

Smallest eigenvalues:
 [1]  0.26260530  0.21686847  0.19140481  0.18325633  0.15980163  0.06528655
 [7]  0.03317500 -0.01989466 -0.02473640 -1.32647737

Largest  eigenvalues:
 [1] 65137609 59739526 56861443 55352361 54609599 53063802 51844055 51464858
 [9] 51354641 50984481

Smallest eigenvalues:
 [1]  0.49605156  0.47801544  0.38649387  0.32656970  0.29630198  0.29523228
 [7]  0.27247007  0.23548578 -0.01054134 -4.59470119

Largest  eigenvalues:
 [1] 65458625 60933445 58171282 56502806 55889848 54203623 52785493 52380574
 [9] 52298581 51335343

Smallest eigenvalues:
 [1]  0.46684321  0.36387549  0.27705717  0.25738809  0.18158818  0.17546580
 [7]  0.11212597  0.09262325 -0.04820603 -2.14074394

Largest  eigenvalues:
 [1] 64472340 59723600 56643172 55327342 54632084 53111796 51594997 51417633
 [9] 51103578 50351645

Smallest eigenvalues:
 [1]  0.12619207  0.11150809 -0.02642782 -0.11883213 -0.20232777 -0.26620876
 [7] -0.29929589 -0.33377198 -0.40606544 -2.12884828

Largest  eigenvalues:
 [1] 65215394 60451497 57823944 55590231 55242169 53697723 52268919 51749697
 [9] 51616911 51551837

Smallest eigenvalues:
 [1]  0.5134272  0.4424175  0.4241758  0.4106739  0.2890797  0.2725983
 [7]  0.2428147  0.1979289  0.1501808 -0.3316823

Largest  eigenvalues:
 [1] 65618110 60382275 57637651 56388302 54993976 53577224 52547187 51891132
 [9] 51701511 51075420

Smallest eigenvalues:
 [1]  0.59023219  0.58918366  0.47027725  0.45783010  0.32727309  0.31447231
 [7]  0.26417584  0.23580021  0.09613169 -0.19109745

Largest  eigenvalues:
 [1] 66106226 60462707 57873612 56510852 55256661 53910668 52629003 52425409
 [9] 51906728 51459859

Smallest eigenvalues:
 [1]  0.45392489  0.37648662  0.36913566  0.34349880  0.27966157  0.22471334
 [7]  0.19231751  0.15185063 -0.04310512 -0.54915024

Largest  eigenvalues:
 [1] 65138793 60799831 58083511 56522591 55289786 54000798 52439949 52299768
 [9] 52066025 51152576

Smallest eigenvalues:
 [1]  0.4809745  0.4590980  0.4387196  0.3687736  0.3483114  0.3247535
 [7]  0.2592652  0.2098659  0.1649771 -0.2093161

Largest  eigenvalues:
 [1] 64917145 59591691 56585076 56403815 54415806 52955504 52227002 51755799
 [9] 51457858 50476682

Smallest eigenvalues:
 [1]  0.5524188  0.5253289  0.5077754  0.4161437  0.3520868  0.3513292
 [7]  0.2103284  0.2087082  0.1859932 -0.1284037

Largest  eigenvalues:
 [1] 63837922 60245945 57035962 55380949 55326319 53792924 52322533 52050087
 [9] 51476482 51299291

Smallest eigenvalues:
 [1]  0.34254222  0.33927761  0.31655651  0.28933653  0.25041960  0.14760181
 [7]  0.14038325  0.10272106  0.09726858 -0.04434161

Largest  eigenvalues:
 [1] 62043686 60363468 57442009 55964839 55030812 54198462 52667039 52376837
 [9] 51524088 51024495

Smallest eigenvalues:
 [1]  0.5968017  0.5715338  0.5118664  0.4725151  0.4217953  0.4008595
 [7]  0.3050661  0.2051502  0.1252929 -0.6374712

Largest  eigenvalues:
 [1] 64160435 60688682 57059963 55706722 55619054 54010276 52354304 52204999
 [9] 51551473 51087770

Smallest eigenvalues:
 [1]  0.43921422  0.42016738  0.35638344  0.30966081  0.26502777  0.24474031
 [7]  0.18751967  0.10361093  0.09089492 -0.24473658

Largest  eigenvalues:
 [1] 65926783 60097564 57534009 57235572 54874892 53467654 53210909 52079431
 [9] 52018865 51148221

Smallest eigenvalues:
 [1]  0.4080132  0.3844416  0.3041990  0.2304309  0.1596702  0.1284254
 [7]  0.1103804 -0.1029656 -0.4918004 -6.7413261

Largest  eigenvalues:
 [1] 65643124 60330007 57714685 56891546 55069589 53498821 52869298 52499837
 [9] 52343252 51841262

Smallest eigenvalues:
 [1]  0.41389349  0.40761232  0.40226160  0.31894818  0.22299817  0.21388907
 [7]  0.16096874  0.03526162 -0.25323135 -0.37868853

Largest  eigenvalues:
 [1] 63486960 60336516 56992318 55336170 54965194 53270669 52033524 51574922
 [9] 51378816 51136791

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	3.279887	0.7437776	16.15451	0.025	2.603456	2.992705

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

EDA ~ alt + n + speed + PM25

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- EDA_fd
covariates <- list(altitude = altitude_fd, 
                   noise = noise_fd,
                   speed = speed_fd,
                   pollution = pollution25_fd)
path_plot <- 'figures/model_EDA_alt_noise_speed_PM25_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     noise = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     speed = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     pollution = list(nbetabasis = 80, norder = 4, lambda = 1e3))

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, HR = HR, 
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 20.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 552 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Smallest eigenvalues:
 [1]  0.4871369  0.4371022  0.3969283  0.3897641  0.3730379  0.2673980
 [7]  0.2008282  0.1900299  0.1361075 -0.3468347

Largest  eigenvalues:
 [1] 68059266 64101840 60644122 58736466 58716578 57068833 55627800 54815286
 [9] 54654377 54536680

Smallest eigenvalues:
 [1]  0.31626973  0.26059966  0.23993168  0.21653830  0.19324014  0.10787567
 [7]  0.08651189 -0.28053069 -0.30436903 -0.42319472

Largest  eigenvalues:
 [1] 68770392 64169545 60674221 59601290 58063150 56494814 55448851 55198213
 [9] 54695329 54499491

Smallest eigenvalues:
 [1]  0.43298209  0.39065054  0.32038564  0.31580052  0.27135299  0.23095625
 [7]  0.20945298  0.19700370  0.08325258 -0.41730796

Largest  eigenvalues:
 [1] 67770450 63208445 60343961 58687915 58280158 56793741 55070711 54572301
 [9] 54536838 53659641

Smallest eigenvalues:
 [1]  0.43237843  0.39038460  0.34811747  0.33055939  0.31228261  0.25721830
 [7]  0.14359522  0.08298407 -0.13808340 -0.62250939

Largest  eigenvalues:
 [1] 67811971 62987753 59541897 59247626 57265095 55165720 54978367 54645876
 [9] 54120743 53559691

Smallest eigenvalues:
 [1]  0.4404208  0.3973378  0.3768946  0.2737752  0.2050022  0.1869457
 [7]  0.1405393  0.1161547  0.1069949 -0.1166931

Largest  eigenvalues:
 [1] 67137597 63620292 60580274 58578451 58299324 56627449 55069595 54935718
 [9] 54450249 53882219

Smallest eigenvalues:
 [1]  0.4361153  0.4326552  0.3869301  0.3522986  0.3027189  0.2735660
 [7]  0.1994096  0.1946225 -0.1716368 -0.8596436

Largest  eigenvalues:
 [1] 68084219 63736704 60353725 59617447 58281549 56405027 55941119 55218463
 [9] 54652844 54529492

Smallest eigenvalues:
 [1]  0.38927997  0.37610068  0.35684531  0.34063844  0.31202250  0.27494319
 [7]  0.27244318  0.23238277  0.16768573 -0.02078581

Largest  eigenvalues:
 [1] 67387409 63146916 60185673 58730138 58419765 56802746 54846634 54774673
 [9] 54583931 53767885

Smallest eigenvalues:
 [1]  0.45607174  0.41654925  0.35855495  0.33982063  0.29229437  0.21420155
 [7]  0.18843033  0.11117026  0.01735056 -0.36860044

Largest  eigenvalues:
 [1] 68361349 63183905 60546176 59889133 57425627 55737221 55510477 54616628
 [9] 54518969 53666258

Smallest eigenvalues:
 [1]  0.49811625  0.46528024  0.43474154  0.36427775  0.35894018  0.33293173
 [7]  0.28401616  0.26487715  0.10022111 -0.06254842

Largest  eigenvalues:
 [1] 68064710 62670534 59709023 58503314 57846340 56015128 54596787 54425121
 [9] 54202304 53272207

Smallest eigenvalues:
 [1]  0.3593228887  0.3433896281  0.3369084233  0.3132160259  0.2576256241
 [6]  0.1771936430  0.0555107639  0.0002109515 -0.0042069481 -1.7101748456

Largest  eigenvalues:
 [1] 68395305 62396380 59498750 59466638 57367625 55769806 55239370 54171465
 [9] 54091163 52995028

Smallest eigenvalues:
 [1]  0.51350430  0.51159491  0.47357855  0.39443796  0.37486979  0.35960475
 [7]  0.35264703  0.35242619  0.01385313 -0.10981068

Largest  eigenvalues:
 [1] 68858102 63357473 60530783 59180159 57635973 55961754 55123054 54263050
 [9] 54161199 53137821

Smallest eigenvalues:
 [1]  0.53093655  0.51995572  0.48821032  0.47648058  0.46355993  0.31445682
 [7]  0.31291593  0.23488736 -0.03642857 -0.34042996

Largest  eigenvalues:
 [1] 68424485 63190125 59891761 58884313 57566614 55831695 54697181 54461233
 [9] 54276996 53538246

Smallest eigenvalues:
 [1]  0.5174449  0.5021500  0.4412483  0.3880284  0.3130337  0.2963612
 [7]  0.2473445  0.2330143  0.1785020 -0.2004829

Largest  eigenvalues:
 [1] 67645049 63634076 60086272 58794605 58313547 56647524 54851828 54824342
 [9] 54603160 53441398

Smallest eigenvalues:
 [1]  0.4665770015  0.4069988808  0.3895608957  0.3856017392  0.2619467891
 [6]  0.2502397556  0.2181061500  0.0007206708 -0.0504037136 -0.1134290527

Largest  eigenvalues:
 [1] 66632318 63520905 60254586 58655310 57823329 56068446 54601011 54391995
 [9] 54350224 53388102

Smallest eigenvalues:
 [1]  0.45818700  0.37136770  0.29148577  0.27702628  0.24315137  0.21055155
 [7]  0.19510489  0.01871583  0.01108419 -0.72363063

Largest  eigenvalues:
 [1] 69183118 64459976 61163657 60194874 58849131 57346541 55796547 55683673
 [9] 55507089 54488472

Smallest eigenvalues:
 [1]  0.47726477  0.46309090  0.43523194  0.39681253  0.28294893  0.20860649
 [7]  0.19858134  0.17230710 -0.02344266 -0.57905785

Largest  eigenvalues:
 [1] 69363412 64124990 60920367 60247435 58125390 56259240 56042633 54948944
 [9] 54526296 53691877

Smallest eigenvalues:
 [1]  0.45139613  0.43086785  0.41039084  0.35391708  0.34869672  0.32162403
 [7]  0.27304407  0.18773427  0.07331108 -0.12103944

Largest  eigenvalues:
 [1] 66963884 63545029 60317747 58632379 58325131 56537075 54772232 54415200
 [9] 54369365 53375125

Smallest eigenvalues:
 [1]  0.43709837  0.38000027  0.34314821  0.32264968  0.32256152  0.29458365
 [7]  0.27292184  0.14086888 -0.05545111 -0.15267781

Largest  eigenvalues:
 [1] 67072042 62650767 59544403 58387544 57213244 55349123 54186067 54158601
 [9] 53816704 52846055

Smallest eigenvalues:
 [1]  0.422189092  0.404023271  0.383861175  0.317653503  0.316002243
 [6]  0.294476889  0.092847498  0.049750875  0.008568628 -1.148264890

Largest  eigenvalues:
 [1] 68199451 62355141 59796309 58810834 57084186 55633965 54676434 54473218
 [9] 53890661 53565731

Smallest eigenvalues:
 [1]  0.36601341  0.34884508  0.32397289  0.30520595  0.22180805  0.20022794
 [7]  0.19795086  0.02900890 -0.08856656 -0.55525858

Largest  eigenvalues:
 [1] 68551210 63238500 60182506 59475762 57766437 55928747 55276650 54688690
 [9] 54346976 53404496

Smallest eigenvalues:
 [1]  0.5236764  0.5192387  0.5022011  0.4842300  0.4085521  0.3715304
 [7]  0.3193392  0.3005085  0.2890489 -0.2175593

Largest  eigenvalues:
 [1] 67928828 63663113 60863678 59257439 58003601 56485819 55303790 55043862
 [9] 54898748 54170244

Smallest eigenvalues:
 [1]  0.48284305  0.45986782  0.36174236  0.35885619  0.31053144  0.25346649
 [7]  0.21006018  0.19946098 -0.06829768 -0.29319774

Largest  eigenvalues:
 [1] 68103616 62978338 60173316 59292523 57509879 55866911 55020144 54497332
 [9] 54141711 53538661

Smallest eigenvalues:
 [1]  0.4950097  0.4636102  0.4341808  0.3521315  0.2925940  0.2902679
 [7]  0.2731803  0.2567635  0.1783970 -0.1862945

Largest  eigenvalues:
 [1] 68172085 62937912 60183781 59824308 57500008 55959923 55500437 54658056
 [9] 54407035 53536824

Smallest eigenvalues:
 [1]  0.39768985  0.39122856  0.37494588  0.33651524  0.26772258  0.19871315
 [7]  0.16946260  0.08006802  0.02121582 -0.34346341

Largest  eigenvalues:
 [1] 65940319 62344604 59691727 58142836 57630444 55823040 54544779 54469383
 [9] 53818081 53290574

Smallest eigenvalues:
 [1]  0.4365127  0.3614570  0.2775098  0.2773886  0.2513917  0.2427106
 [7]  0.1893908  0.1661593  0.1588374 -0.2544476

Largest  eigenvalues:
 [1] 67122286 63509849 60780775 58325872 58055733 56501379 54870908 54419206
 [9] 54139163 53607976

Smallest eigenvalues:
 [1]  0.420597619  0.410745867  0.368259699  0.310143784  0.227328357
 [6]  0.204441963  0.039067837 -0.008790068 -0.328413604 -0.346530671

Largest  eigenvalues:
 [1] 66037014 64224088 60699255 58555412 58153110 56617827 55225662 54783167
 [9] 54331770 53885360

Smallest eigenvalues:
 [1]  0.52748599  0.46638658  0.45179256  0.42314000  0.40293589  0.36212396
 [7]  0.27969146  0.27198076 -0.07221661 -2.62416503

Largest  eigenvalues:
 [1] 66513698 63278026 59855593 58213011 57996845 55829530 54336266 54132971
 [9] 54067279 53109153

Smallest eigenvalues:
 [1]  0.45634931  0.44209161  0.41576289  0.35035815  0.32261647  0.30067384
 [7]  0.30023702  0.19512978  0.11790271 -0.04748266

Largest  eigenvalues:
 [1] 65878907 62898650 59728870 58297646 57719713 55993283 54640176 54230520
 [9] 53822797 53075670

Smallest eigenvalues:
 [1]  0.50510552  0.48768840  0.46010217  0.44683777  0.31004613  0.24806864
 [7]  0.22691530  0.14519283 -0.05051331 -0.35949256

Largest  eigenvalues:
 [1] 67498749 64060536 60110675 59531468 58726183 56835254 55162004 55064940
 [9] 54728857 53538259

Smallest eigenvalues:
 [1]  0.3094222  0.2595862  0.2541490  0.2522295  0.1958157  0.1856597
 [7]  0.1216368 -0.1725698 -0.3185201 -0.3619991

Largest  eigenvalues:
 [1] 67300507 62096933 59508524 58926534 56793849 55251736 54585475 54136001
 [9] 53513805 52672732

Smallest eigenvalues:
 [1]  0.5033218  0.4783948  0.4262774  0.4234277  0.3057034  0.3038685
 [7]  0.2768524  0.2434997 -0.1691813 -0.3278553

Largest  eigenvalues:
 [1] 66518757 63269474 60191380 58260125 58206584 56574526 54827894 54489678
 [9] 53923445 53540435

Smallest eigenvalues:
 [1]  0.48918706  0.47462820  0.42909671  0.39800639  0.33585951  0.33112584
 [7]  0.27284565  0.07943919 -0.11571926 -0.92037649

Largest  eigenvalues:
 [1] 69222807 64030303 60448521 59222388 58384903 56699450 55126458 55021546
 [9] 54838160 54105682

Smallest eigenvalues:
 [1]  0.416985886  0.378743453  0.345784576  0.330311833  0.200104660
 [6]  0.174274331  0.148573109  0.065419697  0.005920638 -1.084810571

Largest  eigenvalues:
 [1] 68318679 63736977 60757475 58951832 58752474 56951645 55566161 55182307
 [9] 54919181 54481657

Smallest eigenvalues:
 [1]  0.3744231  0.3733671  0.3553443  0.3411885  0.2518314  0.2415413
 [7]  0.2252323  0.1888753  0.1035058 -2.9700488

Largest  eigenvalues:
 [1] 67099045 63272366 60170863 58372070 58290558 56543802 54743651 54509254
 [9] 54340226 53270275

Smallest eigenvalues:
 [1]  0.4203994  0.3446973  0.3410058  0.3307456  0.2955211  0.2714684
 [7]  0.2323524  0.2140012  0.1143990 -0.2032699

Largest  eigenvalues:
 [1] 68156692 63357485 60278084 59227975 57812680 56098633 55203506 55077256
 [9] 54354781 54129890

Smallest eigenvalues:
 [1]  0.5906458  0.5873059  0.5847440  0.5490714  0.5127235  0.5012821
 [7]  0.4849396  0.4395064  0.3227387 -1.8935748

Largest  eigenvalues:
 [1] 68256622 63370189 60222910 59017165 57862824 55976164 54783492 54743614
 [9] 54087691 53621602

Smallest eigenvalues:
 [1]  0.42976933  0.39700879  0.37356246  0.27685748  0.24309946  0.17745138
 [7]  0.15359435  0.11145381  0.09396638 -1.23292036

Largest  eigenvalues:
 [1] 68328598 62888364 60037456 59129174 57488789 56159645 55030792 54555726
 [9] 54525131 53890837

Smallest eigenvalues:
 [1]  0.55004545  0.50210387  0.48044303  0.42128365  0.39004892  0.33616378
 [7]  0.31727410  0.23817137  0.08922346 -0.01835973

Largest  eigenvalues:
 [1] 68283398 63863469 60994535 59810602 57589428 55697948 55405464 54616766
 [9] 54224875 53503845

Smallest eigenvalues:
 [1]  0.44027896  0.43283983  0.38029104  0.36565636  0.33521763  0.27004087
 [7]  0.24172554  0.23630925  0.17518938 -0.06797854

Largest  eigenvalues:
 [1] 66241033 63553237 60238572 58838239 57768728 56908731 55221327 54618512
 [9] 53860584 53717247

Smallest eigenvalues:
 [1]  0.55314140  0.49808467  0.48119124  0.36321582  0.34659613  0.28693376
 [7]  0.24198914  0.09408923 -0.02784464 -0.28214494

Largest  eigenvalues:
 [1] 69018227 64128690 60998433 59808183 58279589 56333682 55690260 55181213
 [9] 55090343 54206642

Smallest eigenvalues:
 [1]  0.4726470  0.4269587  0.4037764  0.3664048  0.3500020  0.2975436
 [7]  0.1772066  0.1757382  0.1420796 -0.8633437

Largest  eigenvalues:
 [1] 68040339 63681881 60855726 59001226 58357501 56717739 54947036 54628022
 [9] 54489538 53852312

Smallest eigenvalues:
 [1]  0.34868348  0.32606343  0.31571882  0.27297998  0.23888565  0.14540253
 [7]  0.03916881  0.03131517 -0.13332400 -0.41710638

Largest  eigenvalues:
 [1] 65314961 63401131 60103251 58095865 57531950 56113046 54588320 54360131
 [9] 53671897 53061319

Smallest eigenvalues:
 [1]  0.45496708  0.45452662  0.43290031  0.37788800  0.31918824  0.24126342
 [7]  0.18284014  0.11407919 -0.02109173 -0.05402286

Largest  eigenvalues:
 [1] 68081190 62822194 59940799 58848160 57844185 55881097 55357211 54602444
 [9] 54046184 53943930

Smallest eigenvalues:
 [1]  0.53875611  0.49638694  0.41383932  0.38415113  0.36157461  0.32026101
 [7]  0.31343084  0.26991871  0.24705935 -0.03186374

Largest  eigenvalues:
 [1] 69001612 63164956 60726358 59677718 57398271 55411495 55386894 54665716
 [9] 53788714 53391130

Smallest eigenvalues:
 [1]  0.48073317  0.42625166  0.42333368  0.36812326  0.34516524  0.32162632
 [7]  0.25500258  0.23415890  0.14881881 -0.09277153

Largest  eigenvalues:
 [1] 66989365 63625402 60341405 58491793 58176755 56548718 54937409 54680466
 [9] 54376037 53990071

Smallest eigenvalues:
 [1]  0.4843283  0.4585012  0.3983035  0.3808898  0.3084147  0.3023291
 [7]  0.2436740  0.2001448  0.1122935 -0.1753386

Largest  eigenvalues:
 [1] 67029232 63198647 60164788 58287771 58247208 56586577 54931100 54339653
 [9] 54196997 53487574

Smallest eigenvalues:
 [1]  0.4834365  0.3988858  0.3403165  0.3177665  0.2802590  0.2531752
 [7]  0.2239748  0.2084495  0.1905648 -0.4318380

Largest  eigenvalues:
 [1] 69301709 63929047 61231528 60135504 57879806 56589298 55746805 54905347
 [9] 54612772 54084649

Smallest eigenvalues:
 [1]  0.592315926  0.572323127  0.468126026  0.408312690  0.361957586
 [6]  0.357558641  0.197612349  0.192047716 -0.001285125 -0.034488330

Largest  eigenvalues:
 [1] 67217736 62820734 60044831 58419511 57804653 56175814 54647397 54571362
 [9] 54249515 53643527

Smallest eigenvalues:
 [1]  0.5201938  0.4894251  0.4531740  0.4039184  0.3455898  0.3265580
 [7]  0.3225675  0.2822306  0.2317851 -1.5090775

Largest  eigenvalues:
 [1] 68071045 62771423 59977836 59051581 57525083 56035625 54797724 54063812
 [9] 53729617 52613633

Smallest eigenvalues:
 [1]  0.50513942  0.44915861  0.37602448  0.33991175  0.32276343  0.24378112
 [7]  0.20372369  0.13740468  0.07695445 -0.92755240

Largest  eigenvalues:
 [1] 69115278 63621572 60675863 58967918 58352685 56793236 55486177 54945916
 [9] 54824275 54522138

Smallest eigenvalues:
 [1]  0.36663659  0.36649950  0.34293067  0.26896848  0.22819671  0.20576198
 [7]  0.19777934  0.19599314 -0.09180112 -1.02862132

Largest  eigenvalues:
 [1] 68868587 63716566 60727672 59626044 58191992 56840329 55426208 54928084
 [9] 54575558 53713146

Smallest eigenvalues:
 [1]  0.37785008  0.36373303  0.30286342  0.27407066  0.26981205  0.26946474
 [7]  0.24734828  0.20137140  0.05640455 -0.05977492

Largest  eigenvalues:
 [1] 69574215 63520521 60786643 59687911 58117146 56592206 55504509 54738375
 [9] 54547611 53827033

Smallest eigenvalues:
 [1]  0.43409418  0.42218964  0.35141293  0.34250855  0.27221329  0.27099634
 [7]  0.22145390  0.02206452 -0.04109297 -6.00719540

Largest  eigenvalues:
 [1] 67808576 64202059 60482193 59399268 58548623 56436186 55644613 55188764
 [9] 54320223 53789302

Smallest eigenvalues:
 [1]  0.3442454230  0.3376436772  0.3197629749  0.3160097179  0.2390944073
 [6]  0.1229629268  0.1128499044 -0.0007692301 -0.5166756526 -0.6933854505

Largest  eigenvalues:
 [1] 67748172 63422645 60256715 59469845 57416920 55997381 55164768 54641503
 [9] 54574920 53541980

Smallest eigenvalues:
 [1]  0.412677630  0.339258553  0.310752531  0.263551865  0.226463623
 [6]  0.219127498  0.193101447  0.181948708  0.006700095 -0.397420613

Largest  eigenvalues:
 [1] 66238531 62217525 59573641 58105371 57310025 55599109 53930816 53928528
 [9] 53806505 52648330

Smallest eigenvalues:
 [1]  0.5489729  0.5071630  0.4302460  0.4207504  0.3020158  0.2796464
 [7]  0.2681556  0.2107831  0.1066990 -0.8239525

Largest  eigenvalues:
 [1] 67568552 64139242 60504948 59421811 58595022 56700774 55282716 54966169
 [9] 54835593 53904665

Smallest eigenvalues:
 [1]  0.51088162  0.48506500  0.38909132  0.33015270  0.31119151  0.26728222
 [7]  0.19934615  0.14503639  0.05533713 -0.11641848

Largest  eigenvalues:
 [1] 66461710 64442104 60786409 58715408 58338083 56802141 55110712 55083895
 [9] 54540940 54118942

Smallest eigenvalues:
 [1]  0.5138599  0.4419077  0.4138884  0.3804675  0.3782512  0.3487442
 [7]  0.3478423  0.2303019 -0.1612810 -3.4902104

Largest  eigenvalues:
 [1] 68691678 63525039 59755017 59479030 58325403 56226754 55319968 54788780
 [9] 54502533 53705743

Smallest eigenvalues:
 [1]  0.4891512  0.4788613  0.4436544  0.3933629  0.3898036  0.3063964
 [7]  0.3001360  0.2847364  0.2757718 -0.5226982

Largest  eigenvalues:
 [1] 67435567 62794678 59867014 59112816 56957478 55138808 54709138 53869882
 [9] 53655681 52875429

Smallest eigenvalues:
 [1]  0.36259907  0.35417442  0.30301563  0.26373907  0.23797479  0.21026581
 [7]  0.19887019  0.19604302  0.02928042 -0.05492904

Largest  eigenvalues:
 [1] 68587333 63293933 60630711 59375226 57943250 56001434 55374620 55091061
 [9] 54138537 53947498

Smallest eigenvalues:
 [1]  0.59517572  0.54654609  0.53926798  0.46474824  0.37709382  0.32447032
 [7]  0.30067989  0.27527320 -0.07630564 -0.09355798

Largest  eigenvalues:
 [1] 68456935 64160158 60954533 58868578 58596662 56813391 55452523 54924358
 [9] 54839387 54358757

Smallest eigenvalues:
 [1]  0.47018455  0.43618346  0.34724248  0.34407028  0.31301957  0.13881482
 [7]  0.13161609  0.08359004 -0.03143958 -0.05128687

Largest  eigenvalues:
 [1] 68167649 63262086 60546633 58653525 57437255 55762432 54507266 54180272
 [9] 54088867 53321232

Smallest eigenvalues:
 [1]  0.5624139  0.4773664  0.4147852  0.4048095  0.4011495  0.3813351
 [7]  0.2762676  0.2732593  0.2420925 -0.4028556

Largest  eigenvalues:
 [1] 67494281 63288147 59985830 59263398 57709501 55991989 54621552 54579444
 [9] 54440505 53439909

Smallest eigenvalues:
 [1]  0.48987627  0.45855660  0.41213000  0.32369859  0.28594498  0.23581489
 [7]  0.20627680  0.03657812 -0.00553368 -0.12320354

Largest  eigenvalues:
 [1] 68743350 64198814 60864391 59241318 58602183 56754061 55461578 55070750
 [9] 54941056 54471558

Smallest eigenvalues:
 [1]  0.51390023  0.48430507  0.45595817  0.44183864  0.39999669  0.39393468
 [7]  0.34396878  0.25019694  0.20905366 -0.03458746

Largest  eigenvalues:
 [1] 66549646 63156820 59869802 58547853 57996506 56095636 54541956 54474939
 [9] 54326771 53281674

Smallest eigenvalues:
 [1]  0.23579131  0.19797926  0.16348135  0.12675588  0.06501839  0.04211488
 [7]  0.02641495 -0.10843971 -0.26184509 -2.61208018

Largest  eigenvalues:
 [1] 68414965 63715588 60853508 58941952 58452414 57158519 55347011 55132302
 [9] 54650319 54300148

Smallest eigenvalues:
 [1]  0.5507021  0.4952098  0.4530175  0.4346892  0.3841613  0.3242088
 [7]  0.3039139  0.1624287 -0.1888110 -3.6390781

Largest  eigenvalues:
 [1] 69471437 63077083 60005960 59427265 57527032 55693380 55253195 54745026
 [9] 54559209 54080556

Smallest eigenvalues:
 [1]  0.42502247  0.39646002  0.38823320  0.36176840  0.33014068  0.32227665
 [7]  0.31464403  0.01439214 -0.02400790 -0.06026872

Largest  eigenvalues:
 [1] 67949595 63196962 60457910 58595311 57566260 56193568 54572674 54190056
 [9] 54152649 53368084

Smallest eigenvalues:
 [1]  0.46865458  0.43429456  0.32142795  0.28741370  0.26576764  0.11121914
 [7]  0.10182332  0.07441637 -0.01045278 -0.03944125

Largest  eigenvalues:
 [1] 66942469 63505685 60665260 58294776 58233816 56730174 55047953 54697459
 [9] 54269623 53972202

Smallest eigenvalues:
 [1]  0.3740484  0.3026676  0.2790268  0.2637559  0.2370925  0.2157886
 [7]  0.2036167  0.1749273  0.1554799 -0.7774389

Largest  eigenvalues:
 [1] 67399605 62789251 59958220 58497737 57564868 55983800 54482127 54233563
 [9] 53621660 52467550

Smallest eigenvalues:
 [1]  0.36378565  0.31921817  0.30553080  0.28393074  0.27513078  0.03152577
 [7]  0.03149619 -0.03901565 -0.15937589 -2.13047391

Largest  eigenvalues:
 [1] 67016536 63680093 60575587 58663041 58497538 57071723 55415775 54773926
 [9] 54341155 54149353

Smallest eigenvalues:
 [1]  0.55302651  0.45022239  0.37309786  0.36430415  0.33107637  0.31883252
 [7]  0.28099918  0.23378306  0.16817241 -0.02547947

Largest  eigenvalues:
 [1] 67277337 63179174 60205816 58697082 57873336 56218961 54538533 54489877
 [9] 54257981 53389249

Smallest eigenvalues:
 [1]  0.61041244  0.59586829  0.54510813  0.50578135  0.44193619  0.40141562
 [7]  0.36415673  0.33638829  0.29494625 -0.05460051

Largest  eigenvalues:
 [1] 68167338 63860055 60495694 59697066 57814700 56072107 55331137 55148906
 [9] 54304412 54079808

Smallest eigenvalues:
 [1]  0.4376435  0.4049017  0.3787041  0.3223802  0.2171088  0.2151866
 [7]  0.1585135  0.1442549  0.1206910 -0.4251732

Largest  eigenvalues:
 [1] 68184531 63667509 60623166 59712027 57955988 56503627 55424063 55226090
 [9] 54617339 53973308

Smallest eigenvalues:
 [1]  0.37390983  0.36285367  0.35459864  0.27937323  0.20137449  0.18593865
 [7]  0.18167535  0.07005072  0.03350012 -1.23029729

Largest  eigenvalues:
 [1] 65423518 62099073 59592072 57851324 57446447 55362180 54455760 54438164
 [9] 53522444 53218576

Smallest eigenvalues:
 [1]  0.44359425  0.42939751  0.34020097  0.30385384  0.20538030  0.10849466
 [7]  0.04643053 -0.01631910 -0.38642925 -0.88464119

Largest  eigenvalues:
 [1] 67708789 63534685 60681200 58907560 58495488 56751640 55652641 55256451
 [9] 54749033 54422734

Smallest eigenvalues:
 [1]  0.4662827  0.4510253  0.3861807  0.2878057  0.2210033  0.2192955
 [7]  0.1654335  0.1385009  0.1301377 -2.5833472

Largest  eigenvalues:
 [1] 68955976 64378731 61037748 60113421 58598958 57120552 55959259 55535063
 [9] 55102042 54680941

Smallest eigenvalues:
 [1]  0.40304525  0.38922916  0.37960931  0.31481611  0.31065750  0.26681945
 [7]  0.09155275  0.07165704  0.02106968 -0.42524862

Largest  eigenvalues:
 [1] 68180980 63172381 59864587 58943633 57585141 56092622 54806168 54600239
 [9] 54280325 53451268

Smallest eigenvalues:
 [1]  0.53020409  0.46862655  0.43102286  0.33622462  0.26806288  0.24654839
 [7]  0.21547387  0.19878633  0.17243970 -0.06501671

Largest  eigenvalues:
 [1] 68191452 64073179 61012483 59480633 58318972 56513983 55709349 55139905
 [9] 54673376 54521249

Smallest eigenvalues:
 [1]  0.454399678  0.368957238  0.361311930  0.344483347  0.309491776
 [6]  0.222550549  0.105645979 -0.009634668 -0.283283940 -1.350372683

Largest  eigenvalues:
 [1] 67865449 63461592 60926667 59305856 58166427 56834269 55057311 54828865
 [9] 54701708 53644860

Smallest eigenvalues:
 [1]  0.385489074  0.339088948  0.337854291  0.323149018  0.229454991
 [6]  0.207186884  0.114152561  0.068643349 -0.006851919 -0.344605356

Largest  eigenvalues:
 [1] 68214176 63199159 60348321 59418587 58028890 56340267 55290403 55070394
 [9] 55061825 54019966

Smallest eigenvalues:
 [1]  0.31946836  0.30438363  0.29937308  0.26339950  0.22114627  0.21299499
 [7]  0.21186254  0.19713965  0.09901826 -0.06406513

Largest  eigenvalues:
 [1] 65103446 62167472 59747186 57724216 57064933 56013837 54352832 53791164
 [9] 52828173 52790421

Smallest eigenvalues:
 [1]  0.49466537  0.47530245  0.47448685  0.46329900  0.38954014  0.26461205
 [7] -0.03224441 -0.16083733 -0.21264541 -1.52598581

Largest  eigenvalues:
 [1] 68682833 63500509 60367217 59650131 57719444 55751671 55331398 54641935
 [9] 54407742 53684650

Smallest eigenvalues:
 [1]  0.38816449  0.34084715  0.29729645  0.28189568  0.25817663  0.19675391
 [7]  0.16909634 -0.03988069 -0.18518397 -1.30201892

Largest  eigenvalues:
 [1] 68558799 63417656 60643518 60346566 57416310 56071488 55807297 54730713
 [9] 54342711 53481197

Smallest eigenvalues:
 [1]  0.41356748  0.41283024  0.37793226  0.35407525  0.24610008  0.19083224
 [7]  0.07852834  0.06874451  0.05868728 -0.15215231

Largest  eigenvalues:
 [1] 64973706 63507134 60225300 58644948 57370591 56861049 55393714 54754736
 [9] 53672061 53434798

Smallest eigenvalues:
 [1]  0.52853457  0.51067878  0.41846842  0.39989648  0.37170678  0.30852560
 [7]  0.08824105  0.04665996 -0.01549561 -0.12295605

Largest  eigenvalues:
 [1] 65169538 62863778 59811828 57797566 57246051 55991193 54376681 54363859
 [9] 53239029 53047793

Smallest eigenvalues:
 [1]  0.4383703  0.4111223  0.3452179  0.2534708  0.2198715  0.2110006
 [7]  0.1684109  0.1371931 -0.3066051 -0.3522867

Largest  eigenvalues:
 [1] 67488654 64168456 60293962 59057188 58758893 56901662 55728262 54814559
 [9] 54612011 54484284

Smallest eigenvalues:
 [1]  0.09077574  0.07985318  0.07161046 -0.06546924 -0.12357081 -0.16574267
 [7] -0.21544949 -0.48774375 -0.83137836 -1.98341432

Largest  eigenvalues:
 [1] 66195681 64278486 60842737 58947202 58620138 56907207 55835488 55177032
 [9] 54779117 54593055

Smallest eigenvalues:
 [1]  0.4749992  0.4588567  0.4417316  0.3748957  0.3720367  0.3162966
 [7]  0.3140249  0.2632057 -0.0280806 -2.0185636

Largest  eigenvalues:
 [1] 68978953 64357723 60924403 60487418 58066529 56268462 56176150 55668085
 [9] 54406992 53989675

Smallest eigenvalues:
 [1]  0.3630992  0.3002337  0.2967818  0.2834526  0.2188619  0.2176326
 [7]  0.1361318  0.0295708 -0.1960163 -3.0776484

Largest  eigenvalues:
 [1] 67324951 63763746 60236085 59100481 58484849 56469610 55154252 55036454
 [9] 54423842 53840466

Smallest eigenvalues:
 [1]  0.4393979  0.4335799  0.3535523  0.3416898  0.3262382  0.3198756
 [7]  0.2599242  0.2244695  0.2188060 -0.3704628

Largest  eigenvalues:
 [1] 69389725 63379986 60416549 59945552 57850181 56166456 55908720 54662160
 [9] 54479225 53752139

Smallest eigenvalues:
 [1]  0.5088960  0.4617664  0.4360174  0.3913409  0.3876926  0.3313498
 [7]  0.2930483  0.2128162  0.1721470 -0.3028481

Largest  eigenvalues:
 [1] 67548263 62922130 59965643 58899477 57449254 55952148 54783006 54624333
 [9] 54236373 53645519

Smallest eigenvalues:
 [1]  0.521842376  0.520011459  0.497703415  0.478549456  0.326143515
 [6]  0.291596374  0.260953709  0.194431572  0.027887885 -0.007009047

Largest  eigenvalues:
 [1] 66771614 63725955 60100392 58829551 57896168 56108666 55124980 54572437
 [9] 54513456 53914225

Smallest eigenvalues:
 [1]  0.4313105  0.3445489  0.3442898  0.2853614  0.2807683  0.2501643
 [7]  0.1619296  0.1004652 -0.8247342 -7.2402608

Largest  eigenvalues:
 [1] 67131179 63154484 59929993 58892666 57761317 55989821 54759196 54373410
 [9] 53828908 52983938

Smallest eigenvalues:
 [1]  0.37640735  0.36416540  0.29618411  0.21635469  0.20268014  0.17298621
 [7]  0.13174738  0.05457955 -0.18058773 -0.21500361

Largest  eigenvalues:
 [1] 68609531 64134758 60414755 60234951 58115936 56284038 55834964 55082088
 [9] 54911624 53600040

Smallest eigenvalues:
 [1]  0.50247460  0.47260993  0.38647617  0.36478648  0.36288107  0.30084449
 [7]  0.25583464  0.24388533  0.08722445 -0.33180412

Largest  eigenvalues:
 [1] 68531566 63888273 60130973 59667500 58693034 56660728 55541734 55177951
 [9] 54660654 53924702

Smallest eigenvalues:
 [1]  0.4928859  0.4831381  0.4545999  0.4173196  0.3830974  0.2714029
 [7]  0.2088009  0.1708331  0.1314161 -0.8384515

Largest  eigenvalues:
 [1] 67826879 63397132 60822273 59282953 57974316 56742458 55057886 54898142
 [9] 54868155 53958399

Smallest eigenvalues:
 [1]  0.20543543  0.16406222  0.13946428  0.13155527  0.01737225 -0.04304625
 [7] -0.12514565 -0.22232352 -1.03993087 -2.18440288

Largest  eigenvalues:
 [1] 65918912 61917774 59546108 57733513 57663878 55908569 54218269 53742805
 [9] 53539442 52857183

Smallest eigenvalues:
 [1]  0.4933460  0.4516526  0.4407941  0.4010209  0.3965264  0.3463170
 [7]  0.3341390  0.1981114  0.1618570 -0.4107189

Largest  eigenvalues:
 [1] 68014649 63020138 59777877 59393790 57196425 55288574 55022353 54149971
 [9] 53671496 52608983

Smallest eigenvalues:
 [1]  0.4550006  0.4235911  0.3334757  0.3229685  0.2805139  0.2758863
 [7]  0.2751037  0.2352111  0.1790599 -3.4237993

Largest  eigenvalues:
 [1] 67948630 62608888 59981010 59039138 57814452 56067304 54870319 54209206
 [9] 53740478 52912651

Smallest eigenvalues:
 [1]  0.40014581  0.36849807  0.30293426  0.28140058  0.23684477  0.13934769
 [7]  0.06755045 -0.02203300 -0.10866453 -0.18224245

Largest  eigenvalues:
 [1] 67876387 63134415 59976381 58919291 58412697 56716895 55282204 54996769
 [9] 54744138 53999243

Smallest eigenvalues:
 [1]  0.5033202  0.4097102  0.3990640  0.3883469  0.3517175  0.2437599
 [7]  0.2431688  0.1988100  0.1392137 -0.4830344

Largest  eigenvalues:
 [1] 67044114 63213891 60130967 58860348 57627075 56179643 54488399 54321776
 [9] 54197509 53350164

Smallest eigenvalues:
 [1]  0.45060840  0.42807831  0.30089375  0.29628542  0.29603247  0.29542166
 [7]  0.15964715  0.14897590 -0.01336732 -0.25958192

Largest  eigenvalues:
 [1] 68413752 63601725 60822801 59808151 58036723 56607045 56015639 55492248
 [9] 54960583 54658739

Smallest eigenvalues:
 [1]  0.5904692  0.4976456  0.4702491  0.3976988  0.3738093  0.3645971
 [7]  0.3240381  0.3184169  0.2746071 -0.2363938

Largest  eigenvalues:
 [1] 68362988 63671482 60460396 59788598 57546347 56181868 55450546 54608953
 [9] 54336991 53479769

Smallest eigenvalues:
 [1]  0.5710800  0.5640956  0.5442517  0.4381953  0.4163381  0.4114387
 [7]  0.4016177  0.2740346  0.2240140 -0.5849995

Largest  eigenvalues:
 [1] 67517055 63211161 59963090 59216642 57716013 56118148 54780751 54403143
 [9] 54351313 53122785

Smallest eigenvalues:
 [1]  0.5144350  0.4717993  0.3905050  0.3899166  0.2978297  0.2316817
 [7]  0.2020666  0.1547138  0.0225471 -0.7302839

Largest  eigenvalues:
 [1] 66894031 63944070 60013529 58857412 58483601 57074872 55154840 54865255
 [9] 54229713 53585708

Smallest eigenvalues:
 [1]  0.44725665  0.44573068  0.43751959  0.42946557  0.33754621  0.29625245
 [7]  0.26160239  0.23080588  0.20363386 -0.06763161

Largest  eigenvalues:
 [1] 66918101 63491317 59858200 59013190 57495495 55998288 54491613 54277216
 [9] 54028111 52879966

Smallest eigenvalues:
 [1]  0.4425354  0.3690194  0.3584283  0.3528590  0.3514590  0.3355940
 [7]  0.3000671  0.1211724  0.1082390 -0.6851168

Largest  eigenvalues:
 [1] 66528197 63166261 60377521 58705088 57827724 56148189 55677762 54492141
 [9] 54209331 54147771

Smallest eigenvalues:
 [1]  0.3953901  0.3540681  0.2987046  0.2740494  0.2271158  0.1969634
 [7]  0.1546901  0.1240115 -0.3236322 -0.5011239

Largest  eigenvalues:
 [1] 69023359 63184524 60399164 59359283 57600309 55734814 55266961 54521889
 [9] 54342755 53310978

Smallest eigenvalues:
 [1]  0.45563190  0.37823123  0.33830151  0.33148410  0.30596916  0.25124252
 [7]  0.22863720  0.14232750  0.12419326 -0.08990773

Largest  eigenvalues:
 [1] 66043011 63222739 60234088 58235574 57967486 56423212 54673119 54554982
 [9] 53879930 53246138

Smallest eigenvalues:
 [1]  0.24604180  0.21493893  0.20040227  0.09773293 -0.02546299 -0.04815794
 [7] -0.05146104 -0.78119750 -1.31136695 -1.69888129

Largest  eigenvalues:
 [1] 67683422 62380245 59673150 58290138 57526124 55897587 54851571 54304464
 [9] 54152766 53388444

Smallest eigenvalues:
 [1]  0.55078292  0.51338187  0.50589985  0.41717784  0.33959169  0.31521354
 [7]  0.21719589  0.12176297 -0.07072099 -0.37853862

Largest  eigenvalues:
 [1] 69139029 63693011 60114237 59691291 58146325 56002469 55567959 55524284
 [9] 54508372 54364076

Smallest eigenvalues:
 [1]  0.4351992  0.3987839  0.3824598  0.3378732  0.2606060  0.2508343
 [7]  0.2151245  0.1898829  0.1023967 -0.6948539

Largest  eigenvalues:
 [1] 68733663 64134850 60727968 59915740 57962986 56407405 55630953 55312853
 [9] 54297335 54258940

Smallest eigenvalues:
 [1]  0.53484588  0.42556523  0.41570369  0.39366101  0.38426783  0.36058011
 [7]  0.25899550  0.25342828  0.19805837 -0.05033832

Largest  eigenvalues:
 [1] 67122253 63358040 60485393 58986995 57363422 55971787 54592712 54527424
 [9] 54323654 53760752

Smallest eigenvalues:
 [1]  0.46508605  0.40510691  0.29925393  0.27044472  0.23636723  0.23429491
 [7]  0.22232868  0.13777595  0.06874249 -0.77713298

Largest  eigenvalues:
 [1] 68180216 63197853 60579100 59476964 57527674 56175957 55326442 54706216
 [9] 54512863 53698090

Smallest eigenvalues:
 [1]  0.43334345  0.41197094  0.37364522  0.34752942  0.30926025  0.27936114
 [7]  0.20318198  0.19349993 -0.03850194 -0.18890380

Largest  eigenvalues:
 [1] 68235858 63641755 61109297 60028696 57442462 55652697 55589629 54667081
 [9] 54187876 53549769

Smallest eigenvalues:
 [1]  0.6197192  0.5443604  0.4970049  0.4502359  0.4325619  0.3099852
 [7]  0.3037181  0.2719893  0.2187992 -4.3173235

Largest  eigenvalues:
 [1] 68741002 63389623 60732652 59074596 58047664 56450568 54987006 54756860
 [9] 54650662 53974077

Smallest eigenvalues:
 [1]  0.50637323  0.49061049  0.43122512  0.43080375  0.28762009  0.28469532
 [7]  0.26850906 -0.01901069 -0.14258580 -0.20492768

Largest  eigenvalues:
 [1] 68349894 62941431 59769307 59015252 57570044 55898782 54866580 54716095
 [9] 54611928 53774586

Smallest eigenvalues:
 [1]  0.38204869  0.34709909  0.33077802  0.32353933  0.30607034  0.21910549
 [7]  0.18169733  0.15562452 -0.04396911 -0.84144077

Largest  eigenvalues:
 [1] 69978042 62940249 60083432 60072850 57324308 55931636 55782780 54740508
 [9] 54342107 53974136

Smallest eigenvalues:
 [1]  0.3724431  0.3455962  0.3414101  0.3114556  0.3009087  0.2945569
 [7]  0.2011349  0.1404208  0.1375942 -1.5617201

Largest  eigenvalues:
 [1] 70255071 63776450 61399597 60899760 58027722 56292554 56017732 55570819
 [9] 54615887 54437528

Smallest eigenvalues:
 [1]  0.39604516  0.39351708  0.32995606  0.26447135  0.25137016  0.18067785
 [7]  0.15859488  0.14919848 -0.04081838 -0.20996525

Largest  eigenvalues:
 [1] 68492762 64198715 61251004 59567579 58458310 56978995 55330504 55272862
 [9] 55110370 54201685

Smallest eigenvalues:
 [1]  0.42853376  0.40284336  0.36222066  0.31929266  0.25211957  0.20408867
 [7]  0.13287602  0.07981155  0.04949470 -1.07206364

Largest  eigenvalues:
 [1] 70149479 63623083 60875447 59604711 57572748 55818266 55625866 54758699
 [9] 54225160 54132430

Smallest eigenvalues:
 [1]  0.4134856  0.3272312  0.2795836  0.2554193  0.2108288  0.1440820
 [7] -0.1641066 -0.4342838 -2.1496383 -2.4938596

Largest  eigenvalues:
 [1] 66811542 63366094 60431009 59121716 57488377 55650388 54744204 54525253
 [9] 53771403 53075530

Smallest eigenvalues:
 [1]  0.41257337  0.38604746  0.34035932  0.30968326  0.29953331  0.26542595
 [7]  0.11580983  0.06510327  0.02043763 -0.06679304

Largest  eigenvalues:
 [1] 68676446 63157113 60525932 59653409 57624309 56220373 55536444 54439066
 [9] 54291899 53264470

Smallest eigenvalues:
 [1]  0.40979146  0.37910311  0.36331590  0.34947441  0.31481149  0.26545673
 [7]  0.25635612  0.03800147 -0.07982756 -0.09810509

Largest  eigenvalues:
 [1] 66973152 62751168 59555968 58342374 57528375 55803141 54255639 54202246
 [9] 53431692 52518936

Smallest eigenvalues:
 [1]  0.47739111  0.42157482  0.40364665  0.35183985  0.34761427  0.34046791
 [7]  0.23104382 -0.02181021 -0.06972688 -0.08068021

Largest  eigenvalues:
 [1] 66965675 62079761 59356953 58068905 57120695 54815450 53894385 53587637
 [9] 53362247 52417503

Smallest eigenvalues:
 [1]  0.46215341  0.41857618  0.41177900  0.40378570  0.33789643  0.30447158
 [7]  0.01017379 -0.13362746 -0.31025824 -1.40944793

Largest  eigenvalues:
 [1] 68732522 63335363 59860942 59579664 57404224 55369431 55287669 54171420
 [9] 53940059 53018396

Smallest eigenvalues:
 [1]  0.3095818  0.2778032  0.2545463  0.2197349  0.1953447  0.1852127
 [7]  0.1472302 -0.1423292 -0.1739088 -7.7728334

Largest  eigenvalues:
 [1] 67334819 62941735 60102184 58869760 57340064 55814185 54706507 54674878
 [9] 54641267 53415065

Smallest eigenvalues:
 [1]  0.50115690  0.48429533  0.44553863  0.40515728  0.34452359  0.30252002
 [7]  0.27072430  0.08791954  0.06078579 -0.80934514

Largest  eigenvalues:
 [1] 68672614 63395526 59991608 59129944 58140288 56482990 54858718 54695680
 [9] 54461345 53753595

Smallest eigenvalues:
 [1]  0.3860044  0.3824185  0.3206108  0.2997718  0.2540411  0.2315155
 [7]  0.1360335 -0.2639487 -0.5670442 -0.7219225

Largest  eigenvalues:
 [1] 67282238 63562389 60128636 58625375 58517712 56931965 54997354 54555117
 [9] 54185018 53635801

Smallest eigenvalues:
 [1]  0.30325056  0.29874419  0.23979320  0.20915818  0.20475933  0.17085431
 [7]  0.11078222  0.09518855 -1.80241987 -2.32152462

Largest  eigenvalues:
 [1] 69949807 64121589 61201566 59557393 58314949 56754865 55518420 55232282
 [9] 54786552 54360565

Smallest eigenvalues:
 [1]  0.5656168  0.5459389  0.5307897  0.5071578  0.4788590  0.4242468
 [7]  0.2676424  0.1972563  0.1701764 -0.1489015

Largest  eigenvalues:
 [1] 69666734 63432673 60377362 60127470 57885457 56487122 55792032 55080301
 [9] 54688257 54145775

Smallest eigenvalues:
 [1]  0.5263281  0.4612386  0.4441120  0.4208742  0.3836335  0.2636897
 [7]  0.2454053  0.2242008  0.1952285 -0.3667273

Largest  eigenvalues:
 [1] 67887378 63084368 59704785 59171495 57341098 55716494 54895080 54373154
 [9] 54259558 53490263

Smallest eigenvalues:
 [1]  0.44011677  0.41593644  0.40595178  0.37867142  0.31194354  0.29370175
 [7]  0.26200139  0.17180736  0.09959999 -0.08855659

Largest  eigenvalues:
 [1] 69132237 63959573 60198890 59909500 58147258 56127210 55574416 55200340
 [9] 54329539 54222982

Smallest eigenvalues:
 [1]  0.49582636  0.48170465  0.45545788  0.41535396  0.31666443  0.29850157
 [7]  0.23190553  0.05164566 -0.01182284 -0.87743788

Largest  eigenvalues:
 [1] 68830882 63416373 60488564 59737195 57641430 56116078 55500207 54338978
 [9] 54214870 53182409

Smallest eigenvalues:
 [1]  0.38370556  0.35542697  0.30085070  0.26385480  0.25050507  0.24841977
 [7]  0.22510366  0.17700562 -0.07308743 -2.36891544

Largest  eigenvalues:
 [1] 68707693 63730190 60768678 59825413 58441912 56974564 55420380 55035742
 [9] 54914929 53976469

Smallest eigenvalues:
 [1]  0.3332730  0.3156874  0.3089196  0.2948094  0.2923146  0.2672954
 [7]  0.1809407  0.1010079  0.0764179 -0.5716010

Largest  eigenvalues:
 [1] 67311033 63228047 59675813 58754173 58158345 56392368 54518937 54508048
 [9] 53829478 52778975

Smallest eigenvalues:
 [1]  0.46599774  0.46389302  0.43408618  0.34884094  0.34790297  0.30601859
 [7]  0.24181956  0.23707329  0.20018916 -0.08858747

Largest  eigenvalues:
 [1] 67160353 63173780 59973832 59054165 57924193 56125013 54971145 54673344
 [9] 54209699 53723958

Smallest eigenvalues:
 [1]  0.39410693  0.35767248  0.35460259  0.28428720  0.23976973  0.18395171
 [7]  0.11804654  0.04405101 -0.15458088 -0.79080988

Largest  eigenvalues:
 [1] 66872622 62380480 59279307 57980076 57539566 55897162 54393556 53901042
 [9] 53845919 53136358

Smallest eigenvalues:
 [1]  0.323264964  0.309539847  0.294746452  0.258753508  0.258534033
 [6]  0.254078357  0.193114427  0.120513092  0.017501962 -0.006173376

Largest  eigenvalues:
 [1] 67342453 63754033 60881660 58716735 57926063 56536263 55011066 54656585
 [9] 54516927 53935285

Smallest eigenvalues:
 [1]  0.387625408  0.362205506  0.257718358  0.247279385  0.206357377
 [6]  0.195219648  0.188117232  0.045500866  0.003735276 -1.262557776

Largest  eigenvalues:
 [1] 68854102 63530864 60778998 59356633 58323291 56404055 55715708 55279950
 [9] 54741653 54625630

Smallest eigenvalues:
 [1]  0.41296135  0.38172985  0.35421380  0.34992552  0.33355387  0.31326266
 [7]  0.27215212  0.16163363 -0.04750187 -0.13886336

Largest  eigenvalues:
 [1] 69230303 63705965 60894754 59507015 57739908 56248699 55373937 54827714
 [9] 54457926 53885244

Smallest eigenvalues:
 [1]  0.36513525  0.36193873  0.34250046  0.33617873  0.33064104  0.26574666
 [7]  0.14706563  0.11578097  0.09993230 -0.08604741

Largest  eigenvalues:
 [1] 64456429 62837209 59534654 57840833 57251885 56114038 54669652 53717257
 [9] 52983381 52782008

Smallest eigenvalues:
 [1]  0.48485933  0.42069863  0.40256858  0.35026141  0.31637754  0.31356426
 [7]  0.30505936  0.05131425 -0.95163903 -2.04058040

Largest  eigenvalues:
 [1] 69570851 64228249 60759833 59722423 58920403 57145768 55752327 55566770
 [9] 55069884 54404837

Smallest eigenvalues:
 [1]  0.47194590  0.41309073  0.40014234  0.30010011  0.29816836  0.29024273
 [7]  0.27052271  0.21007136  0.16463066 -0.06046053

Largest  eigenvalues:
 [1] 68282255 64054315 60937099 59102480 58833402 57000556 55213628 55015420
 [9] 54758449 54153609

Smallest eigenvalues:
 [1]  0.537597484  0.492863763  0.464689635  0.428751814  0.368095968
 [6]  0.355371242  0.353818236  0.096839378  0.051521737 -0.007289211

Largest  eigenvalues:
 [1] 68736655 63339851 60293118 59380859 57924835 56079712 55257034 54652647
 [9] 54476647 53445724

Smallest eigenvalues:
 [1]  0.52023083  0.40615967  0.31544967  0.30963637  0.17914254  0.16709164
 [7]  0.08086812 -0.03036284 -0.15910660 -1.27972192

Largest  eigenvalues:
 [1] 68186444 64078137 61082381 59142149 58684496 57354949 55562564 55510046
 [9] 54835038 54619162

Smallest eigenvalues:
 [1]  0.32733711  0.31082986  0.20455389  0.16333363  0.12632839  0.06093062
 [7] -0.01848520 -0.11618604 -0.18585931 -0.26415818

Largest  eigenvalues:
 [1] 67899617 63297020 60679025 58375123 58252942 56802139 55165285 55050192
 [9] 54316920 53845937

Smallest eigenvalues:
 [1]  0.49579345  0.46459471  0.43557574  0.29234085  0.26424607  0.25963971
 [7]  0.19443362  0.14473023  0.05374592 -0.72163710

Largest  eigenvalues:
 [1] 67890755 64452171 60561760 59327590 59107234 57495625 56225733 54928055
 [9] 54882863 54310321

Smallest eigenvalues:
 [1]  0.29852432  0.28351856  0.26586747  0.26402343  0.25586058  0.17655433
 [7]  0.09652747  0.09495147  0.04924579 -0.11484047

Largest  eigenvalues:
 [1] 67176787 63092420 60105910 58462954 57801828 56379539 54925036 54616274
 [9] 54313983 53835274

Smallest eigenvalues:
 [1]  0.32836460  0.30499321  0.28355256  0.15258405  0.08491753  0.04164644
 [7] -0.03807749 -0.08645150 -0.31818180 -0.60286359

Largest  eigenvalues:
 [1] 67059557 62783770 60072832 58359237 58099412 56733309 55503191 54400056
 [9] 54074523 53550498

Smallest eigenvalues:
 [1]  0.5257537  0.4932001  0.4632578  0.4131117  0.3733560  0.3715883
 [7]  0.3697265  0.1941975  0.1067847 -0.3125859

Largest  eigenvalues:
 [1] 68245429 63676309 60691629 58838523 58231211 56609586 54765110 54725448
 [9] 54443838 53699365

Smallest eigenvalues:
 [1]  0.49046269  0.43748772  0.43342034  0.39623538  0.33814282  0.30552026
 [7]  0.26359161  0.23405429  0.05289384 -0.13666884

Largest  eigenvalues:
 [1] 69342463 63610162 60345885 60276266 57528439 55826900 55415827 54705205
 [9] 54245417 53804470

Smallest eigenvalues:
 [1]  0.50868109  0.45056586  0.40874208  0.38956552  0.29551761  0.27297426
 [7]  0.27077064  0.15408753  0.07846835 -0.01533921

Largest  eigenvalues:
 [1] 69087481 64070081 61056296 59878754 58356241 56597491 55790881 55671557
 [9] 54620406 54301427

Smallest eigenvalues:
 [1]  0.42850410  0.36611559  0.33661665  0.31296854  0.26844534  0.23802056
 [7]  0.18473688  0.17913251  0.04415692 -0.02595416

Largest  eigenvalues:
 [1] 67781283 63135575 60337201 58872838 57957242 56478162 54875613 54624185
 [9] 54429774 53746833

Smallest eigenvalues:
 [1]  0.4108388  0.4003424  0.3775023  0.3625002  0.3052690  0.2909786
 [7]  0.1950105  0.1336236  0.1032076 -0.4821160

Largest  eigenvalues:
 [1] 68976083 63873456 61226796 59859088 58056251 56486218 55790005 55228703
 [9] 54987220 54315881

Smallest eigenvalues:
 [1]  0.37882266  0.34028489  0.28705626  0.26170249  0.24619553  0.17425355
 [7]  0.16158144  0.11732694 -0.04609683 -1.10893350

Largest  eigenvalues:
 [1] 67749864 63616492 60111534 59026426 58182680 56305287 55448915 54968516
 [9] 54279533 54019571

Smallest eigenvalues:
 [1]  0.4798319  0.4454601  0.3938914  0.3606507  0.3057518  0.2902040
 [7]  0.2477077  0.2428912  0.1587395 -2.7392064

Largest  eigenvalues:
 [1] 68044711 63274631 60667276 58839697 57836413 55999262 54582860 54362046
 [9] 54326062 53505627

Smallest eigenvalues:
 [1]  0.46417098  0.43023522  0.42322877  0.40789499  0.36801713  0.21655523
 [7]  0.16262262  0.10214514  0.05279603 -0.15676510

Largest  eigenvalues:
 [1] 65712904 63717841 59689605 58626942 57841128 56553391 54756752 54320370
 [9] 53704723 52984965

Smallest eigenvalues:
 [1]  0.55106524  0.54802720  0.50303284  0.44560899  0.34724666  0.33847477
 [7]  0.31636077  0.30070953  0.21958703 -0.01086172

Largest  eigenvalues:
 [1] 69221438 63380157 60330865 59337338 57836217 55564543 55231978 54676586
 [9] 54179991 53677315

Smallest eigenvalues:
 [1]  0.43012514  0.41874317  0.39875714  0.34869051  0.31249787  0.29565942
 [7]  0.22504537  0.20714737  0.04095898 -0.08909213

Largest  eigenvalues:
 [1] 66441008 62507192 59569895 58727718 57046833 55532876 54601424 54320194
 [9] 54169040 53495582

Smallest eigenvalues:
 [1]  0.40916664  0.36614031  0.30417047  0.29798446  0.26853259  0.24112690
 [7]  0.22265145  0.02821519 -0.33540255 -0.83608679

Largest  eigenvalues:
 [1] 67482497 64304200 60871376 59604191 57979890 56399350 55363758 54980386
 [9] 54889828 53684091

Smallest eigenvalues:
 [1]  0.4547845  0.4300995  0.4189329  0.3504711  0.3441597  0.3419499
 [7]  0.3155616  0.2645905  0.1773215 -0.3105974

Largest  eigenvalues:
 [1] 68213336 63662094 60163718 60110510 57418897 55691108 55628095 54332052
 [9] 54166569 53192626

Smallest eigenvalues:
 [1]  0.48390015  0.42550764  0.42173499  0.39036001  0.35219322  0.27956112
 [7]  0.21300613  0.19468117  0.06588118 -1.76354249

Largest  eigenvalues:
 [1] 69639245 63716058 61190746 60264969 57942840 56544018 56022362 55360739
 [9] 54931729 54489852

Smallest eigenvalues:
 [1]  0.5298590  0.5069894  0.4662907  0.4047080  0.3812657  0.2823521
 [7]  0.2457399  0.2298946  0.0538540 -0.1068527

Largest  eigenvalues:
 [1] 67888953 63530478 60194116 59087938 58257303 56498519 55072814 54652178
 [9] 54642283 53888628

Smallest eigenvalues:
 [1]  0.4566794  0.4446798  0.3696830  0.3068844  0.2957746  0.2673373
 [7]  0.2383926  0.1906433  0.1005098 -0.1087566

Largest  eigenvalues:
 [1] 68696523 63781110 61156342 60096574 58406416 56793309 56197309 55791804
 [9] 54928720 54785650

Smallest eigenvalues:
 [1]  0.25249009  0.23245851  0.22627027  0.18396258  0.01163844 -0.07939703
 [7] -0.09495438 -0.58986388 -0.66825005 -1.70776729

Largest  eigenvalues:
 [1] 69485490 62924798 60607100 59499719 57273861 56176941 55635130 54463270
 [9] 54436525 53405039

Smallest eigenvalues:
 [1]  0.50272694  0.40052646  0.37716362  0.35186956  0.29382745  0.21145639
 [7]  0.19738354  0.18916578 -0.02930844 -0.43794715

Largest  eigenvalues:
 [1] 66900119 64026035 60284963 58804417 58524095 56805535 55409122 54693253
 [9] 54533074 54264585

Smallest eigenvalues:
 [1]  0.63739465  0.57175472  0.55022995  0.50560296  0.44949819  0.39750131
 [7]  0.35224521  0.34635449  0.07455013 -3.22365343

Largest  eigenvalues:
 [1] 68852866 63350712 60343595 59684610 57920927 56247034 55294411 54765593
 [9] 54572809 53855816

Smallest eigenvalues:
 [1]  0.5207391  0.5142735  0.4861362  0.4029976  0.3511577  0.3455516
 [7]  0.2927575  0.1394520  0.1170988 -0.7762447

Largest  eigenvalues:
 [1] 69889954 63881345 60843346 60006099 58474527 56689224 55982669 55163124
 [9] 55091285 54106856

Smallest eigenvalues:
 [1]  0.46135243  0.42983944  0.42809203  0.36286342  0.28613569  0.22629540
 [7]  0.21359433  0.16522174  0.05703338 -0.59080377

Largest  eigenvalues:
 [1] 67994672 64291231 60864099 59518830 57955202 56463691 55335853 55208964
 [9] 54532483 54335958

Smallest eigenvalues:
 [1]  0.5213761  0.5207476  0.5128386  0.4979757  0.4749098  0.4695813
 [7]  0.4001223  0.3385715  0.1582069 -0.1607803

Largest  eigenvalues:
 [1] 69167679 63324840 60634900 59608886 57250170 55517239 55401924 54769634
 [9] 54149388 54007453

Smallest eigenvalues:
 [1]  0.25856838  0.24665044  0.24489504  0.23235943  0.19930672  0.15852512
 [7]  0.13717906  0.01666857 -0.02776673 -0.50285010

Largest  eigenvalues:
 [1] 65986973 62143773 59465511 57755233 57506666 56218883 54879872 53946852
 [9] 53365903 53226171

Smallest eigenvalues:
 [1]  0.58714210  0.47006647  0.34736291  0.34421435  0.34005165  0.19490583
 [7]  0.17862964  0.15453040  0.01972939 -0.11823883

Largest  eigenvalues:
 [1] 66552103 62658163 59908456 57889779 57555281 56115107 54572919 54339424
 [9] 53874322 53495371

Smallest eigenvalues:
 [1]  0.5302539  0.5223155  0.4865758  0.4796674  0.3714350  0.3429008
 [7]  0.2921189  0.1653057  0.1246505 -0.1421293

Largest  eigenvalues:
 [1] 67206999 63986993 60655200 58667163 58406358 57064499 55221359 55039279
 [9] 54207721 54021999

Smallest eigenvalues:
 [1]  0.43097740  0.36119222  0.35838787  0.28543899  0.27788424  0.21188469
 [7]  0.18678654  0.08748722  0.01695237 -0.05088439

Largest  eigenvalues:
 [1] 66617876 63924570 60584731 58779846 58212317 57034539 55294458 54808089
 [9] 54062145 53805637

Smallest eigenvalues:
 [1]  0.47416793  0.44683285  0.40797109  0.33429500  0.26514514  0.23089591
 [7]  0.19579139  0.08867551 -0.20059096 -0.48923356

Largest  eigenvalues:
 [1] 66466941 63774615 60616645 58536259 58286395 56652530 55324124 55017871
 [9] 54287375 53796901

Smallest eigenvalues:
 [1]  0.4432598  0.4253506  0.4041308  0.3716867  0.3505375  0.3274370
 [7]  0.1997087  0.1666967  0.1479205 -2.4286655

Largest  eigenvalues:
 [1] 68211517 62942820 59945834 59031554 57586094 55651543 54828102 54401591
 [9] 54258548 53568387

Smallest eigenvalues:
 [1]  0.5044178  0.4773572  0.4551132  0.3889971  0.3423413  0.3131601
 [7]  0.2767880  0.2192109  0.1183464 -0.0288965

Largest  eigenvalues:
 [1] 67859339 63739809 60699298 59192003 58429059 56986299 55249817 55036646
 [9] 54884982 54099007

Smallest eigenvalues:
 [1]  0.58036095  0.56370544  0.50840478  0.45951838  0.37749878  0.30823749
 [7]  0.29143405  0.18325271  0.08676596 -0.04918784

Largest  eigenvalues:
 [1] 68221607 64100266 60397961 59601221 58770486 56798370 56085484 55384020
 [9] 54930181 54530510

Smallest eigenvalues:
 [1]  0.56334307  0.42905597  0.39833222  0.37102248  0.31738319  0.31435292
 [7]  0.29634007  0.19169255  0.03645459 -0.62273629

Largest  eigenvalues:
 [1] 69274645 64097060 60563961 59517089 58599951 56519908 55811457 55581030
 [9] 54561710 54529193

Smallest eigenvalues:
 [1]  0.4627699  0.4295349  0.3676500  0.3326736  0.2583977  0.2157022
 [7]  0.1785384  0.1710148 -0.1107456 -0.1404629

Largest  eigenvalues:
 [1] 66685059 64050620 60533397 59359343 58519099 57440118 55913902 55364086
 [9] 54458645 54263029

Smallest eigenvalues:
 [1]  0.31768345  0.31519332  0.24220521  0.23307781  0.17096665  0.13534950
 [7]  0.02486383 -0.09316573 -0.15928319 -0.85290381

Largest  eigenvalues:
 [1] 68939046 64548078 61671751 60419034 58333971 56774926 56008016 55679848
 [9] 55058223 54504138

Smallest eigenvalues:
 [1]  0.40452432  0.34448307  0.28112042  0.23524077  0.15734818  0.14537830
 [7]  0.13758854  0.05135597 -0.21189954 -3.52815528

Largest  eigenvalues:
 [1] 66756008 62872871 60374397 58027024 57595475 56590070 54984280 54443287
 [9] 53711410 53458626

Smallest eigenvalues:
 [1]  0.5210834  0.4889263  0.4083012  0.3784572  0.3563570  0.3036359
 [7]  0.2738420  0.2694066 -0.1280490 -0.3505927

Largest  eigenvalues:
 [1] 70237578 63605156 60827521 60062509 57655145 55983684 55850525 55149277
 [9] 54377280 54173550

Smallest eigenvalues:
 [1]  0.5204368  0.5194599  0.5033069  0.4891839  0.4806208  0.4400889
 [7]  0.2759457  0.2096628  0.1496838 -0.0593476

Largest  eigenvalues:
 [1] 68136620 63159699 59482451 59326600 57198409 55205953 54939704 54379928
 [9] 53815445 53375852

Smallest eigenvalues:
 [1]  0.38969161  0.38315464  0.36131414  0.34546239  0.33726275  0.27192500
 [7]  0.03590317 -0.19033606 -0.69665955 -0.98629475

Largest  eigenvalues:
 [1] 69127822 62617158 60247437 59253959 57788972 56368379 55060311 54407406
 [9] 54188420 53370453

Smallest eigenvalues:
 [1]  0.34593493  0.30201249  0.29565687  0.29215138  0.25012501  0.19698128
 [7]  0.17561478  0.07455176 -0.03460790 -1.31420064

Largest  eigenvalues:
 [1] 67926262 63820612 60472580 59447779 58856238 57209177 56077264 55339617
 [9] 54864131 54599225

Smallest eigenvalues:
 [1]  0.40966603  0.37720460  0.36806271  0.31562833  0.30590466  0.28104597
 [7]  0.21621038  0.19218372 -0.09152827 -0.14372583

Largest  eigenvalues:
 [1] 67632840 63462449 60435860 59326959 58221857 56478398 55437687 55078080
 [9] 54884132 54053719

Smallest eigenvalues:
 [1]  0.36027296  0.32639957  0.31594191  0.29757818  0.29337772  0.27743922
 [7]  0.17998490  0.16819169  0.05842588 -0.19578529

Largest  eigenvalues:
 [1] 67124105 63790202 60644324 59343422 58073543 56650578 54996738 54942811
 [9] 54638317 53462731

Smallest eigenvalues:
 [1]  0.486770243  0.420912309  0.413817556  0.376600861  0.344528465
 [6]  0.340294688  0.329593280  0.269510305  0.002281095 -0.004255621

Largest  eigenvalues:
 [1] 66111632 62849630 59951962 57973663 57331027 56123645 54713321 53881129
 [9] 53341270 53125909

Smallest eigenvalues:
 [1]  0.3883417489  0.3491045749  0.3067350792  0.2550572622  0.2265003420
 [6]  0.2199862098  0.1553286948  0.0944263835  0.0008516599 -0.0638146778

Largest  eigenvalues:
 [1] 66710781 63364037 60030581 58623604 57397682 56775190 54946210 54786644
 [9] 53842643 53490967

Smallest eigenvalues:
 [1]  0.5637528  0.5419897  0.4428667  0.4052040  0.3920259  0.3795125
 [7]  0.3319619  0.2212743  0.2018714 -0.4536793

Largest  eigenvalues:
 [1] 67394205 62967051 60004731 58415027 57965492 56338287 54606630 54558045
 [9] 54393535 53694973

Smallest eigenvalues:
 [1]  0.50889819  0.50369422  0.46528257  0.39200883  0.38769059  0.26292213
 [7]  0.22940326  0.16108537  0.07277549 -0.14992666

Largest  eigenvalues:
 [1] 67668353 63392549 60736805 59060604 57668846 56301989 55021685 54888573
 [9] 54477546 53594814

Smallest eigenvalues:
 [1]  0.331786777  0.319749116  0.295548008  0.221645425  0.069216329
 [6]  0.068289592 -0.006212043 -0.088377661 -0.341037488 -0.657373652

Largest  eigenvalues:
 [1] 66966124 62073207 59971408 58686235 56824330 55470968 54421775 54054261
 [9] 53909143 53196207

Smallest eigenvalues:
 [1]  0.30590336  0.28922804  0.10887320  0.09883375  0.05815187  0.05679819
 [7]  0.02731384 -0.23627284 -0.35662313 -7.93883679

Largest  eigenvalues:
 [1] 67240229 63723331 60637707 58604015 58562130 56715067 55386736 54744412
 [9] 54712574 53862751

Smallest eigenvalues:
 [1]  0.55174974  0.53528330  0.53228765  0.46254542  0.41690105  0.39356970
 [7]  0.36313971  0.32095499  0.26018024 -0.08127162

Largest  eigenvalues:
 [1] 67404684 63163572 59827497 58974898 57900966 56223716 54729504 54556207
 [9] 54117681 53059642

Smallest eigenvalues:
 [1]  0.43075575  0.39124024  0.32650863  0.29738639  0.23100032  0.16361357
 [7]  0.12570836  0.09121337  0.03889566 -0.12293219

Largest  eigenvalues:
 [1] 66480973 62450578 59377719 57906683 57901375 56120410 54868064 54093249
 [9] 53705747 53078279

Smallest eigenvalues:
 [1]  0.3333896  0.2936180  0.2833411  0.2768416  0.2739611  0.2350702
 [7]  0.1751081  0.0591253 -0.1704813 -0.5133930

Largest  eigenvalues:
 [1] 67500055 62932190 59801651 58406708 58231666 56561117 54788438 54326507
 [9] 53816784 52926055

Smallest eigenvalues:
 [1]  0.43979422  0.42807794  0.40683904  0.34816100  0.32690375  0.27245654
 [7]  0.25250254  0.15518672  0.09406743 -0.25774783

Largest  eigenvalues:
 [1] 69053542 63695355 60709179 59919692 58039180 56399379 55695709 55307966
 [9] 54650301 54282431

Smallest eigenvalues:
 [1]  0.485980102  0.461631430  0.431649288  0.336399157  0.322719495
 [6]  0.315954722  0.291855992  0.119460054 -0.003092713 -1.478181867

Largest  eigenvalues:
 [1] 66015547 62561504 59757316 57760920 57398464 56001216 54654940 54188613
 [9] 53656815 53302225

Smallest eigenvalues:
 [1]  0.4779414  0.4559354  0.4332499  0.3491799  0.3285141  0.2913935
 [7]  0.2784286  0.2572038  0.1390236 -0.4300199

Largest  eigenvalues:
 [1] 68887680 63229451 60326789 59821294 57507402 55639506 55337575 54602750
 [9] 53977024 53448250

Smallest eigenvalues:
 [1]  0.49978400  0.49573154  0.49325425  0.36725057  0.28500298  0.27938672
 [7]  0.17906587  0.09536708  0.01228579 -1.07660768

Largest  eigenvalues:
 [1] 67745428 63773297 60124556 59871277 57945368 55964544 55237248 54997079
 [9] 54620604 53778960

Smallest eigenvalues:
 [1]  0.47488027  0.45723033  0.43219627  0.33945542  0.32413592  0.31755705
 [7]  0.25362649  0.14262922 -0.09124982 -3.69536574

Largest  eigenvalues:
 [1] 69125412 63355495 60005174 59769902 57502985 55639155 55536923 55318360
 [9] 54459464 54028735

Smallest eigenvalues:
 [1]  0.3356955  0.3280880  0.2647143  0.2372037  0.1697187  0.1693662
 [7]  0.1498740  0.1486174 -0.1842534 -0.3377884

Largest  eigenvalues:
 [1] 69216772 62757763 60465658 59781037 57255711 55690319 55533579 54220016
 [9] 54066408 53324171

Smallest eigenvalues:
 [1]  0.47580857  0.45699867  0.43824024  0.36566893  0.34206670  0.30629217
 [7]  0.25846419  0.20816451  0.03757381 -0.63351762

Largest  eigenvalues:
 [1] 67834927 62774763 59447134 59165436 57153056 55638065 54799999 54349132
 [9] 53957783 52992106

Smallest eigenvalues:
 [1]  0.346771178  0.316619816  0.287468248  0.219000071  0.206334503
 [6]  0.192261995  0.130587622  0.073194629  0.040934389 -0.005896099

Largest  eigenvalues:
 [1] 66232252 63351333 60660963 58299984 58202038 56786341 54989687 54473253
 [9] 54051326 53414650

Smallest eigenvalues:
 [1]  0.4912986  0.3952202  0.3814746  0.3488784  0.2959755  0.2849064
 [7]  0.2793402  0.1879415 -0.4514353 -1.9625740

Largest  eigenvalues:
 [1] 69056905 63857148 60819086 60015951 58689176 57023941 55787217 55280506
 [9] 55024017 54181478

Smallest eigenvalues:
 [1]  0.4445259  0.4026287  0.3803546  0.3427683  0.2856042  0.2466100
 [7]  0.1583362  0.1428188 -0.1360472 -1.4697316

Largest  eigenvalues:
 [1] 69261232 63408985 60406547 59322023 58008720 56470992 55321070 55034576
 [9] 54567249 54403317

Smallest eigenvalues:
 [1]  0.4591023  0.4479664  0.4125607  0.3818001  0.3524783  0.3408688
 [7]  0.3404251  0.3223423  0.1867043 -0.0276775

Largest  eigenvalues:
 [1] 68295806 63531261 60667153 59155443 58097175 56599858 54966039 54688705
 [9] 54520366 53663393

Smallest eigenvalues:
 [1]  0.4709050  0.4213692  0.3380607  0.2978260  0.2740392  0.2646879
 [7]  0.2214487  0.1148222  0.0240219 -0.1503111

Largest  eigenvalues:
 [1] 65108933 63545497 60397690 58762416 57265915 56710340 55513448 54495293
 [9] 53944267 53343764

Smallest eigenvalues:
 [1]  0.4659294  0.4509652  0.4467306  0.3837532  0.3815056  0.2303242
 [7]  0.1827741  0.1626047  0.1445543 -0.2696805

Largest  eigenvalues:
 [1] 68762246 63285103 60373690 59612562 57299987 55896714 55443082 54278679
 [9] 53991150 53176194

Smallest eigenvalues:
 [1]  0.4130568  0.3937870  0.3540565  0.3334333  0.3153374  0.2656520
 [7]  0.2142584  0.2043796  0.1956920 -0.4876508

Largest  eigenvalues:
 [1] 67851308 63309761 59892240 58764935 58118804 56243355 54976757 54554690
 [9] 54245116 53881182

Smallest eigenvalues:
 [1]  0.45316964  0.43292136  0.39861938  0.37706568  0.35216640  0.33946179
 [7]  0.28631334  0.11490725 -0.06549247 -0.22008776

Largest  eigenvalues:
 [1] 67332033 62548035 59512894 58558878 57261798 55680329 54397932 54227645
 [9] 53533525 52608895

Smallest eigenvalues:
 [1]  0.5746084  0.5682279  0.5399228  0.4946502  0.4557642  0.4391461
 [7]  0.3905207  0.3149719  0.2419134 -0.6311985

Largest  eigenvalues:
 [1] 68151008 63470656 59643043 59505941 57728660 55577923 55188416 54840522
 [9] 54012822 53435845

Smallest eigenvalues:
 [1]  0.3768203  0.3434568  0.3126892  0.2950423  0.2544676  0.2255260
 [7]  0.1743748  0.1322102  0.1145547 -0.0961093

Largest  eigenvalues:
 [1] 65712751 62698276 59831129 57728718 57610849 56089067 54497838 54022855
 [9] 53395013 52868310

Smallest eigenvalues:
 [1]  0.4852878  0.4304419  0.4118543  0.3411607  0.3038525  0.2995367
 [7]  0.2914871  0.1188802  0.1060944 -1.3614202

Largest  eigenvalues:
 [1] 68698349 63559586 60137020 59527629 58468102 56630664 55393651 55019879
 [9] 54408631 53559306

Smallest eigenvalues:
 [1]  0.40513875  0.32228698  0.20760785  0.08278121  0.07702146 -0.11317236
 [7] -0.11620439 -0.21119055 -0.22898326 -0.78761168

Largest  eigenvalues:
 [1] 69539785 63706416 60579101 59917096 57744039 56123245 55772537 55163401
 [9] 54940126 54247446

Smallest eigenvalues:
 [1]  0.44740360  0.41517168  0.34890028  0.31478864  0.31055619  0.30083396
 [7]  0.18983695  0.16786851  0.03759635 -0.11236091

Largest  eigenvalues:
 [1] 68242810 64109695 60999037 58471536 58103312 56620391 54818470 54690284
 [9] 54457817 54089293

Smallest eigenvalues:
 [1]  0.50054299  0.46327774  0.42029263  0.30535303  0.28293509  0.27114140
 [7]  0.25601392  0.25529800  0.14855946 -0.08291632

Largest  eigenvalues:
 [1] 68900162 63133721 60207133 59639781 57448509 55841760 55421997 54651878
 [9] 54535198 53809789

Smallest eigenvalues:
 [1]  0.293757386  0.276471050  0.275218610  0.269484817  0.236108237
 [6]  0.224047966  0.138025746  0.004741941 -0.036013199 -0.353486436

Largest  eigenvalues:
 [1] 66165437 62315372 59500547 58598045 57156983 55461878 54231739 54036165
 [9] 53945915 52624723

Smallest eigenvalues:
 [1]  0.4850139  0.4514526  0.4437194  0.4253488  0.3793953  0.3006255
 [7]  0.2667503  0.2557637  0.0299274 -0.1443655

Largest  eigenvalues:
 [1] 67513769 63372692 60105520 59184759 57382971 55785918 54909098 54523552
 [9] 54202915 53553967

Smallest eigenvalues:
 [1]  0.46381824  0.46247489  0.40969333  0.36169458  0.34140814  0.32574838
 [7]  0.32124210  0.30876319  0.07176867 -0.25426278

Largest  eigenvalues:
 [1] 68353520 62943922 60224341 59346588 57701510 56120219 55048774 54580258
 [9] 54200269 53504580

Smallest eigenvalues:
 [1]  0.46517982  0.44353266  0.42161907  0.41404655  0.38660814  0.34034229
 [7]  0.28858964  0.25333331  0.06548184 -0.03590323

Largest  eigenvalues:
 [1] 67631864 62609567 59563041 59442309 56682136 55006488 54700611 53950109
 [9] 53220431 52800842

Smallest eigenvalues:
 [1]  0.49972925  0.41066026  0.37879492  0.37387974  0.32384214  0.28792519
 [7]  0.24825119  0.22821467 -0.09198361 -0.25175615

Largest  eigenvalues:
 [1] 66485856 63453702 59946325 58190615 58138205 56331349 54857692 54257828
 [9] 54042639 53589507

Smallest eigenvalues:
 [1]  0.38236950  0.36252778  0.35518183  0.32109615  0.31132048  0.12973617
 [7]  0.06858247  0.05588445  0.01891915 -1.54063118

Largest  eigenvalues:
 [1] 67640788 63113247 60357375 59537122 57211823 55513741 55020230 54576960
 [9] 54342418 53637604

Smallest eigenvalues:
 [1]  0.37626169  0.37454948  0.34151930  0.33883409  0.22495147  0.17039998
 [7]  0.09780854 -0.01694977 -0.03569648 -0.07035893

Largest  eigenvalues:
 [1] 68825265 63944158 61224766 59872223 57912496 56360597 55451368 54831289
 [9] 54579134 54048424

Smallest eigenvalues:
 [1]  0.4028121  0.3654165  0.3442723  0.3251275  0.2734337  0.2619761
 [7]  0.1808446  0.1716327  0.1350898 -0.2098837

Largest  eigenvalues:
 [1] 67044132 63573216 60060729 58849598 57824055 56318506 54778629 54704382
 [9] 54438820 53551248

Smallest eigenvalues:
 [1]  0.37152193  0.33571232  0.33042411  0.30923594  0.28258308  0.27769724
 [7]  0.20850121  0.09408740  0.02577425 -1.21695942

Largest  eigenvalues:
 [1] 68871626 63371527 60425725 58927158 57895211 56213067 54769140 54695561
 [9] 54109213 53671082

Smallest eigenvalues:
 [1]  0.5677888  0.5536590  0.4428736  0.4323306  0.4280742  0.3636788
 [7]  0.2196662  0.1740491  0.1077036 -0.6101697

Largest  eigenvalues:
 [1] 67937695 63314232 60171600 58781868 58138257 56413155 54756651 54701341
 [9] 54570676 53518915

Smallest eigenvalues:
 [1]  0.49809300  0.44337765  0.42807016  0.41802416  0.34540485  0.33412024
 [7]  0.31144208  0.23798913  0.18562467 -0.05492108

Largest  eigenvalues:
 [1] 68062421 63697796 60593136 59552228 58234918 56506804 55299233 55133074
 [9] 54950037 54059247

Smallest eigenvalues:
 [1]  0.530591237  0.437449000  0.374083324  0.370243806  0.326711207
 [6]  0.310179887  0.274516916  0.242786647  0.004471943 -0.238329279

Largest  eigenvalues:
 [1] 67968475 62832019 59973366 58829103 57978083 56366358 54748601 54636909
 [9] 54520714 53413307

Smallest eigenvalues:
 [1]  0.32599051  0.31399632  0.28705203  0.27001397  0.26717055  0.25506547
 [7] -0.08922359 -0.15344583 -0.62533560 -1.35547096

Largest  eigenvalues:
 [1] 68987267 63274815 60374122 58473577 57658601 56222886 55061467 54340630
 [9] 54032886 53980107

Smallest eigenvalues:
 [1]  0.42160650  0.35904724  0.33444561  0.32658770  0.26567538  0.24531821
 [7]  0.24250461  0.14482566  0.06342946 -0.13186043

Largest  eigenvalues:
 [1] 67791964 62743910 60137863 58548149 57284572 56087195 54318484 54205844
 [9] 54186618 53530986

Smallest eigenvalues:
 [1]  0.6836037  0.6217672  0.5978494  0.5498190  0.5083277  0.4399588
 [7]  0.4095982  0.3863816  0.0622130 -1.1377070

Largest  eigenvalues:
 [1] 68652716 63570369 60406762 59669134 57551189 55869989 55543487 54534804
 [9] 54244071 53530981

Smallest eigenvalues:
 [1]  0.5047807  0.4994762  0.4122991  0.4029489  0.3798612  0.3150421
 [7]  0.3134479  0.0657160  0.0108828 -0.6921051

Largest  eigenvalues:
 [1] 68358978 62742148 59501161 59430063 57141470 55241072 55172982 54676178
 [9] 53821392 53740363

Smallest eigenvalues:
 [1]  0.3763180  0.3507675  0.3493824  0.2961508  0.2739005  0.1557431
 [7]  0.1302856  0.1261891 -0.2716968 -0.4572453

Largest  eigenvalues:
 [1] 67180795 62911076 60073112 58386807 58112446 56674710 55161103 54807199
 [9] 54282991 54180180

Smallest eigenvalues:
 [1]  0.51825678  0.50858523  0.42941099  0.42306856  0.39313864  0.22992365
 [7]  0.22205427  0.19883580  0.19600634 -0.02382812

Largest  eigenvalues:
 [1] 68181934 63145992 59659215 58919826 57725549 55927573 54839037 54640696
 [9] 54068664 53756894

Smallest eigenvalues:
 [1]  0.4633487  0.4089110  0.3756067  0.3143089  0.3023882  0.1936310
 [7]  0.1726981 -0.1575451 -0.4906537 -0.5769257

Largest  eigenvalues:
 [1] 64955854 62161712 58988272 57262286 57254612 55405918 54277190 53296123
 [9] 53026158 52479693

Smallest eigenvalues:
 [1]  0.39552453  0.37047145  0.36670792  0.24629472  0.23971954  0.14586112
 [7]  0.13673154 -0.04348396 -0.15668267 -0.56399889

Largest  eigenvalues:
 [1] 68298698 63929417 61040720 60052672 57819846 55931852 55771931 55236090
 [9] 54607004 54270295

Smallest eigenvalues:
 [1]  0.42446653  0.39159520  0.35423284  0.34430443  0.29714359  0.25938481
 [7]  0.25180424  0.14552813  0.09512778 -0.11624616

Largest  eigenvalues:
 [1] 66032737 62563711 59881113 57503525 57406172 55800232 54184552 53762312
 [9] 53352452 52950988

Smallest eigenvalues:
 [1]  0.3832133  0.3489829  0.3068655  0.3048139  0.3000095  0.2789882
 [7]  0.1540770  0.1416989 -0.2099711 -0.9700794

Largest  eigenvalues:
 [1] 69517741 64405677 61410171 60407288 58116706 56294448 56093023 55293185
 [9] 55015539 54576537

Smallest eigenvalues:
 [1]  0.2836505  0.2547205  0.2507809  0.2224711  0.2145461  0.1984757
 [7]  0.1615289  0.1440709 -0.3590197 -0.4561003

Largest  eigenvalues:
 [1] 68651131 62321621 59771441 58764079 57191412 55822610 54611615 54390949
 [9] 54094265 53366955

Smallest eigenvalues:
 [1]  0.3708670  0.3635761  0.3495319  0.2979047  0.2372318  0.1643570
 [7]  0.1465032 -0.1035248 -0.1314490 -0.2417842

Largest  eigenvalues:
 [1] 67694000 64053819 60958185 58740855 58541042 57108237 55440717 54945849
 [9] 54360874 54250904

Smallest eigenvalues:
 [1]  0.44880820  0.42050503  0.31156625  0.26309513  0.23900131  0.20363458
 [7]  0.19989044  0.11729259 -0.07132550 -0.09552985

Largest  eigenvalues:
 [1] 66653118 62878353 60197566 58079952 57874826 55943823 54964024 54326527
 [9] 53833988 53738221

Smallest eigenvalues:
 [1]  0.448244881  0.404920565  0.362042597  0.307030662  0.301790021
 [6]  0.258899783  0.160408036  0.043616490 -0.003838654 -0.530364133

Largest  eigenvalues:
 [1] 69203780 63421071 60736407 59956557 57971693 56633540 55646901 54851995
 [9] 54646063 53799205

Smallest eigenvalues:
 [1]  0.30832109  0.30290703  0.29744492  0.28623086  0.24144231  0.17139600
 [7]  0.15012809  0.08034095  0.04922354 -0.24868645

Largest  eigenvalues:
 [1] 67646850 63156763 60201264 58451285 58445884 56754989 55088177 54791549
 [9] 54261161 54138415

Smallest eigenvalues:
 [1]  0.45065556  0.43737500  0.38831661  0.35646101  0.29493733  0.18030761
 [7]  0.12602206  0.09632597 -0.11693194 -0.18091574

Largest  eigenvalues:
 [1] 67624081 63637872 60533553 59485109 58297720 56598346 55453947 55253931
 [9] 54955942 54048958

Smallest eigenvalues:
 [1]  0.41784367  0.32521033  0.31102864  0.26715289  0.26584775  0.22800509
 [7]  0.22498055  0.10782533  0.04786251 -0.12939108

Largest  eigenvalues:
 [1] 70302812 64179176 61383662 60838684 58293156 56571291 56280951 55912332
 [9] 54649619 54607514

Smallest eigenvalues:
 [1]  0.393649688  0.372842841  0.354945582  0.349008816  0.328542169
 [6]  0.317043129  0.184946141  0.007390064 -0.783130531 -1.948406149

Largest  eigenvalues:
 [1] 67450969 62758798 59591944 58830869 57704911 55553369 54877964 54530648
 [9] 54102733 53680829

Smallest eigenvalues:
 [1]  0.46860713  0.46239686  0.45295201  0.44201698  0.44193431  0.43672782
 [7]  0.26643439  0.21654264  0.21229470 -0.04520859

Largest  eigenvalues:
 [1] 68102872 62937716 60344309 58652360 57371733 55660525 54646250 54384382
 [9] 54351567 53517245

Smallest eigenvalues:
 [1]  0.49758394  0.45560524  0.37870836  0.34423149  0.34030691  0.34000913
 [7]  0.33840585  0.30264441  0.08925985 -0.16088976

Largest  eigenvalues:
 [1] 68725625 63612653 60563425 59669488 58395371 56827968 55361537 55215632
 [9] 54941235 54031188

Smallest eigenvalues:
 [1]  0.425125954  0.387635306  0.341521915  0.311202876  0.239901374
 [6]  0.231726547  0.085294774  0.006931304 -0.311120142 -2.225111217

Largest  eigenvalues:
 [1] 68863164 63826591 60708603 59172030 58490436 56756964 55487968 55158893
 [9] 55065146 54368408

Smallest eigenvalues:
 [1]  0.5416901  0.5271960  0.4258205  0.4202488  0.3494735  0.3213776
 [7]  0.2880699  0.2575588  0.2019687 -0.2598267

Largest  eigenvalues:
 [1] 67939891 62739597 60119727 59434790 57423568 55695307 55135217 54633227
 [9] 54026657 53419061

Smallest eigenvalues:
 [1]  0.31225383  0.30544928  0.26850826  0.17986269  0.14336040  0.13030417
 [7]  0.06201104 -0.03830613 -0.15659227 -0.29048895

Largest  eigenvalues:
 [1] 67163772 63473914 60601418 58575514 58135691 56890375 55143402 54745048
 [9] 54113053 53746479

Smallest eigenvalues:
 [1]  0.4727472  0.4691994  0.4501722  0.4028427  0.3858024  0.3290316
 [7]  0.2674321  0.1979201  0.1811703 -0.2418189

Largest  eigenvalues:
 [1] 65197422 62373019 58780215 57690399 56944712 55100278 53747463 53617162
 [9] 53296019 52525406

Smallest eigenvalues:
 [1]  0.5063383  0.4704246  0.4204252  0.4197903  0.3184487  0.2387832
 [7]  0.1757686 -0.1409839 -0.3207694 -0.6494330

Largest  eigenvalues:
 [1] 65689191 62984871 59245209 58221885 57632471 56117723 54857213 54022418
 [9] 53486398 52974100

Smallest eigenvalues:
 [1]  0.44124369  0.40868116  0.40222964  0.39687547  0.33409267  0.28605030
 [7]  0.22890833  0.07327806 -0.06400052 -0.22477040

Largest  eigenvalues:
 [1] 68195237 63531696 60932280 58926731 58223147 56637479 55280356 54885106
 [9] 54874861 54260226

Smallest eigenvalues:
 [1]  0.454254871  0.329592826  0.301647363  0.271155425  0.255158375
 [6]  0.244713836  0.233237724  0.199850360 -0.005549621 -0.467316118

Largest  eigenvalues:
 [1] 67656981 63468181 60716410 59040325 58306341 57292780 55333416 54503824
 [9] 54281491 53684607

Smallest eigenvalues:
 [1]  0.50613606  0.50381202  0.45803082  0.41468776  0.34529966  0.29451282
 [7]  0.28436838  0.12874275  0.09821892 -0.47573820

Largest  eigenvalues:
 [1] 67759726 63343574 59947532 58707569 57979512 56250118 54949616 54663768
 [9] 54227219 53606373

Smallest eigenvalues:
 [1]  0.372309844  0.351216404  0.334377786  0.263121217  0.198661172
 [6]  0.179596051  0.128893817 -0.002515832 -0.050900013 -0.254004209

Largest  eigenvalues:
 [1] 66970250 63162098 59753706 59008547 57310481 55864711 54578655 54502447
 [9] 54153270 53412254

Smallest eigenvalues:
 [1]  0.47426332  0.46430120  0.45889123  0.40811858  0.23946386  0.21502667
 [7]  0.15522436  0.13121184 -0.02172012 -0.15090394

Largest  eigenvalues:
 [1] 66571748 63732176 60472004 58630965 58312718 56695047 55283922 54756135
 [9] 54523643 53671557

Smallest eigenvalues:
 [1]  0.396596029  0.336302539  0.303739109  0.300955582  0.295736212
 [6]  0.260966197  0.236422764  0.001843176 -0.057501008 -0.074746393

Largest  eigenvalues:
 [1] 66819605 63459343 60573301 59194679 57569448 57284109 55236684 54508792
 [9] 53589348 53385769

Smallest eigenvalues:
 [1]  0.51552605  0.43666436  0.30035377  0.29591066  0.29208691  0.26076158
 [7]  0.24058473  0.18602721  0.02476071 -0.23402836

Largest  eigenvalues:
 [1] 69770509 64361611 61057088 59995823 58377931 56428145 55894330 55785766
 [9] 54654906 54555726

Smallest eigenvalues:
 [1]  0.56470572  0.50588077  0.47947149  0.43431331  0.34032455  0.31899979
 [7]  0.29135479  0.17363892 -0.03550081 -0.28290935

Largest  eigenvalues:
 [1] 68455299 63004133 59723327 58719955 57858247 56128182 54663313 54553178
 [9] 54225166 53671462

Smallest eigenvalues:
 [1]  0.53744992  0.51559164  0.43617141  0.40549472  0.39952799  0.35042383
 [7]  0.29227735  0.26250785  0.08102647 -0.06432642

Largest  eigenvalues:
 [1] 67391163 63194894 60062440 58089671 58081414 56383140 54877747 54588991
 [9] 54216561 53565979

Smallest eigenvalues:
 [1]  0.5018316  0.4918023  0.4339991  0.4157014  0.3986044  0.3506516
 [7]  0.2807431  0.2291521  0.0934334 -0.0584853

Largest  eigenvalues:
 [1] 67300709 63823405 60183360 58692884 58078821 56252441 54614957 54560685
 [9] 54522041 53636039

Smallest eigenvalues:
 [1]  0.47207251  0.36469351  0.32309107  0.26178794  0.23794596  0.23186462
 [7]  0.19870700  0.05662681 -0.37153384 -0.44245137

Largest  eigenvalues:
 [1] 68793872 63426624 60587469 59162963 58454774 56774403 55205037 55090901
 [9] 54975605 54234976

Smallest eigenvalues:
 [1]  0.5255225  0.4883308  0.4551543  0.4514007  0.4337803  0.3867593
 [7]  0.3433901  0.3216794  0.2508531 -2.9569345

Largest  eigenvalues:
 [1] 69347666 63397312 60514697 59833624 57652962 55942988 55664629 54540927
 [9] 54273996 53242716

Smallest eigenvalues:
 [1]  0.560753792  0.547886828  0.510229081  0.356931321  0.306964763
 [6]  0.274470833  0.250072836  0.182874705 -0.001990526 -0.141899379

Largest  eigenvalues:
 [1] 67979265 63023992 60276003 59206151 57469953 55744508 54946029 54450801
 [9] 54423329 53510800

Smallest eigenvalues:
 [1]  0.39640059  0.38156982  0.37859740  0.34502951  0.14118752  0.13238061
 [7]  0.05070692  0.03636033 -0.09169851 -0.14404358

Largest  eigenvalues:
 [1] 67895997 62661851 60275114 58999771 57765170 55874360 54880441 54662662
 [9] 54438562 53743481

Smallest eigenvalues:
 [1]  0.33355124  0.30084792  0.24421787  0.17078673  0.12672063  0.09061280
 [7]  0.07342554  0.01751195 -0.53350167 -0.89030732

Largest  eigenvalues:
 [1] 69108501 62890224 60229127 59963547 57767422 56345601 55697523 55112006
 [9] 54752032 53900508

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	3.340348	0.677209	15.52464	0.095	2.288869	2.013395

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

EDA ~ alt + n + steps + PM25

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- EDA_fd
covariates <- list(altitude = altitude_fd, 
                   noise = noise_fd,
                   steps = steps_fd,
                   pollution = pollution25_fd)
path_plot <- 'figures/model_EDA_alt_noise_steps_PM25_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 80, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     noise = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     steps = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     pollution = list(nbetabasis = 80, norder = 4, lambda = 1e3))

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, HR = HR, 
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 19.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Warning message in `^.fd`((outcome - yhatfd), 2):
"The maximum error exceeds the tolerance level."
Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 538 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Smallest eigenvalues:
 [1]  0.582138894  0.534270824  0.513420139  0.471838431  0.454178749
 [6]  0.452357755  0.393288732  0.113200758 -0.006292351 -0.133889058

Largest  eigenvalues:
 [1] 65148070 60331692 57513833 56575966 54963080 53273464 52536849 51999059
 [9] 51763132 50909537

Smallest eigenvalues:
 [1]  0.46398058  0.39857378  0.39331619  0.37421683  0.36338730  0.32369954
 [7]  0.32296612  0.15405775 -0.01615417 -0.18726688

Largest  eigenvalues:
 [1] 65365443 59982211 57005455 56300591 54952863 53026541 52524947 52464909
 [9] 51458872 51418732

Smallest eigenvalues:
 [1]  0.61684261  0.56821037  0.47210371  0.44629476  0.41884613  0.40352989
 [7]  0.35217761  0.25119561 -0.01777933 -0.02260171

Largest  eigenvalues:
 [1] 64122964 60205133 57641181 55742245 55138462 53481183 52205342 51782133
 [9] 51754441 51215694

Smallest eigenvalues:
 [1]  0.51802920  0.44278317  0.41322929  0.39435893  0.27396285  0.24895037
 [7]  0.15988356  0.12814283 -0.02027725 -1.02468671

Largest  eigenvalues:
 [1] 63430096 61116951 57769770 55940737 55403638 54005666 52794869 52490549
 [9] 51932366 51680794

Smallest eigenvalues:
 [1]   0.504300412   0.459567766   0.375101290   0.285114588   0.271590294
 [6]   0.249079905   0.190424226   0.004701724  -4.305062954 -21.397355310

Largest  eigenvalues:
 [1] 63439869 59701325 56726978 55426873 54994492 53721540 52006049 51663306
 [9] 51107182 50744442

Smallest eigenvalues:
 [1]  0.35979152  0.23292737  0.16802264  0.10782127  0.08170898 -0.35660917
 [7] -0.85496108 -0.95355993 -4.62522331 -9.86603748

Largest  eigenvalues:
 [1] 65283344 59961148 57436028 56133285 54867695 53301782 52223246 52091618
 [9] 51563510 51245435

Smallest eigenvalues:
 [1]  0.44183621  0.40462111  0.35524045  0.30993226  0.24503424  0.22476122
 [7]  0.12210689  0.09114042  0.05777706 -1.96546590

Largest  eigenvalues:
 [1] 64463560 60747596 57381735 56142060 55769820 53970691 52847121 52108864
 [9] 51826902 51528514

Smallest eigenvalues:
 [1]  0.49726825  0.40720772  0.35411498  0.33787783  0.32780184  0.32227653
 [7]  0.22797604  0.01210434 -0.40294898 -1.17102763

Largest  eigenvalues:
 [1] 65366604 60578524 58145310 56790936 55198690 53971974 52688634 52494451
 [9] 52266766 51859224

Smallest eigenvalues:
 [1]  0.4920397  0.4383502  0.4284378  0.3534792  0.3144894  0.2845287
 [7]  0.2798502  0.2204291  0.2004139 -1.9568552

Largest  eigenvalues:
 [1] 65244776 60233986 57325326 56361126 55401399 53859713 52441787 52411283
 [9] 52280202 51408821

Smallest eigenvalues:
 [1]  0.40962955  0.37548295  0.30511974  0.29634871  0.25324465  0.19755470
 [7] -0.07159127 -1.07562920 -1.29689904 -2.51595934

Largest  eigenvalues:
 [1] 64955628 59937525 56601139 56562623 54588278 52787426 52548497 52250312
 [9] 51766836 51318097

Smallest eigenvalues:
 [1]  0.5026986  0.4713707  0.3848784  0.3323492  0.2938468  0.2310180
 [7]  0.2201860  0.2159269 -0.2715102 -0.4560355

Largest  eigenvalues:
 [1] 63971864 59877286 57293862 55884049 54757521 53247516 52297372 51843815
 [9] 51716600 51110906

Smallest eigenvalues:
 [1]  0.45536481  0.32896107  0.29719832  0.24224524  0.22137155  0.21727199
 [7]  0.09774093  0.08624682 -0.09241553 -3.87359645

Largest  eigenvalues:
 [1] 64619204 60527206 58122772 55730758 55443362 54197920 52821484 52213299
 [9] 51976204 51801919

Smallest eigenvalues:
 [1]  0.55306088  0.53278941  0.51247437  0.46124527  0.40592721  0.29763718
 [7]  0.29088174  0.21484414 -0.02570754 -0.07793213

Largest  eigenvalues:
 [1] 64785922 60126556 57323918 55879194 55294659 53081383 52272564 52030897
 [9] 51784885 51323664

Smallest eigenvalues:
 [1]   0.45227127   0.36288271   0.34911706   0.34402992   0.31049747
 [6]   0.28662176   0.19562599  -0.03826123  -0.62125560 -11.03690181

Largest  eigenvalues:
 [1] 65111750 60515801 57931089 56540355 55908765 54419429 52607342 52323743
 [9] 52209386 51424588

Smallest eigenvalues:
 [1]  0.47581333  0.43768791  0.37763536  0.31873869  0.31350395  0.30127597
 [7]  0.21202479  0.16111747  0.07821737 -0.35123742

Largest  eigenvalues:
 [1] 64325626 61342753 57571151 56351455 56291213 54409813 53980487 52392028
 [9] 52174093 52034966

Smallest eigenvalues:
 [1]  0.5253661  0.4845086  0.3974313  0.3598291  0.2593125  0.2515001
 [7]  0.2293299  0.1831083  0.1597757 -5.6348275

Largest  eigenvalues:
 [1] 63402595 59957512 57202232 55295724 54905354 53704976 52228116 52111130
 [9] 51426013 51080035

Smallest eigenvalues:
 [1]  0.4059256  0.4057105  0.3507398  0.2603932  0.2410954  0.2277764
 [7]  0.1984418  0.1607915 -1.4570600 -6.1546804

Largest  eigenvalues:
 [1] 64944363 59796905 57230546 56608424 54857074 53384537 52607956 52243509
 [9] 51559732 50844034

Smallest eigenvalues:
 [1]  0.5190173  0.4664545  0.4273429  0.2802843  0.2520270  0.2505320
 [7]  0.2303871  0.1175148 -0.6385760 -2.6030769

Largest  eigenvalues:
 [1] 65109952 59585481 56872588 56043457 54997874 53350166 52230234 52026720
 [9] 51945870 51294711

Smallest eigenvalues:
 [1]   0.2420610   0.2255808   0.1831371   0.1809581  -1.2235746  -1.3653772
 [7]  -3.1410483  -4.1044177  -4.2362828 -28.9074058

Largest  eigenvalues:
 [1] 66371214 59388341 57310200 56728275 54116990 53324108 52626495 51397946
 [9] 51190232 50592708

Smallest eigenvalues:
 [1]  0.5094121  0.4505063  0.4141838  0.3351829  0.1230920  0.0796625
 [7] -0.2902778 -1.4702984 -1.6376954 -9.4512125

Largest  eigenvalues:
 [1] 63433418 60169569 56874462 55324326 55065103 53543681 52073229 51447085
 [9] 50909756 50599958

Smallest eigenvalues:
 [1]  0.303186030  0.292375825  0.004067745 -0.113120212 -0.137378876
 [6] -0.323482728 -0.832901818 -0.988534255 -1.380347465 -2.243194540

Largest  eigenvalues:
 [1] 66600855 60618822 57946490 57342227 55129390 53458960 53273553 53016655
 [9] 51738112 51574550

Smallest eigenvalues:
 [1]  0.43203119  0.31957562  0.23781789  0.19365725  0.18396453  0.05542385
 [7]  0.05058566 -0.01991147 -0.40707677 -3.08390338

Largest  eigenvalues:
 [1] 65853369 60593154 57064085 56842854 55209617 53559969 52804240 52322603
 [9] 52101278 51351213

Smallest eigenvalues:
 [1]  0.457397457  0.320457769  0.242980153  0.207149740  0.149612218
 [6]  0.011288135  0.009577169 -2.026699135 -4.616648523 -6.649590643

Largest  eigenvalues:
 [1] 63511584 59974555 57165485 55456214 54970351 53888720 52509155 51886746
 [9] 51071567 50969646

Smallest eigenvalues:
 [1]  0.5108705  0.4763138  0.4498411  0.3954863  0.2899137  0.2800442
 [7]  0.2375158  0.2154875  0.2004713 -0.6332202

Largest  eigenvalues:
 [1] 64367888 61559209 58169235 56693481 55732368 54101490 52856923 52594194
 [9] 52541862 51853392

Smallest eigenvalues:
 [1]  0.4384280  0.3981057  0.3757465  0.3625340  0.3061225  0.3012047
 [7]  0.2125695  0.1989462  0.1115701 -0.7583390

Largest  eigenvalues:
 [1] 64909383 61174234 58096617 56495606 56491848 54788326 53128603 52664620
 [9] 52385494 51783872

Smallest eigenvalues:
 [1]  0.59479476  0.57035441  0.56250614  0.53616134  0.47446022  0.46023683
 [7]  0.43611164  0.24748370  0.06581347 -0.16892236

Largest  eigenvalues:
 [1] 65278986 60361879 57595282 56808569 55013132 53206151 52712570 51855195
 [9] 51595625 50817231

Smallest eigenvalues:
 [1]  0.4270195  0.3747766  0.3380101  0.3298966  0.2549301  0.2512072
 [7]  0.2473302  0.1969076 -0.6914395 -0.7782192

Largest  eigenvalues:
 [1] 64836123 60299158 57089401 56008101 54977677 53420146 52058688 52002657
 [9] 51640461 50969779

Smallest eigenvalues:
 [1]   0.3707116   0.3389766   0.3311187   0.2886437   0.1036859  -0.3543006
 [7]  -1.7384674  -3.2047003  -4.7830826 -24.1133702

Largest  eigenvalues:
 [1] 63309190 60412405 57228517 55767639 54917999 53192534 51992913 51830170
 [9] 51750055 50838745

Smallest eigenvalues:
 [1]  0.5417332  0.4896123  0.4644829  0.4233054  0.4160776  0.3555748
 [7]  0.2914740  0.2241525  0.2123182 -0.8281746

Largest  eigenvalues:
 [1] 63994471 59863448 57345239 55277102 54535078 53077700 52014300 51441019
 [9] 51209151 51167725

Smallest eigenvalues:
 [1]  0.50725782  0.41934090  0.41383705  0.27729561  0.26473499  0.23669258
 [7]  0.17127266  0.03307805 -0.57878346 -4.67633636

Largest  eigenvalues:
 [1] 65209401 59456049 56827009 55725679 54816956 53240920 51939064 51701773
 [9] 51507516 50728759

Smallest eigenvalues:
 [1]   0.3180695   0.2985033   0.2545072   0.2017825   0.1681180   0.1351658
 [7]  -3.8766700  -6.7190289 -14.7524683 -22.4548769

Largest  eigenvalues:
 [1] 65861406 60532406 57961349 56826820 55219815 53522510 53087901 52841837
 [9] 52092955 51999934

Smallest eigenvalues:
 [1]  0.38039276  0.34481875  0.25907228  0.25181584  0.24961091  0.20629351
 [7]  0.03516675 -0.71212194 -0.98498885 -1.77684346

Largest  eigenvalues:
 [1] 63291128 60576290 57848278 55876190 55127893 54513421 52852185 52534439
 [9] 51507267 51205484

Smallest eigenvalues:
 [1]  0.2935939  0.2815964  0.2526242  0.2324772  0.1792697 -0.2801462
 [7] -0.2824761 -0.6372673 -0.8530628 -1.3696133

Largest  eigenvalues:
 [1] 65085877 59958688 57295578 56122876 55159137 53349778 52187254 52153897
 [9] 51622367 51249778

Smallest eigenvalues:
 [1]  0.4636495  0.4241973  0.3813827  0.3650177  0.3357125  0.2721257
 [7]  0.2604671  0.1814510  0.1254497 -0.6653157

Largest  eigenvalues:
 [1] 63618500 59215353 57076645 55608960 54538361 52994120 51666115 51566125
 [9] 51515881 50645429

Smallest eigenvalues:
 [1]   0.36652231   0.31603571   0.30783626   0.13851873   0.03389022
 [6]  -0.01334603  -0.19900935  -0.67484224 -37.53127421 -53.79307327

Largest  eigenvalues:
 [1] 61202534 59118674 56207698 54922278 54195322 53011050 51880984 50910060
 [9] 50188861 50018904

Smallest eigenvalues:
 [1]  0.37641638  0.28160544  0.27859626  0.23586849  0.13527819  0.01134310
 [7] -0.04573632 -0.45534468 -2.69101621 -3.28285552

Largest  eigenvalues:
 [1] 64969306 61160124 58300373 55738628 55645285 54314350 52544668 52063148
 [9] 51756705 51512001

Smallest eigenvalues:
 [1]  0.45972451  0.44296116  0.39388481  0.30788031  0.29992387  0.24619009
 [7]  0.04157764 -0.34971618 -0.42829049 -7.68965393

Largest  eigenvalues:
 [1] 63054700 60658304 57455065 55580160 55501400 54207960 52569415 52142197
 [9] 51433681 51039231

Smallest eigenvalues:
 [1]  0.39433129  0.36679916  0.31585773  0.21358950  0.21355444  0.20967491
 [7]  0.18896538  0.16737422  0.15641722 -0.07897234

Largest  eigenvalues:
 [1] 63117354 60446388 57348222 55529660 55310689 53699526 52854294 52041619
 [9] 51677137 51450404

Smallest eigenvalues:
 [1]  0.53190929  0.52449781  0.50310948  0.42464075  0.35520278  0.33621567
 [7]  0.31666149  0.25626923  0.22748197 -0.05643541

Largest  eigenvalues:
 [1] 64921528 61126484 57810905 56702431 55673861 54077357 52841896 52665160
 [9] 52439567 51872118

Smallest eigenvalues:
 [1]  0.44402409  0.42693470  0.29321791  0.26607362  0.25239042  0.14994960
 [7]  0.04118788 -0.04611271 -0.39470826 -0.69863187

Largest  eigenvalues:
 [1] 62465018 59542945 56247025 55450127 54488539 52757899 51905864 51575396
 [9] 51059429 50281760

Smallest eigenvalues:
 [1]  0.4905395  0.4679585  0.4323883  0.3402013  0.3265913  0.3046923
 [7]  0.2180993  0.1836426  0.1279358 -0.4123913

Largest  eigenvalues:
 [1] 64685935 60047766 57665155 56052304 55401798 53968115 52258216 52202880
 [9] 52009997 51523502

Smallest eigenvalues:
 [1]  0.5808287  0.5181906  0.4884345  0.3982290  0.3938184  0.3780191
 [7]  0.3550720  0.3309355  0.3187282 -0.7128785

Largest  eigenvalues:
 [1] 64606963 60711096 57811545 56277666 55802660 54242915 52451850 52276209
 [9] 52250244 51371187

Smallest eigenvalues:
 [1]  0.29573646  0.28548900  0.13631423  0.09101294  0.04886930  0.03415961
 [7] -0.02282863 -0.82249094 -1.11838746 -3.33712727

Largest  eigenvalues:
 [1] 64589676 60226187 56738802 56347785 55388184 53393661 52622638 52322757
 [9] 52267541 51292064

Smallest eigenvalues:
 [1]  0.384471971  0.291343405  0.262767255  0.225331121  0.177028896
 [6]  0.155569637  0.111332297 -0.009455158 -1.238470055 -7.872201515

Largest  eigenvalues:
 [1] 64109416 58895242 56559304 55894560 54075817 52357987 51815190 51352236
 [9] 51100554 50050191

Smallest eigenvalues:
 [1]  0.4420265  0.4379181  0.4309511  0.4058506  0.3543849  0.3011116
 [7]  0.2885254  0.2551085  0.2346812 -0.1523098

Largest  eigenvalues:
 [1] 61903871 59891528 56951910 55140813 54734514 53539882 52175722 51527357
 [9] 50791050 50585166

Smallest eigenvalues:
 [1]  0.4183948  0.4079354  0.3893765  0.3639861  0.2685296  0.2215397
 [7]  0.1655500  0.1409848 -0.8635024 -3.6238826

Largest  eigenvalues:
 [1] 66587928 60660483 57483247 56511083 55423761 53772725 52623248 52498535
 [9] 51873341 51740835

Smallest eigenvalues:
 [1]  0.3822995  0.3349637  0.3140252  0.3121702  0.2596931  0.2378911
 [7]  0.2081925  0.1764116 -0.5094574 -0.5130824

Largest  eigenvalues:
 [1] 64674264 60844739 58311335 55890716 55696876 54346296 52850263 52536215
 [9] 51867134 51617760

Smallest eigenvalues:
 [1]  0.63910144  0.61685112  0.58942740  0.55083323  0.49200432  0.42708875
 [7]  0.37312576  0.25492659  0.07855744 -0.29657984

Largest  eigenvalues:
 [1] 65336058 60461009 57568946 56502202 54941750 53162779 52625073 52213058
 [9] 51384393 50977582

Smallest eigenvalues:
 [1]  0.4857895  0.4292037  0.3959083  0.3657526  0.3458585  0.3435992
 [7]  0.3141451  0.1912363  0.1805988 -0.7261910

Largest  eigenvalues:
 [1] 63247401 59893054 57035835 55228200 55061881 53445060 51770939 51733694
 [9] 51211704 50961798

Smallest eigenvalues:
 [1]  0.4487396  0.3845477  0.3725236  0.3365801  0.2878332  0.2565840
 [7]  0.2547981  0.1805501 -3.5341140 -6.1643446

Largest  eigenvalues:
 [1] 65317504 60018953 57252415 57202693 54597809 53165302 52921615 52087658
 [9] 51973519 51145378

Smallest eigenvalues:
 [1]  0.604535685  0.486314249  0.442001847  0.435220009  0.414558723
 [6]  0.297290354  0.248239666  0.142352946 -0.003398047 -1.114340477

Largest  eigenvalues:
 [1] 65167813 61071672 58152822 56867125 55438591 53496575 53089236 52736231
 [9] 51911704 51789930

Smallest eigenvalues:
 [1]  0.545327466  0.519049578  0.504786705  0.451035254  0.393515566
 [6]  0.358569237  0.329280561  0.279436969  0.277642076 -0.006866797

Largest  eigenvalues:
 [1] 64319420 60700234 57722139 56156459 55835862 54557474 52950277 52138403
 [9] 52020571 51475996

Smallest eigenvalues:
 [1]  0.45141749  0.38253218  0.37977975  0.29862668  0.25247099  0.13523288
 [7]  0.06372699 -0.26592498 -0.62203637 -1.16139540

Largest  eigenvalues:
 [1] 64946327 60677566 58167003 56495731 55173087 53604556 52799028 52550215
 [9] 52175469 51877593

Smallest eigenvalues:
 [1]  0.5631793  0.5461064  0.4875077  0.4562461  0.3638974  0.3584800
 [7]  0.3438786  0.2543562  0.1076786 -0.4530413

Largest  eigenvalues:
 [1] 65311917 59906844 56985900 56476882 54854238 52887579 52450675 52138129
 [9] 51639535 51208866

Smallest eigenvalues:
 [1]  0.5939966  0.5270798  0.5032330  0.4229257  0.3969222  0.3754482
 [7]  0.3449907  0.3354566  0.2908666 -0.1194142

Largest  eigenvalues:
 [1] 64259443 60517548 57668439 55916038 55456470 53745249 51805155 51766615
 [9] 51643978 50728624

Smallest eigenvalues:
 [1]  0.4482323  0.4334117  0.3873700  0.3816662  0.3391291  0.2763107
 [7]  0.2725865  0.1455238 -0.7910155 -1.2416415

Largest  eigenvalues:
 [1] 62818285 60170130 57027997 55333910 55008869 53317013 52036779 52008368
 [9] 51125093 51012129

Smallest eigenvalues:
 [1]  0.52338930  0.51916634  0.51802720  0.40898895  0.38106018  0.34818961
 [7]  0.26314532  0.19972866  0.08942279 -0.12396346

Largest  eigenvalues:
 [1] 62221759 59624694 56743772 55346164 54418424 53507238 51779605 51669336
 [9] 50532283 50384938

Smallest eigenvalues:
 [1]  0.4802773  0.4500428  0.3651332  0.3532638  0.3364786  0.2986449
 [7]  0.2825763  0.1524951  0.1286394 -1.6555082

Largest  eigenvalues:
 [1] 63587639 59643610 56854613 55364657 55134545 53461920 52455268 51913882
 [9] 51518403 51288009

Smallest eigenvalues:
 [1]  0.4750561  0.4666026  0.4491465  0.3618929  0.2969885  0.2441727
 [7]  0.2265190 -0.0994749 -0.1879190 -3.8971143

Largest  eigenvalues:
 [1] 65611200 60444404 57773103 56950411 54705607 53304939 53015738 52132293
 [9] 51514878 51169591

Smallest eigenvalues:
 [1]  0.4990037  0.4419385  0.4303572  0.4170202  0.2810512  0.2518895
 [7]  0.2435805  0.2267070  0.2183130 -0.9566458

Largest  eigenvalues:
 [1] 64323691 60147743 57171880 56096714 55165625 53637034 52493195 52032670
 [9] 51999230 51518835

Smallest eigenvalues:
 [1]  0.40554281  0.39307933  0.35224568  0.29881751  0.25156641  0.21184460
 [7]  0.20582112  0.19764824  0.07209213 -5.25581622

Largest  eigenvalues:
 [1] 64909369 61129126 58428614 56188950 55875786 54473679 52532312 52383440
 [9] 52091219 51615600

Smallest eigenvalues:
 [1]  0.3922102  0.3620180  0.3268108  0.2611272  0.2529055  0.2058618
 [7]  0.1975627  0.1959268  0.1217729 -2.1681830

Largest  eigenvalues:
 [1] 65571747 60568455 57776239 56659420 55308631 53780616 52566828 52247656
 [9] 52071813 51337332

Smallest eigenvalues:
 [1]  0.485370356  0.310864100  0.307989957  0.296572828  0.220046394
 [6]  0.151461521  0.002218544 -0.895487191 -1.530775376 -1.939084785

Largest  eigenvalues:
 [1] 62799527 59710533 56958342 55341016 54909034 53705196 52161778 52126877
 [9] 51083987 50906260

Smallest eigenvalues:
 [1]   0.40943220   0.40923920   0.37720660   0.30750753   0.20546174
 [6]   0.15602178   0.08009306  -0.03155124  -1.08163518 -17.64683617

Largest  eigenvalues:
 [1] 65011877 59902886 56763757 56529187 55043132 53415437 52434734 51972918
 [9] 51757720 51043243

Smallest eigenvalues:
 [1]  0.5696885  0.5200058  0.4349116  0.4035829  0.3020217  0.2704845
 [7]  0.2684303  0.2512133  0.2419236 -1.4535085

Largest  eigenvalues:
 [1] 65543313 60966032 58067480 56512064 55696669 54193156 52723471 52612508
 [9] 52109418 51618272

Smallest eigenvalues:
 [1]  0.40096058  0.35083143  0.32859303  0.32601818  0.28127811  0.22925439
 [7]  0.21195304  0.18646779  0.04865597 -2.01116212

Largest  eigenvalues:
 [1] 65900101 59853999 57187752 56603485 54742607 53457136 52650043 52005321
 [9] 51882321 51182385

Smallest eigenvalues:
 [1]  0.4649486  0.4568153  0.4341013  0.4080081  0.3421340  0.2834149
 [7]  0.2537515  0.2349537  0.2327321 -0.3315201

Largest  eigenvalues:
 [1] 65482613 60816554 58048249 56700024 56120910 54524195 52682598 52448386
 [9] 52371316 51439683

Smallest eigenvalues:
 [1]  0.57068226  0.42211693  0.39747428  0.39689597  0.37707957  0.34723472
 [7]  0.30803484  0.24994537 -0.01339311 -1.00383665

Largest  eigenvalues:
 [1] 66420032 60787081 58063763 57216759 55177665 53603304 53344990 52405416
 [9] 51966515 51598951

Smallest eigenvalues:
 [1]   0.35043920   0.31639147   0.29461594   0.26699996   0.23734749
 [6]   0.14742534   0.10872102   0.08751024  -2.59212710 -12.27370009

Largest  eigenvalues:
 [1] 63968624 60587267 57241963 55858968 55822691 54135264 52990040 52280121
 [9] 52026469 51772628

Smallest eigenvalues:
 [1]  0.4420123  0.4357314  0.3516233  0.3426413  0.3073509  0.1924930
 [7]  0.1805966  0.1346656 -0.2101050 -0.8369537

Largest  eigenvalues:
 [1] 64995062 59643408 57089027 56521548 54277184 52755528 52508285 51475254
 [9] 51245996 50417057

Smallest eigenvalues:
 [1]  0.51048804  0.45580278  0.39095756  0.33934288  0.33473126  0.27488713
 [7]  0.27409689 -0.08764137 -0.30070317 -0.40846445

Largest  eigenvalues:
 [1] 64662438 60857915 58215130 56351829 55531551 54074757 53011058 52349669
 [9] 52283685 52163300

Smallest eigenvalues:
 [1]  0.52884928  0.50887246  0.44794902  0.38208101  0.36930356  0.36792831
 [7]  0.33291083  0.25796138  0.01876542 -0.15594624

Largest  eigenvalues:
 [1] 65348685 60272311 57711004 56410396 55565765 53548089 52669521 52176989
 [9] 51818943 51138695

Smallest eigenvalues:
 [1]  0.5127975  0.4966310  0.4265970  0.4125918  0.3396251  0.2625984
 [7]  0.1666105  0.1434122  0.1429262 -0.2603449

Largest  eigenvalues:
 [1] 63718756 61355276 57782812 56375545 55305516 53859789 52852244 52287447
 [9] 52261508 51912831

Smallest eigenvalues:
 [1]  0.4206898  0.3693107  0.3671705  0.3430170  0.3144401  0.3067283
 [7]  0.1995124  0.1496485 -1.0483970 -4.6744849

Largest  eigenvalues:
 [1] 66348277 60918782 57312876 57301833 55696792 53855646 53311968 52484686
 [9] 52284560 51539900

Smallest eigenvalues:
 [1]  0.4335716  0.4292870  0.3543884  0.3436370  0.2887624  0.2803902
 [7] -0.2580284 -1.5438717 -2.0344285 -3.4414541

Largest  eigenvalues:
 [1] 64464386 59772236 56780844 56401755 54635512 52859047 52177665 52142265
 [9] 51642181 51175340

Smallest eigenvalues:
 [1]  0.47922946  0.39915544  0.31475005  0.30556300  0.22686749  0.21518141
 [7]  0.15850637  0.15257790 -0.06018905 -0.54311125

Largest  eigenvalues:
 [1] 66320847 60187470 58003398 55972624 54950478 53151004 52429283 51802356
 [9] 51365090 51037974

Smallest eigenvalues:
 [1]  0.51891681  0.49664889  0.44967162  0.37073948  0.26787808  0.20476697
 [7]  0.18228656  0.17300728  0.04872697 -1.41871962

Largest  eigenvalues:
 [1] 65598631 61340935 58159376 56931134 55986208 54373636 53563457 52922123
 [9] 52463148 52169973

Smallest eigenvalues:
 [1]   0.365058229   0.323195797   0.300704524   0.107977260   0.091708186
 [6]   0.024732365  -0.006456436  -0.066814925  -3.262360890 -24.195205360

Largest  eigenvalues:
 [1] 63588423 59868185 57053870 55623161 54891888 53290107 52035527 51822195
 [9] 51592733 51031827

Smallest eigenvalues:
 [1]  0.6128888  0.6005414  0.5084246  0.4647590  0.3576826  0.3320714
 [7]  0.2924757  0.2352079  0.2192629 -0.0116011

Largest  eigenvalues:
 [1] 63436488 60677069 57270421 55915963 54984756 53995230 52027421 51859383
 [9] 51096587 50804366

Smallest eigenvalues:
 [1]  0.5429188  0.4624436  0.4484672  0.3660855  0.2859350  0.2802123
 [7] -0.2252810 -3.2127511 -4.0366510 -5.3848628

Largest  eigenvalues:
 [1] 65541444 60253537 57759824 56620516 54984595 53379433 52452385 52386620
 [9] 52035835 51615543

Smallest eigenvalues:
 [1]  0.49384678  0.47034096  0.43110013  0.41232906  0.34579495  0.27326848
 [7]  0.20258560 -0.06413743 -0.15323955 -0.42340140

Largest  eigenvalues:
 [1] 65964400 61049404 58365404 56728603 55751973 54084782 53131516 52679136
 [9] 52557385 52283067

Smallest eigenvalues:
 [1]  0.5178194  0.5068474  0.4966723  0.4001511  0.3682761  0.2510546
 [7]  0.1937007  0.1569781 -0.8098995 -6.3224046

Largest  eigenvalues:
 [1] 64696145 59715023 56604277 56306975 54524378 52795171 52360671 51600397
 [9] 51158899 50489429

Smallest eigenvalues:
 [1]  0.4720272  0.4532888  0.4397408  0.3437993  0.2903784  0.2699869
 [7]  0.2437427  0.2251591  0.1048481 -0.3145790

Largest  eigenvalues:
 [1] 62874802 59644683 56751587 54942486 54725488 53265018 51928608 51313040
 [9] 50887639 50504973

Smallest eigenvalues:
 [1]   0.201544408   0.177171397   0.144626455   0.091076722   0.004548103
 [6]  -0.148259185  -0.289884175  -1.575043898 -13.263955105 -79.579311945

Largest  eigenvalues:
 [1] 66433540 60511774 57856772 56895086 55170876 54014777 52720474 52584682
 [9] 52453225 51907112

Smallest eigenvalues:
 [1]  0.46984889  0.40535815  0.38373415  0.31445632  0.30424470  0.20821907
 [7]  0.20479267  0.05942211 -0.19443799 -0.46006852

Largest  eigenvalues:
 [1] 66295014 60055206 57477136 56958999 54760055 53148485 52942568 52550470
 [9] 51745790 51682275

Smallest eigenvalues:
 [1]  0.4332651  0.4308242  0.3583716  0.2661786  0.2522003  0.2274065
 [7]  0.2265533  0.1934069 -0.3544133 -0.7795985

Largest  eigenvalues:
 [1] 64693328 60433656 57576991 56403901 55390048 53911610 52457037 52451694
 [9] 52257789 51384720

Smallest eigenvalues:
 [1]  0.48280950  0.44458607  0.41297101  0.39655617  0.38245266  0.36329757
 [7]  0.32586276  0.27999321  0.06975889 -6.56738212

Largest  eigenvalues:
 [1] 64854384 59736790 57216159 55827698 54986718 53582752 51994993 51922870
 [9] 51396962 50504492

Smallest eigenvalues:
 [1]  0.39820962  0.37804776  0.35628992  0.34829729  0.33528928  0.26461008
 [7]  0.23280099  0.21468200  0.21248646 -0.09839829

Largest  eigenvalues:
 [1] 64267814 60678050 57849347 56272576 55681003 54238859 52495499 52198944
 [9] 52099877 51544577

Smallest eigenvalues:
 [1]  0.41887154  0.31343041  0.30939448  0.27154099  0.25444678  0.17239703
 [7]  0.15336427  0.09724497  0.03846142 -4.62230843

Largest  eigenvalues:
 [1] 64383814 60560185 57378585 55773472 55580811 53903495 52976999 52062940
 [9] 51987916 51724972

Smallest eigenvalues:
 [1]   0.3321982   0.3099001   0.2951779   0.2923714   0.2593001   0.2387524
 [7]   0.1839233  -0.4091854  -2.7724645 -32.5836795

Largest  eigenvalues:
 [1] 62714617 60840721 57265914 55515224 55452445 53767227 52345127 52260058
 [9] 51422482 51241427

Smallest eigenvalues:
 [1]  0.5511623  0.5137978  0.3973151  0.3698572  0.2714385  0.2601094
 [7]  0.2599047  0.2129028 -0.6039468 -3.7364834

Largest  eigenvalues:
 [1] 62892615 60256629 57165253 55863827 54884526 54202055 52521761 52276902
 [9] 51146891 50914739

Smallest eigenvalues:
 [1]  0.4482666  0.4132002  0.4043009  0.3446677  0.3057986  0.2371929
 [7]  0.2231859  0.1849645 -0.3806293 -1.2192000

Largest  eigenvalues:
 [1] 64912913 60365249 57915971 56245247 55245503 53419182 52538053 52231428
 [9] 52175101 51690647

Smallest eigenvalues:
 [1]  0.5429959  0.5029861  0.4617789  0.3660918  0.3307626  0.3030359
 [7]  0.2941898  0.2423092  0.2093103 -1.4799506

Largest  eigenvalues:
 [1] 65310285 61205449 58387605 56788205 56219393 54775783 53121119 52773489
 [9] 52719250 52173340

Smallest eigenvalues:
 [1]  0.5757681  0.5170118  0.3817440  0.3695223  0.3446561  0.2849770
 [7]  0.2656549  0.1959019  0.1725764 -0.2854450

Largest  eigenvalues:
 [1] 65604887 60614573 57557609 56305090 55216214 53469352 52454467 52402152
 [9] 51998177 51419384

Smallest eigenvalues:
 [1]  0.36186136  0.22478492  0.21982184  0.20091140  0.15866189  0.05321775
 [7] -0.02753659 -0.18814786 -0.73649376 -1.83930125

Largest  eigenvalues:
 [1] 63126554 60013297 57218445 55247689 54841283 53218257 52264101 51445755
 [9] 51232175 51009566

Smallest eigenvalues:
 [1]  0.5889792  0.5325782  0.4799873  0.4081175  0.3822931  0.3360016
 [7]  0.3165796  0.2596338  0.1156711 -0.2926909

Largest  eigenvalues:
 [1] 65118790 60088139 57034713 56302051 54940701 53275640 52253927 51582079
 [9] 51517645 50753394

Smallest eigenvalues:
 [1]  0.5462084979  0.4596289757  0.4425864504  0.4092067562  0.3946468524
 [6]  0.3602657817  0.2447315615  0.1547394310  0.0193964287 -0.0004436288

Largest  eigenvalues:
 [1] 61796298 59213323 56855892 54938033 54377620 53172281 51519650 51155755
 [9] 50459207 50163983

Smallest eigenvalues:
 [1]  0.5161071  0.4864884  0.3918835  0.3876054  0.3870837  0.3559756
 [7]  0.3370716  0.2599319  0.1657500 -0.3115592

Largest  eigenvalues:
 [1] 63609026 59775759 57293552 55094734 55002818 53520016 51926489 51647070
 [9] 51198665 51058964

Smallest eigenvalues:
 [1]  0.3844704  0.2869086  0.2678615  0.2414951  0.1662366  0.1649803
 [7] -0.2931335 -1.8512067 -2.2663332 -2.6126528

Largest  eigenvalues:
 [1] 65399203 60358455 58444718 55669337 55604086 54514489 52942546 52772772
 [9] 51926528 51626828

Smallest eigenvalues:
 [1]  0.40034295  0.36388802  0.34484062  0.25063321  0.22174912  0.18652089
 [7]  0.17892611  0.17140740 -0.07209435 -1.44236241

Largest  eigenvalues:
 [1] 63763732 59405332 57413034 55948630 54263154 52938941 51853268 51781222
 [9] 51477112 50766747

Smallest eigenvalues:
 [1]   0.4313798   0.4229571   0.3923769   0.3760412   0.3112095   0.3109464
 [7]   0.2526391  -0.1554225  -0.8900478 -16.5592499

Largest  eigenvalues:
 [1] 63152583 59993602 57085284 55419122 55064076 53533837 51865233 51627201
 [9] 51350229 50770855

Smallest eigenvalues:
 [1]  0.41276988  0.40321953  0.40185311  0.23765414  0.22292144  0.19771954
 [7]  0.16912023  0.08295498 -0.67170684 -1.12303792

Largest  eigenvalues:
 [1] 64139585 59804873 57183976 56051727 54822511 53324425 52168035 51909804
 [9] 51898737 51015452

Smallest eigenvalues:
 [1]  0.53276256  0.46594849  0.43924900  0.39697820  0.31945362  0.29167345
 [7]  0.28980983  0.25929236 -0.01086218 -0.13285833

Largest  eigenvalues:
 [1] 63273773 59720686 57231816 54882059 54713773 53247788 51957631 51438734
 [9] 50977746 50627827

Smallest eigenvalues:
 [1]  0.46748942  0.34423002  0.31387525  0.24507436  0.24340465  0.15076138
 [7]  0.09617273 -0.69562439 -1.18076695 -4.47359899

Largest  eigenvalues:
 [1] 61526702 59905855 57046257 56146055 54189655 54017569 52814392 51694398
 [9] 50826284 50742824

Smallest eigenvalues:
 [1]  0.4923785  0.3984089  0.3937567  0.3549236  0.3122952  0.3109052
 [7]  0.2706105  0.2394305 -0.2794429 -0.9258592

Largest  eigenvalues:
 [1] 62845171 59886485 57063124 55382063 54919764 53291971 51992605 51803111
 [9] 51226728 50848565

Smallest eigenvalues:
 [1]  0.5459344  0.4891997  0.4786678  0.4104942  0.3288842  0.2848951
 [7]  0.2847681  0.1815102  0.1424909 -0.3119798

Largest  eigenvalues:
 [1] 65061303 60674413 57479748 55796434 55694628 53880747 52647245 52183251
 [9] 52014319 51568813

Smallest eigenvalues:
 [1]   0.4503516   0.4380780   0.3798042   0.3404305   0.2878967   0.2793281
 [7]   0.2346284   0.2103938  -0.1151525 -16.0634542

Largest  eigenvalues:
 [1] 63801784 60786631 57408112 56000477 55902736 54203077 52619103 52096529
 [9] 51947571 51564852

Smallest eigenvalues:
 [1]  0.53132581  0.47939255  0.44143427  0.41821041  0.40036708  0.39283256
 [7]  0.26125258  0.25440452  0.04234018 -0.05788324

Largest  eigenvalues:
 [1] 61908991 60921013 57583495 55719933 55087847 53944109 52199272 52187053
 [9] 51311269 51051015

Smallest eigenvalues:
 [1]  0.55633858  0.55459905  0.51682411  0.45409873  0.36279853  0.28371626
 [7]  0.27734235  0.24286158  0.16919659 -0.04879497

Largest  eigenvalues:
 [1] 65870742 60146762 57478444 56195525 55011350 53145199 52490917 51801209
 [9] 51725161 51007665

Smallest eigenvalues:
 [1]  0.29941142  0.28255724  0.26899353  0.26408874  0.24559457  0.18665779
 [7]  0.03204212 -0.16302223 -0.62465421 -0.77217633

Largest  eigenvalues:
 [1] 64692988 61448493 58366388 56660214 55912037 54073882 53831609 52892771
 [9] 52302123 52147463

Smallest eigenvalues:
 [1]  0.4999409  0.4392076  0.3276502  0.3157298  0.2767293  0.2717452
 [7]  0.2070822 -0.2590587 -0.8639667 -1.6282596

Largest  eigenvalues:
 [1] 67366903 60256808 57940051 57564310 55064301 53967328 53436716 52456655
 [9] 51710071 51405849

Smallest eigenvalues:
 [1]  0.5156335  0.4515649  0.3378194  0.3355335  0.3027039  0.2655431
 [7]  0.1546276 -0.2241411 -0.6055852 -2.8591961

Largest  eigenvalues:
 [1] 64976128 59853182 57012931 55533646 54739601 53080864 52033152 51713440
 [9] 51370904 51200155

Smallest eigenvalues:
 [1]  0.45290694  0.44925560  0.40351757  0.30919014  0.25459596  0.17384010
 [7]  0.17026083  0.11022259 -0.02776676 -0.31821990

Largest  eigenvalues:
 [1] 61432810 59985832 57193901 54767519 54531619 53265460 51504147 51440013
 [9] 50665853 50507831

Smallest eigenvalues:
 [1]  0.52622357  0.50680189  0.46369968  0.38817044  0.25210285  0.20384335
 [7]  0.20338961  0.19141173  0.12685740 -0.07178254

Largest  eigenvalues:
 [1] 66202026 60897045 58063314 57194555 55475013 53311879 53307392 52911864
 [9] 52169260 52040648

Smallest eigenvalues:
 [1]  0.52234995  0.45402038  0.43663174  0.41554924  0.40579497  0.28840887
 [7]  0.13245821  0.08557838 -0.75062913 -2.86560419

Largest  eigenvalues:
 [1] 65374252 60863355 57518564 57202689 55322858 53729674 52938897 52731382
 [9] 52403820 51485447

Smallest eigenvalues:
 [1]  0.39084695  0.36914184  0.30025457  0.26474489  0.24560916  0.13375087
 [7] -0.05033575 -0.05521544 -1.65185785 -4.82023978

Largest  eigenvalues:
 [1] 65400558 61101185 57473590 56295735 56083895 54190276 53128989 52606597
 [9] 52276979 51737422

Smallest eigenvalues:
 [1]  0.5780271  0.5484737  0.4845899  0.4175106  0.3248807  0.3082034
 [7]  0.2996564  0.2535816  0.1127043 -1.8725486

Largest  eigenvalues:
 [1] 64195941 60285711 57416563 56098671 55456384 53595903 52126600 52038599
 [9] 51843900 50875133

Smallest eigenvalues:
 [1]  0.4125340  0.3617126  0.3277186  0.3125530  0.2747283  0.2422840
 [7]  0.2351366 -0.0112572 -0.1799453 -3.4878682

Largest  eigenvalues:
 [1] 63717076 59716227 57283402 55579766 55459389 53816847 51984241 51458117
 [9] 51418582 50617527

Smallest eigenvalues:
 [1]   0.158950216   0.138747110   0.095224104  -0.003804913  -0.234584077
 [6]  -0.376242437  -1.934583821  -2.615940916 -11.366270562 -42.885478214

Largest  eigenvalues:
 [1] 62210639 59008470 56523613 54883978 54828048 53128814 52077971 51570901
 [9] 50778089 50548099

Smallest eigenvalues:
 [1]  0.5606641  0.5178252  0.4550787  0.4136515  0.4128867  0.3802478
 [7]  0.2519912  0.1598622  0.1547290 -0.8574677

Largest  eigenvalues:
 [1] 64056664 60121490 56752301 55494222 55381324 53671925 52297441 51526186
 [9] 51485984 50661714

Smallest eigenvalues:
 [1]  0.3618078  0.3443411  0.3132744  0.3096701  0.2477763  0.1948330
 [7]  0.1731113  0.1549858 -0.1465254 -1.7413840

Largest  eigenvalues:
 [1] 65003619 59255885 56773132 56444943 54675165 53113186 52481697 51687999
 [9] 50838184 50270887

Smallest eigenvalues:
 [1]  0.54426953  0.48562884  0.44388094  0.42821535  0.34888349  0.26731143
 [7]  0.23998793  0.12993691 -0.02737212 -0.44424968

Largest  eigenvalues:
 [1] 65550998 60465719 57587850 56121483 55591168 54046566 52740053 52235743
 [9] 52054542 51864556

Smallest eigenvalues:
 [1]  0.42169354  0.39682148  0.39261339  0.33989100  0.32935115  0.22938059
 [7]  0.21809042  0.08154989 -0.51332259 -1.69754904

Largest  eigenvalues:
 [1] 62982266 60428341 57530010 55442263 55109750 53755454 52044607 51863246
 [9] 51237195 50876446

Smallest eigenvalues:
 [1]  0.52459098  0.51053602  0.35515245  0.33980637  0.30118029  0.21321678
 [7]  0.18689065  0.12651958 -0.08038237 -0.27084950

Largest  eigenvalues:
 [1] 62531812 59705008 56872443 55459454 54529444 53538600 52154088 51877923
 [9] 51114746 50752980

Smallest eigenvalues:
 [1]  0.52171155  0.49562694  0.49447592  0.44617475  0.38149637  0.31870354
 [7]  0.29634753  0.25018251  0.24601879 -0.05523009

Largest  eigenvalues:
 [1] 64247196 60702959 57811455 56511277 55326045 53743379 52828963 52591858
 [9] 51993151 51674647

Smallest eigenvalues:
 [1]  0.4856958  0.4851811  0.4698809  0.4536448  0.3643883  0.2650687
 [7] -0.6305192 -2.6167447 -6.9863113 -8.5079493

Largest  eigenvalues:
 [1] 65767631 60192997 57414536 56986437 55017791 53821130 52858098 52238089
 [9] 52077024 51222271

Smallest eigenvalues:
 [1]  0.62210840  0.51544880  0.51387347  0.48528008  0.32260528  0.24645020
 [7]  0.12895498 -0.07462728 -0.42245680 -1.01614870

Largest  eigenvalues:
 [1] 65192444 60626017 57792212 56461719 55435968 53943961 52519697 52470748
 [9] 52090557 51424514

Smallest eigenvalues:
 [1]  0.6123584  0.5180206  0.4697137  0.4490226  0.3160412  0.2512016
 [7]  0.2429981  0.2276873 -0.3757075 -2.4693377

Largest  eigenvalues:
 [1] 64512255 60939379 57510406 55856670 55830455 54158421 52430522 52328012
 [9] 51957775 51395342

Smallest eigenvalues:
 [1]  0.50285305  0.42119011  0.33842476  0.32740418  0.32042739  0.23890470
 [7]  0.19142499  0.08581807 -1.07829160 -1.57508291

Largest  eigenvalues:
 [1] 63212056 60557886 56946985 55900077 55025855 53336499 52238259 51773561
 [9] 51602547 50807734

Smallest eigenvalues:
 [1]  0.45464091  0.43894610  0.40747460  0.35503655  0.31265786  0.29094006
 [7]  0.23802606 -0.01934277 -0.28903710 -4.57884983

Largest  eigenvalues:
 [1] 65020984 59922993 57531605 56134514 54805829 53182111 52268454 51935433
 [9] 51843598 51096607

Smallest eigenvalues:
 [1]  0.56759586  0.56189578  0.41514216  0.38441990  0.37557169  0.33648270
 [7]  0.31638758  0.30483067  0.09840617 -0.14551585

Largest  eigenvalues:
 [1] 63645797 60322326 57525748 55656889 55258278 53726751 52232143 51994825
 [9] 51743852 51118727

Smallest eigenvalues:
 [1]  0.3709913079  0.3575170694  0.3507039142  0.1969533121  0.1864759946
 [6]  0.1562555900  0.0005067288 -0.1428596895 -1.4036005271 -4.8821616389

Largest  eigenvalues:
 [1] 64609448 59304612 56830482 54940485 54928090 53223922 52235880 51373447
 [9] 51291503 50684140

Smallest eigenvalues:
 [1]  0.5378951  0.4152804  0.4125642  0.3603796  0.3574761  0.3439116
 [7]  0.2817114  0.2490014 -1.1908588 -2.1304555

Largest  eigenvalues:
 [1] 63262192 60140606 57396805 55933981 54780326 53424578 52233240 51771048
 [9] 51709538 51262078

Smallest eigenvalues:
 [1]  0.4139446  0.4003821  0.3210964  0.2948652  0.2792177  0.2462764
 [7]  0.1485048 -0.1665783 -0.2396231 -1.1166169

Largest  eigenvalues:
 [1] 65025560 59874668 57719944 55994411 54705952 53532693 52281068 51764539
 [9] 51555256 50870097

Smallest eigenvalues:
 [1]  0.27577537  0.27200639  0.22353516  0.19749033  0.18221636  0.17288771
 [7]  0.14576046  0.06904516  0.04295397 -7.41265447

Largest  eigenvalues:
 [1] 62544032 60326473 57361667 55714935 55141761 53576873 52373218 52255801
 [9] 51519940 50889022

Smallest eigenvalues:
 [1]  0.34824419  0.32624775  0.32412938  0.30055734  0.28486927  0.24196818
 [7]  0.18425453  0.12732401  0.06721902 -1.14091795

Largest  eigenvalues:
 [1] 63695684 59558522 57054951 54907965 54775839 53308952 51675649 51204229
 [9] 51060347 50525826

Smallest eigenvalues:
 [1]  0.4461087  0.4100242  0.3564076  0.3077360  0.2705415  0.2075168
 [7]  0.1856098 -0.2798966 -1.4998011 -1.7307294

Largest  eigenvalues:
 [1] 65060073 59788240 57010817 56374372 54962676 53241951 52533464 52326643
 [9] 51834648 51339657

Smallest eigenvalues:
 [1]  0.4345425  0.3460610  0.3452705  0.3419106  0.2650077  0.1179957
 [7] -0.0407012 -0.0478749 -0.6777024 -2.7087721

Largest  eigenvalues:
 [1] 65968492 59864148 57144255 56690856 54655176 53140523 52731877 52259841
 [9] 51488220 51465275

Smallest eigenvalues:
 [1]  0.5542803  0.5512591  0.5228604  0.4515252  0.4155063  0.3076948
 [7]  0.2845276  0.2396812  0.1807905 -0.3428144

Largest  eigenvalues:
 [1] 63905137 59502253 56433069 55165699 54726656 53026970 51790581 51360145
 [9] 51208848 50453061

Smallest eigenvalues:
 [1]  0.464282566  0.429567178  0.415205333  0.378129428  0.336070306
 [6]  0.259183622  0.216600995  0.033002374  0.006506839 -0.042244432

Largest  eigenvalues:
 [1] 63444504 59522734 56847150 54871722 54615621 53105096 51765857 51333580
 [9] 51148670 50729429

Smallest eigenvalues:
 [1]  0.2372722011  0.2225235054  0.2015075882  0.0929144775 -0.0006222235
 [6] -0.2148215623 -0.2224678712 -0.4906172915 -3.0041167833 -3.3593404025

Largest  eigenvalues:
 [1] 65984700 59620554 56934014 56331887 54491746 53085033 52386737 51831911
 [9] 51436998 51028028

Smallest eigenvalues:
 [1]   0.42762804   0.41302478   0.40983814   0.40478580   0.35859747
 [6]   0.29442122   0.24534593  -0.08207897  -0.22919430 -10.25323178

Largest  eigenvalues:
 [1] 66549384 60508087 58540776 57026439 55228675 53282403 52964350 52299347
 [9] 51874854 51561945

Smallest eigenvalues:
 [1]  0.43601688  0.43273579  0.35929767  0.23928188  0.20507564  0.17869410
 [7]  0.16006524  0.15735591  0.06578892 -0.00884030

Largest  eigenvalues:
 [1] 64630586 60822955 58244976 55906329 55794335 54472403 52524935 52152055
 [9] 52006919 51281686

Smallest eigenvalues:
 [1]  0.40359710  0.29078424  0.28913387  0.24170298  0.13901900  0.09786114
 [7]  0.05907958 -0.07789732 -0.62712754 -1.53270335

Largest  eigenvalues:
 [1] 66245908 60488538 58068049 57335231 54946414 53464666 53188835 52880647
 [9] 51973737 51603106

Smallest eigenvalues:
 [1]  0.5617142  0.5599401  0.5083362  0.4206503  0.4119482  0.3668112
 [7]  0.3366286  0.2675939  0.0604494 -0.3029912

Largest  eigenvalues:
 [1] 63735402 60132302 56906030 55650046 55220216 53401815 51648460 51633654
 [9] 51566797 50685450

Smallest eigenvalues:
 [1]   0.40801604   0.40389371   0.33990475   0.31620434   0.31242965
 [6]   0.29992452   0.19358977   0.05662348  -2.66980776 -16.78142650

Largest  eigenvalues:
 [1] 63715977 60355191 57482558 56348171 55093563 53422203 52593371 52129938
 [9] 51897846 51409226

Smallest eigenvalues:
 [1]  0.4359027  0.3340343  0.3214657  0.3154707  0.2913169  0.2623459
 [7]  0.1672228  0.1357154 -0.1990377 -0.6847689

Largest  eigenvalues:
 [1] 66348176 60141875 57861809 57171768 54956008 53665745 53265811 52015686
 [9] 51831777 51070947

Smallest eigenvalues:
 [1]  0.35136998  0.30718827  0.30041682  0.27201388  0.15773403  0.15405150
 [7]  0.09808916 -0.05159188 -0.41221943 -2.22285813

Largest  eigenvalues:
 [1] 65043567 60219670 57130463 56659700 55000249 53405129 52629781 52582847
 [9] 52067161 51633049

Smallest eigenvalues:
 [1]  0.51304442  0.50070467  0.46793052  0.27801358  0.24674705  0.23081110
 [7] -0.02424976 -0.04756692 -0.45654980 -5.69860578

Largest  eigenvalues:
 [1] 65920403 59915422 57226585 56292137 54626891 53049380 52511637 51598153
 [9] 51550425 50591028

Smallest eigenvalues:
 [1]  0.42857068  0.42233951  0.33428665  0.28511286  0.27304769  0.06738081
 [7]  0.06159214 -0.02269885 -0.04753362 -2.62666136

Largest  eigenvalues:
 [1] 65373132 60371013 57772896 56582558 54839576 53505278 52709407 52231512
 [9] 51683667 51424207

Smallest eigenvalues:
 [1]   0.5527861   0.5191890   0.5109496   0.4552053   0.3569596   0.3308421
 [7]   0.1655400  -0.2481752  -0.2485755 -14.8087171

Largest  eigenvalues:
 [1] 64298426 59365986 56712783 55646048 54461595 52413836 51695841 51218018
 [9] 51195453 50362335

Smallest eigenvalues:
 [1]  0.5879522  0.5586164  0.4919110  0.4150249  0.3334988  0.3268393
 [7]  0.1071417 -0.1503952 -0.3219681 -1.5340869

Largest  eigenvalues:
 [1] 65576323 59905413 56922328 56518290 54638236 52638453 52332864 51549585
 [9] 51496916 50719685

Smallest eigenvalues:
 [1]  0.4452586  0.4253285  0.3897178  0.2382964  0.2189670  0.1750966
 [7]  0.1718941 -0.2858584 -0.8273859 -1.8439859

Largest  eigenvalues:
 [1] 66414068 60487398 57456568 57264512 55076190 53346019 53204558 52899585
 [9] 51922869 51881458

Smallest eigenvalues:
 [1]  0.579322470  0.495724326  0.475819493  0.457585349  0.357925325
 [6]  0.281455716  0.260275895 -0.001111107 -0.025555299 -0.430857479

Largest  eigenvalues:
 [1] 64228370 59963578 56998759 55226178 54795231 53208368 51859128 51758102
 [9] 51371890 51137177

Smallest eigenvalues:
 [1]  0.5053258  0.4497076  0.3842383  0.2980560  0.2917675  0.1977349
 [7]  0.1435539 -0.1076327 -0.1294795 -0.2666228

Largest  eigenvalues:
 [1] 64171263 59863976 57283743 55783843 54713585 53345568 52096852 51865869
 [9] 51747188 50845488

Smallest eigenvalues:
 [1]  0.4874405  0.4831283  0.4762235  0.4539044  0.4132227  0.2655075
 [7]  0.2654035  0.1649278 -0.7497195 -3.6836471

Largest  eigenvalues:
 [1] 64703810 60404872 56947943 56118265 55487160 53720828 51980623 51859404
 [9] 51791012 50951196

Smallest eigenvalues:
 [1]  0.53090711  0.52857996  0.40532111  0.31788968  0.29253928  0.28888361
 [7]  0.19107938  0.15011937  0.09222173 -0.41676164

Largest  eigenvalues:
 [1] 66256197 60857400 58269889 56445434 55358595 53862156 52668530 52366326
 [9] 51998104 51534903

Smallest eigenvalues:
 [1]  0.5632778  0.5368090  0.4897684  0.4513131  0.3952916  0.3864297
 [7]  0.3376703  0.1976449 -0.6951041 -1.5668546

Largest  eigenvalues:
 [1] 65400796 60174958 57188597 56547107 55292785 53800498 52453111 52216088
 [9] 52037523 51347479

Smallest eigenvalues:
 [1]  0.4661901  0.4080849  0.3753071  0.3083683  0.2636065  0.2484938
 [7]  0.2471375  0.2301789  0.1823539 -0.7611671

Largest  eigenvalues:
 [1] 64533648 59908454 56634158 55939317 54790492 53195839 51984942 51947753
 [9] 51519753 50875168

Smallest eigenvalues:
 [1]  0.55301142  0.53508523  0.48531364  0.46827562  0.28645905  0.26865378
 [7]  0.02387740  0.00851412 -0.04974736 -2.88107699

Largest  eigenvalues:
 [1] 65593782 60854360 57499461 55971282 55457354 53540754 52087735 51980213
 [9] 51712925 51238089

Smallest eigenvalues:
 [1]   0.4606986   0.4150882   0.3895332   0.3698456   0.3016220   0.1967325
 [7]  -0.2412423  -0.4353416  -4.2177200 -12.4418833

Largest  eigenvalues:
 [1] 66642222 60497163 58211313 57644600 54848392 53687334 53568098 52186766
 [9] 51817447 51307454

Smallest eigenvalues:
 [1]   0.4444366   0.4443511   0.4334750   0.4235253   0.3942360   0.3622654
 [7]   0.3180757   0.2967322   0.2288908 -26.3081421

Largest  eigenvalues:
 [1] 64396580 59472323 56986246 56387089 54520198 52437651 52340066 52099638
 [9] 51148609 50775198

Smallest eigenvalues:
 [1]  0.4832095  0.4816598  0.4099703  0.4003063  0.3778948  0.3354794
 [7]  0.3217115  0.2173993  0.1108074 -1.8167742

Largest  eigenvalues:
 [1] 64261862 60209997 57363944 55525902 55499370 53860182 51978820 51639716
 [9] 51407576 50509109

Smallest eigenvalues:
 [1]  0.4159491  0.3887005  0.3636342  0.3339376  0.2719207  0.2071950
 [7] -0.1554395 -0.1753642 -1.6493714 -3.1613924

Largest  eigenvalues:
 [1] 65831936 60436230 57527128 56524973 55460560 54029766 52557061 52076846
 [9] 51920156 50700276

Smallest eigenvalues:
 [1]  0.4991566  0.4450847  0.3848060  0.3752293  0.2972533  0.2585703
 [7]  0.2508491  0.1809243  0.1793704 -0.4216766

Largest  eigenvalues:
 [1] 64369103 60376898 57361903 56147636 55339820 53647877 52442006 52110402
 [9] 51926524 51411287

Smallest eigenvalues:
 [1]   0.3919340   0.3685712   0.2556420   0.2305837   0.2224366   0.1234887
 [7]  -0.2761569  -0.3616016 -11.4560427 -16.1561883

Largest  eigenvalues:
 [1] 65412366 59923422 57748249 56026030 55116757 53840008 52628318 52101955
 [9] 52094337 51747853

Smallest eigenvalues:
 [1]  0.5405937  0.4704579  0.4415416  0.3790221  0.3078424  0.2719302
 [7]  0.2296209  0.0186659 -0.0744638 -0.7226621

Largest  eigenvalues:
 [1] 65520519 60275203 57988226 56788103 54892970 53276053 52799941 52066448
 [9] 51868418 51291721

Smallest eigenvalues:
 [1]  0.57591289  0.53984830  0.44469187  0.40822789  0.35845191  0.26293753
 [7]  0.16328850  0.07937359 -0.04800096 -6.00683329

Largest  eigenvalues:
 [1] 64289485 59455696 56834512 55315299 54648085 53056009 51574283 51470745
 [9] 51377222 50566365

Smallest eigenvalues:
 [1]  0.58586685  0.51402486  0.42743002  0.40341103  0.34743473  0.22118159
 [7]  0.16053106  0.08174534  0.06713376 -0.40198544

Largest  eigenvalues:
 [1] 63682699 60558805 57862601 55217118 55062996 53841954 52020460 51958573
 [9] 51242398 51026267

Smallest eigenvalues:
 [1]  0.50906806  0.43992522  0.38269723  0.37411904  0.34578560  0.31168999
 [7]  0.22278832  0.09681184 -0.08672713 -1.92598298

Largest  eigenvalues:
 [1] 65216969 60390600 58111830 55821549 55480546 53756032 52516394 52155805
 [9] 52037381 51570033

Smallest eigenvalues:
 [1]  0.37125346  0.33622651  0.29554754  0.28392163  0.25954336  0.18204743
 [7]  0.10794663  0.07439459 -1.71415284 -1.76398125

Largest  eigenvalues:
 [1] 66281357 60659706 58058772 56696467 55097852 53702741 52758194 52705716
 [9] 52016429 51860011

Smallest eigenvalues:
 [1]  0.4915993  0.4851726  0.4418545  0.4320093  0.4096783  0.3744207
 [7]  0.3444420  0.1834299  0.1197684 -0.1764419

Largest  eigenvalues:
 [1] 61917877 59848034 56853819 54935056 54622197 53424167 51985452 51214462
 [9] 50675931 50435386

Smallest eigenvalues:
 [1]  0.44518733  0.41460183  0.32436259  0.31668699  0.29987897  0.19623957
 [7]  0.19542040  0.07259145 -2.80552716 -2.92745036

Largest  eigenvalues:
 [1] 66640375 61095951 57961718 57353193 56134267 54440333 53381865 53295039
 [9] 52478193 52079181

Smallest eigenvalues:
 [1]  0.4634656  0.3698625  0.3634382  0.3519396  0.3517787  0.3205757
 [7]  0.3197558  0.2100936  0.1818245 -0.3952971

Largest  eigenvalues:
 [1] 64753557 60999215 57910651 56065071 55968898 54252348 52532757 52183472
 [9] 52080847 51572769

Smallest eigenvalues:
 [1]  0.3858889  0.3639822  0.3448909  0.3411816  0.2677283  0.2321544
 [7]  0.1140600 -0.1581726 -0.7332295 -1.4332558

Largest  eigenvalues:
 [1] 65565004 59630014 57366436 56865100 54699649 53420088 52803464 51950272
 [9] 51565967 51071268

Smallest eigenvalues:
 [1]  0.4878207  0.4736053  0.4604077  0.4501137  0.4259043  0.2673243
 [7]  0.2605347  0.2207386  0.1528024 -0.8640331

Largest  eigenvalues:
 [1] 63872043 60705633 57978116 56097159 55768979 54475466 52770612 52723140
 [9] 51950648 51649096

Smallest eigenvalues:
 [1]   0.4226829   0.4049011   0.3693947   0.3473756   0.2799854   0.2396624
 [7]   0.1791423   0.1474199  -4.0729856 -19.3983485

Largest  eigenvalues:
 [1] 64321911 60430367 57812735 55732140 55625407 54268799 52640600 52389440
 [9] 51708865 51207869

Smallest eigenvalues:
 [1]   0.5553300   0.4967537   0.4364663   0.4144603   0.3296271   0.3032553
 [7]   0.2884542   0.2636767   0.1265461 -18.7405014

Largest  eigenvalues:
 [1] 63101342 60157442 57042025 55467023 54738047 53721113 51871042 51779396
 [9] 51009249 50904160

Smallest eigenvalues:
 [1]  0.4966046  0.4709479  0.3776067  0.3097582  0.2638198  0.2393345
 [7]  0.1111486 -0.1408088 -0.8568489 -1.4758753

Largest  eigenvalues:
 [1] 65270513 61372036 57764697 56673041 56384759 54655131 53518208 52651284
 [9] 52366803 51905607

Smallest eigenvalues:
 [1]  0.44346563  0.42564798  0.34981173  0.31166490  0.29445893  0.25320201
 [7]  0.22600226  0.21321413  0.07203382 -1.65710364

Largest  eigenvalues:
 [1] 63898644 59870162 57230832 55478703 54860298 53458313 51864385 51618377
 [9] 51568458 50839329

Smallest eigenvalues:
 [1]  0.46244840  0.38948767  0.37215329  0.26736355  0.19798737  0.16938847
 [7]  0.12489110 -0.01901132 -0.76193337 -3.55169477

Largest  eigenvalues:
 [1] 65952490 59884255 57836859 56179865 55038290 53870873 52556097 52365838
 [9] 52069754 51507352

Smallest eigenvalues:
 [1]  0.42999778  0.38555428  0.37323619  0.36471501  0.32681658  0.32183526
 [7]  0.15807602  0.05987858 -6.59816174 -7.33697480

Largest  eigenvalues:
 [1] 64034822 60439047 57778130 55756713 55345882 54104653 51944458 51895153
 [9] 51443279 50903441

Smallest eigenvalues:
 [1]  0.6424924  0.6164485  0.5648250  0.4252163  0.3786334  0.3785901
 [7]  0.3333032  0.2573348 -0.2328014 -0.3363637

Largest  eigenvalues:
 [1] 65843703 60504600 57741779 56989262 54939473 52987954 52922512 52512440
 [9] 51803876 51612969

Smallest eigenvalues:
 [1]  0.56231586  0.39004207  0.36305529  0.32163075  0.27072760  0.24938666
 [7]  0.22502081  0.08064115 -0.35063075 -0.43664614

Largest  eigenvalues:
 [1] 65587673 60830487 57764657 56726586 55570430 53833902 52855569 52680560
 [9] 52038380 51483534

Smallest eigenvalues:
 [1]  0.4295399  0.3392148  0.3266543  0.3067237  0.2652543  0.2038584
 [7]  0.1140841 -0.1150886 -0.2993984 -1.2668640

Largest  eigenvalues:
 [1] 65242863 60345619 57795897 56458293 55203857 53578015 53318279 52652814
 [9] 51949893 51697251

Smallest eigenvalues:
 [1]   0.430067710   0.422533650   0.298756962   0.277670314   0.149106526
 [6]   0.004114766  -0.151584554  -1.716368655 -14.456496183 -15.246523300

Largest  eigenvalues:
 [1] 64570556 60491679 57362371 55997647 55204651 53481933 51974861 51894203
 [9] 51866692 50972864

Smallest eigenvalues:
 [1]  0.4367080  0.3518828  0.3323773  0.3312061  0.3238202  0.3020763
 [7]  0.2846286  0.2665455 -0.1121726 -1.1884098

Largest  eigenvalues:
 [1] 65735735 60835951 58215531 56787345 55486000 54009957 52739215 52403891
 [9] 52355074 51511373

Smallest eigenvalues:
 [1]  0.34953304  0.34263765  0.33106232  0.28835138  0.28621615  0.27790996
 [7]  0.24896089  0.20303937  0.08655229 -2.27140333

Largest  eigenvalues:
 [1] 65095325 60085501 57590523 56051404 54770889 53440447 52167452 51943210
 [9] 51656173 51275428

Smallest eigenvalues:
 [1]  0.6592048  0.6404003  0.5166595  0.4033482  0.4028323  0.3708722
 [7]  0.3462916  0.2698337  0.2648815 -0.7286708

Largest  eigenvalues:
 [1] 64613077 59920510 57132441 55773065 55111497 53670501 52220693 51902478
 [9] 51703973 50873263

Smallest eigenvalues:
 [1]  0.37891647  0.31123961  0.30510601  0.19230167  0.17716224  0.03259586
 [7] -0.17742905 -0.64515518 -2.02278639 -2.28797808

Largest  eigenvalues:
 [1] 65900707 60756964 58434230 56451026 55575079 54007667 52663257 52506551
 [9] 52413928 51885792

Smallest eigenvalues:
 [1]  0.45556575  0.36751171  0.35966646  0.26996310  0.26295304  0.19468767
 [7]  0.18823328 -0.03956099 -0.15294538 -0.34344492

Largest  eigenvalues:
 [1] 63440266 61070682 56983675 55922306 55303250 54043908 52022979 51873568
 [9] 51411685 50654573

Smallest eigenvalues:
 [1]  0.4905209  0.4643631  0.4284030  0.4142746  0.2207196  0.1673253
 [7] -0.5509606 -1.6271276 -7.1104395 -9.8297614

Largest  eigenvalues:
 [1] 65516259 59914351 57209289 56836790 54941499 52939629 52716622 52506521
 [9] 51921697 51562362

Smallest eigenvalues:
 [1]  0.4106379  0.3301665  0.2167164  0.2040239  0.1352433  0.1261937
 [7] -0.1479056 -1.4012180 -1.9481681 -4.5814904

Largest  eigenvalues:
 [1] 62053635 59553829 56229488 54892512 54870917 53141701 52027549 52017605
 [9] 50939490 50742460

Smallest eigenvalues:
 [1]  0.23339206  0.19264821  0.14566220  0.09516121  0.01871251 -0.10373377
 [7] -0.28396276 -0.87932007 -1.53954870 -2.86300275

Largest  eigenvalues:
 [1] 65363760 61528790 58337241 57320176 55442653 53749587 53451881 52751825
 [9] 52355324 51516724

Smallest eigenvalues:
 [1]  0.46900975  0.45756721  0.45639449  0.42779764  0.38861220  0.27796359
 [7]  0.24700575  0.20415410  0.16402602 -0.02413903

Largest  eigenvalues:
 [1] 62994291 59486543 56982678 54894778 54810845 53335460 52007252 51275553
 [9] 50918118 50544221

Smallest eigenvalues:
 [1]  0.56332150  0.56235172  0.53824983  0.53555934  0.46745360  0.45266697
 [7]  0.38544392  0.23974666  0.09397433 -0.07977456

Largest  eigenvalues:
 [1] 63506834 60585083 57685873 55448152 55411504 53919463 52154542 51873020
 [9] 51453738 50900873

Smallest eigenvalues:
 [1]  0.45586335  0.44886781  0.38949076  0.37173644  0.36319228  0.27477958
 [7]  0.04376298  0.04111338 -0.18370843 -9.00470598

Largest  eigenvalues:
 [1] 65263619 60764933 57655387 57042414 55057333 53274063 53081235 52058941
 [9] 51956356 51192634

Smallest eigenvalues:
 [1]  0.42942178  0.42424857  0.39652557  0.38896025  0.33227749  0.31281139
 [7]  0.26494138 -0.09445423 -0.51650472 -1.42408393

Largest  eigenvalues:
 [1] 64162879 60036713 57612890 55807625 54920771 53641231 51860806 51835422
 [9] 51778135 50900906

Smallest eigenvalues:
 [1]  0.5132643  0.5029630  0.4351605  0.4099295  0.3557336  0.2691699
 [7]  0.2262361  0.1695444  0.1412563 -1.3564060

Largest  eigenvalues:
 [1] 63726205 60267131 57125561 55734594 55459744 53931121 52284879 51836487
 [9] 51321733 50949508

Smallest eigenvalues:
 [1]  0.6947738  0.5524289  0.5163589  0.3769426  0.3621315  0.3343969
 [7]  0.3005910  0.2647608  0.1340909 -0.1257241

Largest  eigenvalues:
 [1] 63915112 60359994 57515484 55705835 55580355 53864952 52717574 51906035
 [9] 51811247 51374724

Smallest eigenvalues:
 [1]   0.17399293   0.14668297   0.13014329   0.10154982   0.05478427
 [6]  -0.07858091  -0.08885453  -0.38554795  -2.55661303 -10.46824644

Largest  eigenvalues:
 [1] 63671141 59391123 56451760 55603415 54857795 53157005 51835080 51557921
 [9] 50900544 50269519

Smallest eigenvalues:
 [1]  0.5565602876  0.4412926206  0.3703934677  0.3242838418  0.2929735410
 [6]  0.2866446591  0.2326488857  0.0004668943 -0.4870154074 -0.5942967261

Largest  eigenvalues:
 [1] 64621816 60829664 57869410 56017177 55439920 53843014 52863578 52242244
 [9] 52173231 51954614

Smallest eigenvalues:
 [1]   0.4294170   0.2906370   0.2838302   0.2368419   0.2036671   0.1859544
 [7]   0.1632616   0.1387046  -1.4531621 -15.6338062

Largest  eigenvalues:
 [1] 64679069 59651279 56971323 56061394 54739390 53132849 52317677 52062137
 [9] 51683223 51105237

Smallest eigenvalues:
 [1]   0.4768358   0.4633440   0.4134908   0.3899816   0.3311158   0.3232596
 [7]   0.2825004  -0.6337067  -6.9747085 -26.9398822

Largest  eigenvalues:
 [1] 64526309 60636211 57295159 56336653 55681572 54043629 52302861 52158735
 [9] 52010805 51129006

Smallest eigenvalues:
 [1]  0.44937738  0.41200232  0.38136894  0.26573141  0.22418340  0.18096288
 [7]  0.15753976  0.12372860  0.01736977 -0.90399644

Largest  eigenvalues:
 [1] 65485371 61207567 58668150 56571645 55672649 54252856 52769983 52643571
 [9] 52480537 51858158

Smallest eigenvalues:
 [1]  0.4927097  0.3541109  0.3403424  0.3067935  0.3039201  0.2957033
 [7]  0.2955304  0.2553524  0.1724951 -0.6452331

Largest  eigenvalues:
 [1] 64363823 59914191 56930183 55718190 54838230 53186891 51957963 51857211
 [9] 51396822 51066086

Smallest eigenvalues:
 [1]  0.4445254  0.4325453  0.4180866  0.3392527  0.3293453  0.2918831
 [7]  0.2819983  0.2135124  0.1794837 -0.9750292

Largest  eigenvalues:
 [1] 65079999 60507571 57459036 56624897 54934481 53631010 52558210 52483901
 [9] 51857988 51722368

Smallest eigenvalues:
 [1]  0.35238406  0.30235391  0.28126035  0.23503907  0.23020427  0.01862637
 [7] -0.54217517 -0.62257215 -1.66134727 -6.06466464

Largest  eigenvalues:
 [1] 64206520 59327298 57117161 55543154 54364857 53267864 51922715 51723964
 [9] 51532529 51021170

Smallest eigenvalues:
 [1]  0.3727948  0.3474193  0.3254185  0.3116484  0.2841517  0.2740666
 [7]  0.2120624  0.1155873 -0.4931777 -3.9524265

Largest  eigenvalues:
 [1] 62045232 59317993 56434316 54636107 54404068 53041601 51763938 51297251
 [9] 50613816 50489818

Smallest eigenvalues:
 [1]  0.3933471  0.3471600  0.3320841  0.3306430  0.2960491  0.2025489
 [7]  0.1797307  0.1717850  0.1313368 -3.8661918

Largest  eigenvalues:
 [1] 64896235 60908382 57840302 56154951 55754018 54406921 52751216 52680298
 [9] 52092783 51906524

Smallest eigenvalues:
 [1]  0.58382175  0.46840075  0.43570285  0.39391324  0.38179398  0.33526374
 [7]  0.33285675  0.15951703 -0.05347295 -9.23003284

Largest  eigenvalues:
 [1] 64021201 60112179 57377663 55482512 55476044 54003150 52367237 52205834
 [9] 51580870 51232105

Smallest eigenvalues:
 [1]  0.5679771  0.5136341  0.4454096  0.4098713  0.3246302  0.2852869
 [7]  0.2810462  0.2742600  0.1594525 -0.9096981

Largest  eigenvalues:
 [1] 62402250 59945731 56876040 55088529 54775174 53395944 51771857 51663222
 [9] 50733360 50563583

Smallest eigenvalues:
 [1]  0.5208800  0.5131013  0.4176284  0.3495412  0.3087863  0.2598037
 [7]  0.2594486  0.1430163  0.1112036 -0.1455603

Largest  eigenvalues:
 [1] 64730411 60918235 58019251 56041332 55812023 54316581 52664103 52328449
 [9] 52179450 51424259

Smallest eigenvalues:
 [1]  0.51429120  0.49676158  0.44222096  0.39439018  0.34219113  0.31474323
 [7]  0.11792681  0.05927812 -0.03319816 -7.07977194

Largest  eigenvalues:
 [1] 63952055 59936772 57256508 55541418 55167004 53683301 52276794 51994404
 [9] 51563416 51075028

Smallest eigenvalues:
 [1]  0.31044308  0.25629393  0.16914060  0.13848943  0.12932323  0.04998798
 [7] -0.53621952 -0.99503219 -1.38720389 -3.18335418

Largest  eigenvalues:
 [1] 62771592 60134043 57204467 55531513 55205386 53424257 52509237 52349368
 [9] 51375022 51158186

Smallest eigenvalues:
 [1]   0.3435085   0.3334230   0.2694998   0.2170939   0.1734174   0.1204316
 [7]   0.1135274  -0.7253679  -5.1454549 -29.7942473

Largest  eigenvalues:
 [1] 65575891 60206493 57181444 56748017 55287651 53731993 52651717 52450969
 [9] 52098622 51678461

Smallest eigenvalues:
 [1]  0.54896002  0.53930877  0.52887691  0.32190308  0.27647123  0.23428633
 [7]  0.22939166  0.06935047 -0.02291231 -0.05160940

Largest  eigenvalues:
 [1] 63033814 60881869 57725918 56353474 54964041 54488758 52888474 52591832
 [9] 51648111 51144277

Smallest eigenvalues:
 [1]  0.53688674  0.50979492  0.35955751  0.34266514  0.33681509  0.22482783
 [7]  0.18510949  0.10494858  0.04029477 -1.21583142

Largest  eigenvalues:
 [1] 63082588 61122435 57922257 56548851 55201858 54717729 52950649 52864058
 [9] 51948054 51283083

Smallest eigenvalues:
 [1]  0.37055333  0.24397796  0.22535539  0.22064736  0.20276503  0.20001838
 [7]  0.16633918  0.05716543 -1.93005306 -6.40058671

Largest  eigenvalues:
 [1] 65278890 59918567 57430993 56262550 54734647 53438270 52354384 52071414
 [9] 51797266 51290060

Smallest eigenvalues:
 [1]  0.457640508  0.434488032  0.415186189  0.378885804  0.370192720
 [6]  0.294331408  0.156670212  0.151513969  0.002483472 -0.068920470

Largest  eigenvalues:
 [1] 64260653 60839144 58165575 56247786 55338077 53814764 52079468 52014303
 [9] 51922844 51010359

Smallest eigenvalues:
 [1]   0.34855723   0.32653035   0.21678353   0.20444853   0.03070099
 [6]  -1.47484974  -2.61706685  -9.63598610 -10.65152405 -11.81698325

Largest  eigenvalues:
 [1] 65085852 59936137 57667199 56556491 55233158 54006823 53023309 52398653
 [9] 52347806 51973266

Smallest eigenvalues:
 [1]   0.3381866   0.3227711   0.3098073   0.2812932   0.2717524   0.2368776
 [7]   0.1772994  -1.2831674  -2.5541371 -15.3659377

Largest  eigenvalues:
 [1] 64668112 60361693 57195391 56379975 54830152 53255052 52520586 52363800
 [9] 51869621 51710322

Smallest eigenvalues:
 [1]  0.6008290  0.5774503  0.5152635  0.4450602  0.4363860  0.4048657
 [7]  0.2738052  0.2437140  0.1016007 -0.2659326

Largest  eigenvalues:
 [1] 65662001 59818585 56814940 56366223 54458983 52704285 52380267 51463555
 [9] 51209721 50711322

Smallest eigenvalues:
 [1]  0.36773786  0.34527390  0.31587361  0.28753809  0.24899620  0.07115531
 [7]  0.07013047  0.02301751 -0.29917983 -0.55715220

Largest  eigenvalues:
 [1] 64833014 59910569 57528814 55484897 55387991 53913139 51807501 51686018
 [9] 51570911 50822061

Smallest eigenvalues:
 [1]  0.42114651  0.41012319  0.27469020  0.21575691  0.20137663  0.09823638
 [7]  0.03508838 -0.45886452 -0.91304983 -2.30407978

Largest  eigenvalues:
 [1] 64361593 60247304 57389767 55946292 55801165 54225426 52448197 52389107
 [9] 51873376 51778606

Smallest eigenvalues:
 [1]   0.5239711   0.4660117   0.4390764   0.4384642   0.2931430   0.2334313
 [7]   0.2302813   0.1873801   0.1763725 -11.2653385

Largest  eigenvalues:
 [1] 63453016 60212635 57687679 55459311 55121073 53799618 52661547 51824672
 [9] 51279725 51028949

Smallest eigenvalues:
 [1]  0.4941352  0.3978747  0.3490921  0.2902397  0.2815614  0.2734541
 [7]  0.2595843  0.2544340 -1.5936816 -4.4238888

Largest  eigenvalues:
 [1] 65845680 59805365 57340790 56821329 54719602 53206672 52712707 52219037
 [9] 51702344 51220631

Smallest eigenvalues:
 [1]   0.51356322   0.49695658   0.49159728   0.43954030   0.34125666
 [6]   0.23246579   0.20326497   0.14610412   0.02726586 -15.33415248

Largest  eigenvalues:
 [1] 64413183 60109496 56859240 56060069 55029419 53201102 52047343 52006692
 [9] 51767086 50956372

Smallest eigenvalues:
 [1]  0.5355418  0.4460271  0.4436493  0.3404052  0.2988852  0.2740152
 [7]  0.2665325  0.2030855 -0.1478093 -0.3066490

Largest  eigenvalues:
 [1] 64688108 60314315 57637293 55560905 55330792 53920476 52587938 52238865
 [9] 51664518 51446987

Smallest eigenvalues:
 [1]  0.50025753  0.44788931  0.37637313  0.34216412  0.28581862  0.27678297
 [7]  0.09094782 -0.01622387 -1.34507222 -6.79008198

Largest  eigenvalues:
 [1] 64534920 59809700 56904018 56148298 55038247 53457244 52232116 52175519
 [9] 51688107 51115216

Smallest eigenvalues:
 [1]  0.48890093  0.38292492  0.36992951  0.35624224  0.23811757  0.23788674
 [7]  0.18817711 -0.05535112 -0.38692746 -1.37068085

Largest  eigenvalues:
 [1] 63534652 59675338 57395507 55357123 54840424 53632265 52284759 51921644
 [9] 51519247 51114186

Smallest eigenvalues:
 [1]  0.50408815  0.43963425  0.41289794  0.38187241  0.35225835  0.34647649
 [7]  0.34299125  0.32091325  0.31336602 -0.02669146

Largest  eigenvalues:
 [1] 62895176 59742572 57136264 55640866 54940740 53281578 51674828 51576426
 [9] 51509171 50484428

Smallest eigenvalues:
 [1]  0.5317972  0.4111299  0.3156682  0.2807998  0.2799069  0.2146495
 [7]  0.1659147  0.1238339 -0.6588994 -0.7753490

Largest  eigenvalues:
 [1] 64118211 60527814 57381779 55982082 55740875 54021148 52745121 52385741
 [9] 52140453 51552308

Smallest eigenvalues:
 [1]   0.50709128   0.49099777   0.40388220   0.37044460   0.35276207
 [6]   0.05156476   0.03688797  -2.64826461  -3.19911244 -10.65902213

Largest  eigenvalues:
 [1] 63856036 60138867 56921212 55829284 55189170 53515160 51835841 51665493
 [9] 51643967 50642379

Smallest eigenvalues:
 [1]  0.513142749  0.395678723  0.356456868  0.339783740  0.223403441
 [6]  0.200601311  0.005595955 -0.353177970 -0.424262348 -1.266350097

Largest  eigenvalues:
 [1] 63734011 59548656 56744384 55444984 54823432 53028764 52564218 51473893
 [9] 51308682 50890905

Smallest eigenvalues:
 [1]   0.41250445   0.36135583   0.23407873   0.12024406   0.02703175
 [6]  -0.59760540  -1.05935942  -1.15977714 -14.21677087 -25.84205488

Largest  eigenvalues:
 [1] 65953425 59815186 57442187 56142899 54845114 53314603 52321618 52044911
 [9] 51935666 50849781

Smallest eigenvalues:
 [1]  0.36615439  0.31326129  0.28495931  0.21551577  0.19159089  0.13238991
 [7]  0.02555591 -1.91107869 -6.16149963 -8.45163422

Largest  eigenvalues:
 [1] 64811459 59869089 57150571 55992868 55291305 53664492 52036887 51766814
 [9] 51265665 50214149

Smallest eigenvalues:
 [1]  0.45007466  0.43451046  0.41871822  0.34876442  0.27131051  0.25260930
 [7]  0.17996303  0.13108908 -0.04422398 -3.82919130

Largest  eigenvalues:
 [1] 62928653 59214590 56752903 54675098 54613992 53038678 51411295 51156372
 [9] 50814684 50462889

Smallest eigenvalues:
 [1]  0.49268166  0.48263594  0.41107868  0.40034653  0.37068409  0.26057429
 [7]  0.14597205  0.07235150  0.03807847 -2.53513236

Largest  eigenvalues:
 [1] 62292103 59532020 56365181 54874367 54688050 53050250 52035823 51398565
 [9] 50818688 50648019

Smallest eigenvalues:
 [1]  0.5278855  0.4758727  0.4338333  0.4282913  0.4171706  0.3689617
 [7]  0.2936994  0.2033135 -0.1243822 -1.4423889

Largest  eigenvalues:
 [1] 65577663 59767918 56997841 56864343 54757559 52901387 52889416 51675037
 [9] 51295138 50629651

Smallest eigenvalues:
 [1]  0.5204820  0.4225804  0.4155447  0.3779917  0.3631986  0.2949551
 [7]  0.2277822 -0.1807936 -1.1845013 -1.5216757

Largest  eigenvalues:
 [1] 65648655 60112696 57563338 56832083 54708105 52908926 52670447 52074726
 [9] 51670763 51203976

Smallest eigenvalues:
 [1]  0.39859094  0.34904025  0.31045039  0.26102341  0.12235162  0.09026301
 [7]  0.02238457  0.02061492 -4.92707840 -5.92397543

Largest  eigenvalues:
 [1] 65156532 61344783 57639545 57079460 56097183 54121380 53700622 52650893
 [9] 52612872 52099386

Smallest eigenvalues:
 [1]  0.37820033  0.35014782  0.33763113  0.33480218  0.28982951  0.26945971
 [7]  0.20797659  0.19721865  0.08415929 -0.95241435

Largest  eigenvalues:
 [1] 66168494 59692238 57024740 56703378 54335689 52848992 52839439 52011249
 [9] 51248214 51202882

Smallest eigenvalues:
 [1]  0.4334646  0.3884285  0.3570164  0.3296284  0.2183761  0.2167296
 [7]  0.1806627  0.1454605 -0.8857873 -2.3714396

Largest  eigenvalues:
 [1] 64370625 59268930 56707960 55440157 54615398 53011247 51796337 51390240
 [9] 51073100 50413122

Smallest eigenvalues:
 [1]  0.58426383  0.58321723  0.53197649  0.44854330  0.40623896  0.39575861
 [7]  0.36774993  0.17371816 -0.04097231 -0.25655805

Largest  eigenvalues:
 [1] 63924784 59492838 56665637 55629089 54358797 52804916 51649014 51467250
 [9] 50915770 50044818

Smallest eigenvalues:
 [1]   0.3318537   0.2901188   0.2727990   0.2651640   0.2297298   0.1693474
 [7]  -0.1287857  -0.1425885  -3.0594349 -21.9744984

Largest  eigenvalues:
 [1] 65592052 60782668 58385805 56880154 55344360 54145498 52816661 52488715
 [9] 52267393 51392132

Smallest eigenvalues:
 [1]  0.45676739  0.44932882  0.36923430  0.34882823  0.30920800  0.27799927
 [7]  0.12146820  0.07497249 -0.27544281 -1.73156160

Largest  eigenvalues:
 [1] 62977568 60268357 57461357 55734827 55323960 54132613 52305680 52225240
 [9] 51333933 51131169

Smallest eigenvalues:
 [1]   0.37591592   0.34939391   0.28394355   0.22288594   0.02183537
 [6]  -0.13688291  -0.89638787  -1.87339689  -4.26093626 -33.15763459

Largest  eigenvalues:
 [1] 65204940 59795188 56925205 55414986 54673291 53127366 51908386 51523503
 [9] 51404041 51047409

Smallest eigenvalues:
 [1]  0.4117747  0.4005399  0.3992011  0.3304966  0.3046413  0.2551265
 [7]  0.1850499  0.1543968  0.1345448 -0.5482180

Largest  eigenvalues:
 [1] 63981840 59956176 57294991 55683757 55268825 53483755 52624990 51617780
 [9] 51583966 51339124

Smallest eigenvalues:
 [1]  0.54588648  0.54438498  0.46984053  0.43218464  0.41920238  0.28237188
 [7]  0.27370193  0.26754378 -0.04608023 -0.24557334

Largest  eigenvalues:
 [1] 64539581 59781570 56704900 55390191 54696216 53173699 51644082 51473733
 [9] 51166525 50415484

Smallest eigenvalues:
 [1]  0.3113205  0.2909393  0.2809136  0.2588262  0.1333198 -1.0004547
 [7] -1.4927454 -2.0314479 -2.2647917 -2.7687152

Largest  eigenvalues:
 [1] 65283855 60509423 57883477 55654332 55307358 53762030 52333977 51810699
 [9] 51671180 51616296

Smallest eigenvalues:
 [1]  0.4837935  0.4553574  0.4505911  0.4154184  0.4053612  0.4034359
 [7]  0.3928558  0.2583591  0.2003834 -0.3563524

Largest  eigenvalues:
 [1] 64274093 60120534 57524312 55883456 55363625 53796518 52096232 51948413
 [9] 51746521 50995978

Smallest eigenvalues:
 [1]  0.48284963  0.37793857  0.36901334  0.33060318  0.26928105  0.26230950
 [7]  0.22734393  0.18096328  0.03577805 -0.62467375

Largest  eigenvalues:
 [1] 63420055 60508344 57049049 55589578 55244582 53565600 52629417 51657562
 [9] 51581482 51412647

Smallest eigenvalues:
 [1]  0.4399150  0.4208253  0.2980640  0.2855796  0.2076432  0.1894704
 [7]  0.1833774  0.1710420 -1.2419875 -2.0152343

Largest  eigenvalues:
 [1] 63836011 60169673 57052417 55458551 55344531 53806757 52367084 52214421
 [9] 51573106 51281117

Smallest eigenvalues:
 [1]  0.53875488  0.47593114  0.38327921  0.38137554  0.36900828  0.35832974
 [7]  0.31410037  0.28686666  0.01598865 -0.63067804

Largest  eigenvalues:
 [1] 65686353 60443186 57702067 56451625 55058677 53640595 52604128 51954061
 [9] 51756421 51141710

Smallest eigenvalues:
 [1]  0.6032834  0.4546018  0.4216246  0.3932967  0.3325949  0.2875735
 [7]  0.2786494  0.2449993  0.2355360 -1.2404562

Largest  eigenvalues:
 [1] 66173796 60524674 57939570 56573687 55321825 53972627 52685442 52488056
 [9] 51963098 51526695

Smallest eigenvalues:
 [1]  0.47471732  0.41001096  0.37543119  0.35652599  0.18515664  0.15704361
 [7]  0.06375342 -0.08862345 -1.52155284 -1.85649957

Largest  eigenvalues:
 [1] 65208262 60859311 58154447 56587520 55354355 54065181 52496298 52355682
 [9] 52128816 51219621

Smallest eigenvalues:
 [1]   0.39010591   0.38772164   0.34102365   0.29848154   0.08962970
 [6]   0.06336244  -0.79794362  -1.84033589  -2.13556826 -15.01566994

Largest  eigenvalues:
 [1] 64984035 59649025 56652940 56467108 54477533 53017444 52281300 51805761
 [9] 51518878 50541685

Smallest eigenvalues:
 [1]  0.565502102  0.481928124  0.450176821  0.444762778  0.254680255
 [6]  0.185377803  0.168778671  0.006248232 -0.791545041 -1.916082975

Largest  eigenvalues:
 [1] 63903269 60301926 57102455 55441762 55389464 53852520 52380464 52100368
 [9] 51532276 51361169

Smallest eigenvalues:
 [1]  0.34335350  0.32955884  0.31210499  0.28523221  0.20733693  0.17953085
 [7]  0.15290637  0.09511059 -0.35694884 -8.53844157

Largest  eigenvalues:
 [1] 62109519 60423723 57509442 56030908 55091527 54258754 52722879 52428320
 [9] 51586847 51080760

Smallest eigenvalues:
 [1]  0.54457663  0.50456799  0.42099679  0.39756795  0.25794836  0.21988428
 [7]  0.09436892  0.03252724 -1.21052870 -2.42474555

Largest  eigenvalues:
 [1] 64225085 60746350 57121270 55768021 55680021 54068193 52412244 52254165
 [9] 51603579 51149800

Smallest eigenvalues:
 [1]  0.4249970  0.4218964  0.3080185  0.2841112  0.2789110  0.2096348
 [7]  0.2081632  0.1909149 -0.8827535 -1.0276920

Largest  eigenvalues:
 [1] 65997044 60156927 57604506 57299503 54940742 53533320 53270265 52143358
 [9] 52073714 51213849

Smallest eigenvalues:
 [1]  0.56352954  0.54750293  0.50053218  0.44036317  0.39531692  0.37396949
 [7]  0.28074698  0.20713717 -0.05200555 -0.50019092

Largest  eigenvalues:
 [1] 63554401 60391406 57058316 55398723 55028791 53332468 52090579 51626648
 [9] 51437210 51198436

Smallest eigenvalues:
 [1]  0.5216278  0.4307288  0.4200359  0.4128112  0.3793602  0.3494066
 [7]  0.3266821  0.2936509  0.2189408 -0.5980169

Largest  eigenvalues:
 [1] 65356849 60605480 58034169 56449423 55321652 53935545 52534872 52302176
 [9] 52238990 51552313

Smallest eigenvalues:
 [1]  0.5670216  0.4868008  0.4643145  0.3776589  0.3357970  0.1967524
 [7] -0.2041937 -0.2798641 -0.3427553 -1.2985528

Largest  eigenvalues:
 [1] 64857935 60050708 57421086 56157476 54776540 53297154 52221990 52155247
 [9] 51937533 51432883

Smallest eigenvalues:
 [1]  0.5204519  0.4595059  0.3175062  0.3045108  0.2837890  0.2703324
 [7]  0.2699931  0.2489191  0.1548238 -0.3876310

Largest  eigenvalues:
 [1] 63658788 59593115 57205743 55884840 54326103 52897787 51868289 51569947
 [9] 51179189 50504370

Smallest eigenvalues:
 [1]  0.60215041  0.52312027  0.43963147  0.40742445  0.36040984  0.32678984
 [7]  0.23726243  0.15771312  0.08797395 -1.64710534

Largest  eigenvalues:
 [1] 63729224 59870168 57103599 55552808 54842836 53335001 51700393 51589148
 [9] 51532808 50732599

Smallest eigenvalues:
 [1]  0.51699535  0.50554701  0.46953293  0.36119902  0.33526766  0.24925559
 [7]  0.20661811  0.01767268 -0.20654133 -2.27933558

Largest  eigenvalues:
 [1] 65474350 59576281 57216172 56437852 54575757 52772914 52502288 51935481
 [9] 51389338 51061769

Smallest eigenvalues:
 [1]  0.5694480  0.5523880  0.5045152  0.5028494  0.4763201  0.4132950
 [7]  0.2830584  0.2491897  0.2015181 -1.2580334

Largest  eigenvalues:
 [1] 64449168 60170429 57194726 56224052 54591774 53132886 52092576 51819879
 [9] 51444546 50890557

Smallest eigenvalues:
 [1]  0.56190068  0.46452296  0.44329888  0.34392623  0.29880342  0.29704275
 [7]  0.23897772  0.22827357  0.10759848 -0.02860955

Largest  eigenvalues:
 [1] 63464266 60584499 57340173 55646098 55046927 53508497 52082130 52056645
 [9] 51779392 51375070

Smallest eigenvalues:
 [1]   0.26208087   0.24585301   0.21944902   0.16933434   0.04943113
 [6]  -0.13696131  -0.21953305  -0.49880907  -7.20362046 -30.09318837

Largest  eigenvalues:
 [1] 64549792 59673595 57439029 57057742 54531930 53038942 52667570 52626709
 [9] 51898041 51161085

Smallest eigenvalues:
 [1]  0.4085359  0.3940913  0.3764065  0.2795715  0.2534743  0.2310830
 [7]  0.2050530 -0.1491286 -0.6555420 -0.7526958

Largest  eigenvalues:
 [1] 66595143 61672174 58871135 57767475 55776318 54171919 53697429 53028618
 [9] 52612064 52299067

Smallest eigenvalues:
 [1]  0.41985536  0.34744602  0.33963154  0.31382586  0.30230572  0.26991030
 [7]  0.07564455 -0.06564710 -0.21107038 -1.26331436

Largest  eigenvalues:
 [1] 64905909 60196206 57572316 56064966 54472796 53404938 52155079 51985153
 [9] 51755697 51473477

Smallest eigenvalues:
 [1]  0.56665657  0.53420415  0.45797345  0.40978592  0.40664044  0.32174511
 [7]  0.31384912  0.25903760  0.21983098 -0.03078901

Largest  eigenvalues:
 [1] 62874763 59657330 56979933 55310913 55017296 53414808 51892802 51589644
 [9] 51130094 50719204

Smallest eigenvalues:
 [1]  0.4523856  0.4283625  0.3907697  0.3051477  0.3035231  0.2303833
 [7]  0.2218429 -0.2850989 -1.8029084 -3.7914718

Largest  eigenvalues:
 [1] 65377809 60305610 57946480 56234647 55036341 53466446 52154180 52099074
 [9] 51646246 51298890

Smallest eigenvalues:
 [1]  0.5122451  0.4252697  0.3474607  0.2704993  0.2536186  0.2107707
 [7] -0.1067480 -0.7252001 -1.4469827 -2.4991351

Largest  eigenvalues:
 [1] 66019221 60793026 58029059 56541345 55605992 54053986 52853602 52756445
 [9] 52535871 51894446

Smallest eigenvalues:
 [1]  0.5480063  0.5343391  0.4154038  0.3745385  0.3115282  0.3097118
 [7]  0.2899511  0.2644871  0.2550387 -1.1419339

Largest  eigenvalues:
 [1] 65957063 60428386 57695892 56899556 55281366 53945526 52960656 52205228
 [9] 52171616 51310725

Smallest eigenvalues:
 [1]  0.42313923  0.40991807  0.35546893  0.26965487  0.25743431  0.21984232
 [7]  0.17762344  0.03473504 -0.20072486 -0.35606531

Largest  eigenvalues:
 [1] 62806641 59341796 57064658 54891543 54129130 53333256 51664474 51193060
 [9] 50610187 50399707

Smallest eigenvalues:
 [1]  0.40742609  0.38145632  0.33882274  0.29279607  0.24472277  0.24151625
 [7] -0.03001365 -0.16345436 -0.65571891 -1.35975963

Largest  eigenvalues:
 [1] 65031702 60393149 57758210 55406343 54893085 53524044 52187803 51585040
 [9] 51402406 51309189

Smallest eigenvalues:
 [1]  0.5486390  0.5156129  0.4195664  0.3918329  0.3564056  0.3364130
 [7]  0.3078334  0.2899076  0.1423248 -0.4230701

Largest  eigenvalues:
 [1] 65568706 59932364 57300922 56389533 54783745 53382263 52496445 51913007
 [9] 51894024 51087781

Smallest eigenvalues:
 [1]  0.5202029  0.5140320  0.5114391  0.4569729  0.3193646  0.2008783
 [7]  0.1655013 -0.1041523 -0.1415162 -1.9817074

Largest  eigenvalues:
 [1] 62284853 59429629 56001815 54760569 54235189 52787325 51521834 50790275
 [9] 50296574 49994857

Smallest eigenvalues:
 [1]  0.458718532  0.438775672  0.346712783  0.292639995 -0.002781101
 [6] -0.488893223 -0.595328606 -0.631138311 -0.997272931 -8.262999017

Largest  eigenvalues:
 [1] 64068459 59915218 57262574 55742748 55510255 53935162 52591694 52047434
 [9] 51691952 51551054

Smallest eigenvalues:
 [1]  0.48634602  0.47936263  0.46160011  0.40297858  0.29135504  0.25391103
 [7]  0.15862343 -0.07041424 -0.27646361 -2.43797582

Largest  eigenvalues:
 [1] 64332644 59897209 56470920 55183410 54838770 52954550 51578078 51243264
 [9] 51196083 50683648

Smallest eigenvalues:
 [1]   0.082846267  -0.005581226  -0.030466258  -0.197740171  -0.296137775
 [6]  -1.473451796  -3.707591644 -15.051128134 -16.126222283 -22.053085868

Largest  eigenvalues:
 [1] 63027655 59188696 56172161 54910120 54447753 52918552 52066746 51512786
 [9] 50886452 50576636

Smallest eigenvalues:
 [1]  0.61443220  0.58391278  0.52931697  0.46519635  0.38714309  0.31769963
 [7]  0.31209848  0.28466427 -0.02873817 -0.26177468

Largest  eigenvalues:
 [1] 64458968 60497059 57228017 56402655 55114734 53271518 52691697 52401047
 [9] 51809570 51546118

Smallest eigenvalues:
 [1]  0.47498698  0.43907139  0.38818481  0.36293211  0.33091355  0.29491259
 [7]  0.09201517 -0.10576516 -0.35183403 -1.04367754

Largest  eigenvalues:
 [1] 63381666 60251291 57431491 55902782 55061044 53274016 52041578 51976478
 [9] 51865078 50966852

Smallest eigenvalues:
 [1]   0.48231828   0.47064359   0.45700345   0.40907645   0.40052300
 [6]   0.22379677   0.20123232   0.12988660   0.04069322 -10.46087346

Largest  eigenvalues:
 [1] 62951268 60869894 57175218 55863040 55280518 53985731 52289225 51903576
 [9] 51316391 51023437

Smallest eigenvalues:
 [1]  0.4530239  0.4006749  0.3989586  0.3836229  0.3066514  0.2944299
 [7]  0.2567527  0.2222983 -0.8898274 -1.8020845

Largest  eigenvalues:
 [1] 65057921 60038553 57735901 56732147 54912000 53663192 52542060 52343902
 [9] 51908462 51562676

Smallest eigenvalues:
 [1]   0.36550792   0.35813549   0.35230397   0.34406144   0.26305876
 [6]   0.24066573   0.23861919  -0.09986753  -1.20440284 -38.91301801

Largest  eigenvalues:
 [1] 64280823 60552879 57440472 56068947 55365706 53849815 52481967 52422169
 [9] 52004825 51428756

Smallest eigenvalues:
 [1]  0.30389990  0.18237623  0.13047252  0.06924863  0.04933696 -0.46901345
 [7] -0.90598384 -2.05739524 -3.17678867 -4.88804782

Largest  eigenvalues:
 [1] 65814289 59346236 56544729 56045852 54180737 52715817 52117799 51668468
 [9] 51386058 50818227

Smallest eigenvalues:
 [1]  0.4704790  0.4511027  0.4456544  0.3703976  0.3397021  0.3101340
 [7]  0.2253259  0.1486695 -0.6726460 -7.8476789

Largest  eigenvalues:
 [1] 64782270 60821047 57882959 55958174 55825667 54258539 53097850 52174524
 [9] 52009772 51779557

Smallest eigenvalues:
 [1]  0.45904995  0.42647196  0.37888662  0.34251901  0.29816932  0.25406977
 [7]  0.18202582  0.14217355 -0.02940969 -0.37898229

Largest  eigenvalues:
 [1] 65024544 60817490 58143012 56262786 55649739 53885789 52846642 52231988
 [9] 52155433 51763212

Smallest eigenvalues:
 [1]  0.5455218  0.5303258  0.5080793  0.3732920  0.3393157  0.2854801
 [7]  0.2603636  0.2111399  0.1835342 -0.2537073

Largest  eigenvalues:
 [1] 61683626 59828641 57000643 55188322 54322432 53347141 52305285 51362369
 [9] 50994008 50451246

Smallest eigenvalues:
 [1]   0.23649434   0.19348165   0.19312155   0.15397270   0.13096985
 [6]   0.10018482  -0.03443138  -1.16534576  -3.06160539 -16.53599980

Largest  eigenvalues:
 [1] 66341359 60227728 57649906 57445546 55089442 53828172 53084267 52272703
 [9] 52117761 51550276

Smallest eigenvalues:
 [1]  0.5319380  0.4680688  0.4220319  0.3854596  0.3137564  0.2823258
 [7]  0.2642564  0.1643395  0.1085846 -0.7460929

Largest  eigenvalues:
 [1] 64284462 61047810 57952905 56361682 56287940 54565769 52995151 52526545
 [9] 52332539 51733625

Smallest eigenvalues:
 [1]   0.3872983   0.3718288   0.2864391   0.2854666   0.2345735   0.1857269
 [7]   0.1423190   0.1057419  -1.5526508 -20.2690897

Largest  eigenvalues:
 [1] 64179396 59689006 56898099 55128441 54901988 53398530 51759432 51524378
 [9] 51175761 50990164

Smallest eigenvalues:
 [1]  0.56961296  0.50211579  0.44720842  0.42223273  0.28130779  0.27534215
 [7]  0.25147123  0.21537915  0.13279976 -0.02095331

Largest  eigenvalues:
 [1] 64184582 60436894 57899031 55767740 54944131 54249461 52922033 51960906
 [9] 51704696 51225030

Smallest eigenvalues:
 [1]  0.53460627  0.48513699  0.45841813  0.41870000  0.35149039  0.26360364
 [7]  0.18542450  0.18530241  0.06283988 -0.02437856

Largest  eigenvalues:
 [1] 65182962 60004574 57855558 55896936 54950303 53383366 52172631 52169501
 [9] 51908222 51320099

Smallest eigenvalues:
 [1]  0.51792872  0.47212651  0.39845731  0.36518041  0.30676181  0.17766244
 [7]  0.16946911  0.02711115 -0.19072387 -1.27581554

Largest  eigenvalues:
 [1] 63289504 60655951 57091378 55756244 55607503 53517099 52384267 51853917
 [9] 51375768 50877973

Smallest eigenvalues:
 [1]   0.35428402   0.31058178   0.24239380   0.22800816   0.14366385
 [6]   0.12448140   0.03062687  -0.47869851  -5.06478606 -23.70376459

Largest  eigenvalues:
 [1] 64145724 59963504 57210943 55354251 55349428 53391942 52545954 51901404
 [9] 51661341 51559959

Smallest eigenvalues:
 [1]  0.51276329  0.49977214  0.45915053  0.43379300  0.30729224  0.21820161
 [7]  0.21343604  0.07972120  0.07041202 -0.47744528

Largest  eigenvalues:
 [1] 64650803 60190840 56983154 55833077 55120328 53489655 52413247 51909332
 [9] 51714069 51121776

Smallest eigenvalues:
 [1]  0.5025642  0.4721828  0.3668636  0.3230614  0.3146502  0.2637488
 [7]  0.2031941 -0.1467369 -1.4206695 -2.1226795

Largest  eigenvalues:
 [1] 63715589 60111156 57618041 56047231 55312315 54392889 52805750 52044473
 [9] 51444691 51115785

Smallest eigenvalues:
 [1]  0.57618936  0.50437109  0.44253556  0.40162290  0.38143383  0.37137165
 [7]  0.34330487  0.30554625  0.29375354 -0.01864911

Largest  eigenvalues:
 [1] 64837960 60267482 57162178 56120568 55417987 53476621 52603059 52252707
 [9] 51659271 51478283

Smallest eigenvalues:
 [1]  0.58747222  0.46247493  0.40615564  0.37252154  0.30938274  0.28769590
 [7]  0.27621797  0.21745839 -0.09714347 -0.32569202

Largest  eigenvalues:
 [1] 62227312 59514272 57100534 55172135 54543366 53429789 51792465 51402797
 [9] 50634725 50505127

Smallest eigenvalues:
 [1]  0.46147735  0.38056247  0.29618611  0.29002196  0.25084440  0.23936072
 [7]  0.16339231  0.08561973 -0.22944040 -0.86014343

Largest  eigenvalues:
 [1] 64639040 60353994 57656192 55508975 55380277 53875566 52403306 52172145
 [9] 51728105 51354625

Smallest eigenvalues:
 [1]  0.57988811  0.51784458  0.51381191  0.45793024  0.37170030  0.25735942
 [7] -0.06295068 -0.13836125 -0.52675154 -1.11966227

Largest  eigenvalues:
 [1] 63573915 59632503 56521656 55296162 54347553 52699011 51471821 51310638
 [9] 51268506 50448895

Smallest eigenvalues:
 [1]  0.5214007  0.4768875  0.4298152  0.4212942  0.3716958  0.3493964
 [7]  0.3239597  0.2362379  0.0699308 -0.1126082

Largest  eigenvalues:
 [1] 62602423 59104969 56230342 54975342 54357951 52666610 51535995 51278994
 [9] 50949311 50449507

Smallest eigenvalues:
 [1]   0.4619851   0.4373467   0.2804770   0.2619680   0.2446529   0.1830913
 [7]   0.1278125  -1.0903324 -10.9656909 -15.0244509

Largest  eigenvalues:
 [1] 62694405 60767248 56922074 55840588 55311746 54200471 52499931 52427577
 [9] 51266031 51192816

Smallest eigenvalues:
 [1]  0.4691136  0.4675890  0.4521460  0.4215578  0.3961748  0.3735821
 [7]  0.3233972  0.3086474  0.2560002 -2.5796506

Largest  eigenvalues:
 [1] 64598599 59810243 57125325 56740307 54552084 53168614 52570067 51720052
 [9] 51627871 50864959

Smallest eigenvalues:
 [1]  0.4950739  0.4182841  0.3632045  0.3131121  0.2895653  0.2741059
 [7]  0.2276522  0.1932157 -2.8474786 -4.3829595

Largest  eigenvalues:
 [1] 65116606 60196932 57591854 55723036 55332585 53907481 52410544 51780837
 [9] 51767593 51596822

Smallest eigenvalues:
 [1]  0.42881371  0.42843055  0.41330292  0.34826939  0.27471201  0.25118000
 [7]  0.22749707  0.05175862 -0.14980698 -0.62629763

Largest  eigenvalues:
 [1] 65562037 60096164 57572794 56167306 55241240 53826638 52312279 52252265
 [9] 52149083 51267152

Smallest eigenvalues:
 [1]  0.4398722  0.3542322  0.3352858  0.3278937  0.2830944  0.2761435
 [7]  0.2545866  0.2401905  0.2218608 -2.2757988

Largest  eigenvalues:
 [1] 64910548 60538846 57331118 56481801 55065655 53573763 52537394 52188850
 [9] 51958811 51082411

Smallest eigenvalues:
 [1]  0.5825820  0.5214181  0.4655219  0.3664353  0.2955329  0.2874229
 [7]  0.2437339  0.1509109  0.0836512 -0.2135389

Largest  eigenvalues:
 [1] 63600227 60522491 58172235 55890903 55116795 54617482 52792353 52355593
 [9] 51564019 51377719

Smallest eigenvalues:
 [1]  0.5395627  0.4969850  0.4725656  0.4008540  0.3506297  0.3187900
 [7]  0.2486233  0.1379814 -0.1586557 -3.6408846

Largest  eigenvalues:
 [1] 65308883 60894089 57845627 55820089 55800405 54306633 52204139 52164038
 [9] 52004589 51414024

Smallest eigenvalues:
 [1]  0.48776266  0.42660923  0.41964758  0.27900997  0.15372980  0.06051094
 [7]  0.04615386  0.03363386 -0.44282030 -0.98324188

Largest  eigenvalues:
 [1] 64127109 59514626 56570703 55316417 54641692 53116269 51745080 51484933
 [9] 51407195 50627684

Smallest eigenvalues:
 [1]  0.4480195  0.4290202  0.3620698  0.3434233  0.2289225  0.2185495
 [7]  0.2069439  0.1831452 -0.3371043 -0.7102083

Largest  eigenvalues:
 [1] 64740647 60270422 57081019 55734153 55635788 53974028 52272544 52230024
 [9] 51709908 51293591

Smallest eigenvalues:
 [1]  0.42985231  0.41042422  0.34230539  0.23361449  0.22150275  0.14118708
 [7] -0.06674456 -0.10785911 -0.23598135 -1.44185056

Largest  eigenvalues:
 [1] 63494786 60188033 57139279 55480965 54894605 53421251 52359781 51744015
 [9] 51676020 51441694

Smallest eigenvalues:
 [1]  0.4120311  0.3530477  0.3252676  0.3194421  0.2684833  0.2350737
 [7]  0.2124143 -0.2327599 -1.7259560 -2.9801417

Largest  eigenvalues:
 [1] 65316751 60665054 57846664 56859640 55050516 53122244 52641226 52524708
 [9] 51873115 51425983

Smallest eigenvalues:
 [1]  0.52949050  0.51977566  0.46030365  0.40256656  0.35034502  0.33285267
 [7]  0.24269094  0.20226650  0.16547097 -0.01262839

Largest  eigenvalues:
 [1] 65187895 60407227 57679795 56043085 55501186 53840607 52319963 52289786
 [9] 52257984 51238223

Smallest eigenvalues:
 [1]  0.5355013  0.4866217  0.4790100  0.4635764  0.3058997  0.2970957
 [7]  0.2919438  0.2288407  0.1453966 -3.0520384

Largest  eigenvalues:
 [1] 65569100 60320504 57311932 57140365 55450412 53761219 53027667 52832023
 [9] 52099835 51575430

Smallest eigenvalues:
 [1]  0.48432657  0.41722013  0.37305041  0.37101165  0.33759755  0.31536109
 [7]  0.23168491  0.10351043  0.01477636 -1.72761011

Largest  eigenvalues:
 [1] 63970672 59407406 56841595 55606637 54763370 53214451 51755641 51679362
 [9] 51332227 50420492

Smallest eigenvalues:
 [1]  0.44908713  0.33672758  0.29858326  0.27079519  0.24723851  0.24280154
 [7]  0.10900399  0.05530902 -0.18665752 -3.96915671

Largest  eigenvalues:
 [1] 62826251 59780839 56951517 55170505 54967555 53287056 51909405 51533791
 [9] 51047624 50584780

Smallest eigenvalues:
 [1]  0.4030885  0.3232050  0.3224300  0.3159119  0.1967794  0.1060946
 [7] -0.2897242 -0.3686685 -1.4298307 -7.2426381

Largest  eigenvalues:
 [1] 65759220 60303184 57770024 56244253 55241131 53816392 52653183 52439571
 [9] 52234521 51364901

Smallest eigenvalues:
 [1]  0.5345002  0.4299528  0.4105145  0.4070320  0.4041669  0.3091196
 [7]  0.2758072  0.2374550  0.0174245 -0.6222161

Largest  eigenvalues:
 [1] 63727698 59807558 56994452 55703662 54611526 53082872 51973343 51831475
 [9] 51644300 50924872

Smallest eigenvalues:
 [1]  0.5726498  0.5451262  0.3782607  0.3726637  0.3318796  0.3125551
 [7]  0.2861111  0.2766571  0.2449393 -1.8759456

Largest  eigenvalues:
 [1] 65742674 60936223 57944267 56924360 55434213 53981498 52850324 52456395
 [9] 52027138 51468123

Smallest eigenvalues:
 [1]  0.38466282  0.34412500  0.31278743  0.30168756  0.23161936 -0.02942748
 [7] -0.25532381 -0.45614524 -4.35004079 -5.87324734

Largest  eigenvalues:
 [1] 65762066 60747064 57700127 56797864 55418049 54033630 52750361 52219799
 [9] 51915712 51537272

Smallest eigenvalues:
 [1]  0.52767391  0.49658116  0.47108715  0.39378270  0.34990204  0.34411725
 [7]  0.33183697  0.31351879  0.26861629 -0.05393078

Largest  eigenvalues:
 [1] 63450183 60049111 57222506 55744530 54958459 53491121 51822211 51784969
 [9] 51723151 50800995

Smallest eigenvalues:
 [1]  0.3995092  0.3728310  0.3359519  0.3328351  0.2261396  0.2118650
 [7]  0.1919549  0.1627495 -0.6917800 -0.8362633

Largest  eigenvalues:
 [1] 65287175 59755730 57164905 56180634 54982685 53480718 52292760 52168119
 [9] 51420429 50551183

Smallest eigenvalues:
 [1]   0.18401539   0.14786746   0.06978497   0.04196946  -0.84799536
 [6]  -2.82244893  -2.91878869  -7.83955027 -10.48930386 -10.72465611

Largest  eigenvalues:
 [1] 63015292 59343386 56806285 54941365 54676381 53133107 51948958 51370627
 [9] 50939976 50505795

Smallest eigenvalues:
 [1]   0.4162112   0.3950567   0.3814943   0.3436694   0.3189936   0.2129440
 [7]   0.1635790  -0.3169176  -0.3860692 -19.4047729

Largest  eigenvalues:
 [1] 65649748 60371426 56967309 56704262 55039215 53297497 52701752 52199412
 [9] 52005626 51578201

Smallest eigenvalues:
 [1]  0.5782234  0.4555175  0.3931808  0.3645335  0.3009528  0.2992097
 [7]  0.2659478  0.2355635  0.1816481 -1.1072331

Largest  eigenvalues:
 [1] 64933711 60068767 57613945 55830360 54769876 53494796 51992486 51883485
 [9] 51870576 51180093

Smallest eigenvalues:
 [1]  0.3864456  0.3462517  0.3379102  0.3135665  0.1996375  0.1664430
 [7]  0.1406302 -0.1032846 -0.7843584 -8.0654301

Largest  eigenvalues:
 [1] 64984888 59654481 57039415 55800905 54704032 53336990 51936026 51840380
 [9] 51777594 51076770

Smallest eigenvalues:
 [1]  0.4050711  0.3740097  0.3333073  0.2391651  0.1913153  0.1636822
 [7]  0.1235815 -0.2511083 -1.3444760 -2.0810993

Largest  eigenvalues:
 [1] 62823361 60091349 56781597 55657152 55344127 53850259 52184449 52093415
 [9] 51217848 50950622

Smallest eigenvalues:
 [1]  0.4314467  0.4165944  0.4120417  0.4038097  0.4012641  0.3845278
 [7]  0.3272880  0.2725798  0.2274015 -1.4135281

Largest  eigenvalues:
 [1] 65653811 60055155 57417268 56343302 55034186 53681498 52401672 52220181
 [9] 52020759 51258859

Smallest eigenvalues:
 [1]  0.4758727  0.4608726  0.4556556  0.4323938  0.3701018  0.2365879
 [7]  0.2144270  0.1550570  0.1502910 -0.5561089

Largest  eigenvalues:
 [1] 63738614 60369039 56690112 55442243 55213960 53556840 52328046 51690484
 [9] 51385012 51218123

Smallest eigenvalues:
 [1]  0.56306153  0.52658127  0.47173434  0.45383100  0.42391527  0.42125430
 [7]  0.20202586  0.19171824  0.11256320 -0.03131913

Largest  eigenvalues:
 [1] 63656171 60871318 58012191 55488091 55388539 53966137 52083580 51992877
 [9] 51481041 51059512

Smallest eigenvalues:
 [1]  0.5011419  0.4319145  0.4033364  0.4013300  0.3480772  0.2668091
 [7]  0.2404480  0.1824264  0.1629935 -1.3841629

Largest  eigenvalues:
 [1] 64912517 60749296 58085408 56624964 55472811 53995104 52562384 52418681
 [9] 51998494 51274172

Smallest eigenvalues:
 [1]   0.020042392  -0.004704113  -0.073676077  -0.306308087  -0.827563103
 [6]  -1.333066779  -1.896066519  -4.566893032 -31.788612443 -95.315975672

Largest  eigenvalues:
 [1] 64822268 60796234 57662204 57111115 55806840 53922927 53290073 52906370
 [9] 52168635 52147320

Smallest eigenvalues:
 [1]   0.41169973   0.37842981   0.29016466   0.23843720   0.22037619
 [6]   0.10446320   0.03065762  -3.20189543  -6.47881696 -20.93161279

Largest  eigenvalues:
 [1] 64472378 60524225 56835352 55875543 55252204 53432428 52377265 51855424
 [9] 51297033 51274609

Smallest eigenvalues:
 [1]  0.44767431  0.43901405  0.41997561  0.37608988  0.35429693  0.29154808
 [7]  0.27659556  0.09143168 -0.21071695 -0.41305720

Largest  eigenvalues:
 [1] 64216696 60158780 57132664 55841669 55023064 53131348 51899238 51828994
 [9] 51677814 50817483

Smallest eigenvalues:
 [1]  0.5741196  0.5505421  0.4556008  0.4103342  0.4017258  0.3393958
 [7]  0.3138406  0.2927986  0.2920543 -0.9103729

Largest  eigenvalues:
 [1] 64753797 60531812 57880718 55843819 55816233 54306976 52496266 52454427
 [9] 51908585 51597589

Smallest eigenvalues:
 [1]  0.3954106  0.3613995  0.3325060  0.3275516  0.2974220  0.2710702
 [7]  0.2502615  0.2367582 -0.6378864 -1.1384685

Largest  eigenvalues:
 [1] 63327263 60199961 57124033 55791567 55489946 53626769 51780834 51686690
 [9] 51605775 50720783

Smallest eigenvalues:
 [1]   0.43212595   0.32741429   0.32567039   0.26011858   0.25440367
 [6]   0.24957935   0.15788884   0.05547981  -1.68471039 -19.49401894

Largest  eigenvalues:
 [1] 66625704 60475109 57803166 57116582 54846214 53455785 53159817 52109215
 [9] 51885727 51418221

Smallest eigenvalues:
 [1]  0.5788304  0.4919517  0.4915447  0.4019376  0.3892566  0.3432942
 [7]  0.2706531  0.2270635  0.2212239 -2.2417639

Largest  eigenvalues:
 [1] 63714784 60193815 57566657 55528026 54809956 53380310 51738601 51726574
 [9] 51665693 50873681

Smallest eigenvalues:
 [1]  0.4161256  0.3370086  0.2706851  0.2617583  0.2553429  0.2475482
 [7]  0.1902336  0.1843731  0.1410241 -2.9327487

Largest  eigenvalues:
 [1] 64423892 60500851 57670418 55968544 55437163 53889326 52529896 52031286
 [9] 51790159 51348478

Smallest eigenvalues:
 [1]  0.48957690  0.47015299  0.46006675  0.37604773  0.30726435  0.29129516
 [7]  0.27364006  0.04752531 -0.39124815 -2.31135055

Largest  eigenvalues:
 [1] 62651510 59904429 56950294 55563333 54590043 53724832 51829871 51815446
 [9] 50687549 50427098

Smallest eigenvalues:
 [1]  0.6039265  0.6017610  0.4566132  0.4070116  0.4021365  0.3577973
 [7]  0.3567614  0.2973197  0.2168300 -0.2109041

Largest  eigenvalues:
 [1] 62583035 60103371 57022040 55489174 54749865 53764644 52200558 51838826
 [9] 50925905 50699356

Smallest eigenvalues:
 [1]  0.3847111  0.3608571  0.2838315  0.2586309  0.1807085  0.1160849
 [7] -0.2037558 -0.9309813 -2.4501460 -7.1487017

Largest  eigenvalues:
 [1] 63856990 59529917 57103437 55498374 54886353 52969433 52444737 51763721
 [9] 51519941 51227290

Smallest eigenvalues:
 [1]  0.4643036  0.4563959  0.3411069  0.3097260  0.3085544  0.2178306
 [7]  0.1817973  0.1560109 -0.1715189 -1.5199293

Largest  eigenvalues:
 [1] 64265624 60475686 57731537 55879962 55602103 54342353 52472337 52274148
 [9] 51857597 51075721

Smallest eigenvalues:
 [1]  0.53319784  0.48387200  0.43300546  0.41839598  0.39414981  0.28614480
 [7]  0.26960483  0.16740033  0.01359703 -0.01666494

Largest  eigenvalues:
 [1] 64780318 59968615 57461963 56077034 55154664 53411297 52749414 52175812
 [9] 51776000 51697869

Smallest eigenvalues:
 [1]  0.5328656  0.5176262  0.4643269  0.4480038  0.4409601  0.4248786
 [7]  0.3531666  0.1299633 -0.3455052 -6.7485879

Largest  eigenvalues:
 [1] 65200333 60587153 57865091 57121154 55281982 53291432 53269892 53163590
 [9] 51778087 51717128

Smallest eigenvalues:
 [1]   0.31608215   0.24069674   0.11354433   0.04292511   0.01785595
 [6]  -0.09365783  -0.28427092  -0.43040014  -0.58442752 -17.43913944

Largest  eigenvalues:
 [1] 65373349 60285595 57009054 56624893 54527763 53111888 52493104 51968697
 [9] 51378361 51278289

Smallest eigenvalues:
 [1]  0.58440307  0.56496377  0.42533665  0.38660801  0.32656081  0.30282690
 [7]  0.26696556  0.26276361  0.22767641 -0.01716992

Largest  eigenvalues:
 [1] 65697616 60555321 58192546 56877296 54969200 53739581 53002544 52134666
 [9] 52075852 51494691

Smallest eigenvalues:
 [1]  0.44304822  0.37265766  0.29829633  0.23858726  0.22991867  0.21105634
 [7]  0.19873996  0.11486178  0.03595543 -1.24070248

Largest  eigenvalues:
 [1] 65342020 61300072 58005750 56454558 56428480 54779343 53309136 52659273
 [9] 52450986 52106185

Smallest eigenvalues:
 [1]  0.38217472  0.36485588  0.35094592  0.26728381  0.23247778  0.16547567
 [7]  0.09538476  0.02860731 -0.21735869 -7.72457098

Largest  eigenvalues:
 [1] 63334095 59538581 56408176 54624483 54402005 52758295 51463953 50776258
 [9] 50634070 50495323

Smallest eigenvalues:
 [1]   0.30397583   0.25558232   0.14471632   0.07601755  -0.60589255
 [6]  -0.61994491  -1.51095916  -2.95515444  -3.28992655 -10.47873558

Largest  eigenvalues:
 [1] 65763203 60741780 58185593 55956732 55824054 54485045 52861625 52690921
 [9] 52135509 51680100

Smallest eigenvalues:
 [1]  0.4991781  0.4334595  0.4152560  0.4009806  0.3702056  0.3682359
 [7]  0.3159687  0.3019355  0.1282064 -0.4315340

Largest  eigenvalues:
 [1] 62955938 60050256 57713871 55067021 54941557 53317947 52294149 51478923
 [9] 51347523 51157836

Smallest eigenvalues:
 [1]  0.5323462  0.4857399  0.4214185  0.3833629  0.3711478  0.3337403
 [7]  0.3203418  0.2487450  0.2050167 -0.7882811

Largest  eigenvalues:
 [1] 62996951 59727261 56551448 55281072 54686373 53071931 51755436 51471138
 [9] 51214747 50837088

Smallest eigenvalues:
 [1]  0.5946170  0.5183249  0.4916747  0.4180030  0.3871741  0.3863442
 [7]  0.3564048  0.3301643  0.2541634 -0.3942726

Largest  eigenvalues:
 [1] 63730409 60186546 57120299 55601606 55461010 53529881 52272292 52027080
 [9] 51440718 51050315

Smallest eigenvalues:
 [1]  0.36330113  0.35735802  0.35020490  0.19922920  0.18943896  0.01681169
 [7] -0.05716524 -0.47010158 -1.07214941 -6.99305943

Largest  eigenvalues:
 [1] 63722148 60829231 58148699 55463999 55318700 53917759 52690089 52480727
 [9] 51897707 51633096

Smallest eigenvalues:
 [1]  0.55222586  0.45823215  0.45177975  0.42486961  0.37224121  0.31678248
 [7]  0.29644523  0.15944283  0.02937954 -3.19650320

Largest  eigenvalues:
 [1] 63376026 59945953 56749059 55369233 55319556 53519502 52251627 51778446
 [9] 51407958 51070679

Smallest eigenvalues:
 [1]  0.58592843  0.52194145  0.47764782  0.44381887  0.44376518  0.40030160
 [7]  0.37257114  0.26480777  0.22298196 -0.07080257

Largest  eigenvalues:
 [1] 63485082 60569211 57530077 55770973 55523739 54042364 52642565 52029172
 [9] 51497996 51340575

Smallest eigenvalues:
 [1]  0.43136605  0.38550549  0.32649466  0.26778635  0.25121159  0.21327358
 [7]  0.13904030  0.09686388 -0.27884036 -4.44577419

Largest  eigenvalues:
 [1] 64448487 59833774 56855923 55369714 54605800 52882258 51626295 51474303
 [9] 51108687 50964307

Smallest eigenvalues:
 [1]  0.54795927  0.53691621  0.52213423  0.46169288  0.39491044  0.36204463
 [7]  0.34326572  0.31803810  0.23958644 -0.05511732

Largest  eigenvalues:
 [1] 65491196 60107113 57099988 55892860 54944890 53350633 52059768 51820849
 [9] 51759235 51251340

Smallest eigenvalues:
 [1]  0.39344414  0.37724984  0.34940665  0.27996271  0.12144554  0.00261382
 [7] -0.02613744 -1.41686733 -1.68098458 -3.46434352

Largest  eigenvalues:
 [1] 65277080 60941411 58112631 56686881 55668835 54300135 52824995 52493835
 [9] 52304768 51892882

Smallest eigenvalues:
 [1]  0.6063189  0.5308484  0.3461956  0.3320219  0.2734973  0.2677669
 [7]  0.2644860  0.2240272 -0.2719019 -1.2216412

Largest  eigenvalues:
 [1] 64558238 60087415 57245728 56167307 55028116 53528956 52308840 52233006
 [9] 51927752 51181048

Smallest eigenvalues:
 [1]  0.56291728  0.45060296  0.43171305  0.37414273  0.30983884  0.25363964
 [7]  0.13281164 -0.03918815 -0.14024569 -1.60148114

Largest  eigenvalues:
 [1] 65287755 60389075 56786491 56654701 54984713 53309914 52584893 51906870
 [9] 51833710 50930864

Smallest eigenvalues:
 [1]  0.51487497  0.48276612  0.43027291  0.36304155  0.30814851  0.27853417
 [7]  0.23836498  0.09051503 -0.05880217 -0.28942108

Largest  eigenvalues:
 [1] 65860429 60418873 58047819 57069157 55026846 53186002 53070411 52928777
 [9] 52127774 51922596

Smallest eigenvalues:
 [1]   0.38513789   0.35329402   0.30083898   0.23472265   0.17805962
 [6]   0.13328944   0.09622418   0.03881459  -1.38401051 -48.34514255

Largest  eigenvalues:
 [1] 65344881 60958579 57688499 56599388 56063322 54457052 52876054 52660175
 [9] 52656877 52090257

Smallest eigenvalues:
 [1]  0.4312859  0.4173851  0.3891183  0.3484750  0.3449000  0.3259633
 [7]  0.2577873  0.2073475  0.1676589 -5.2918387

Largest  eigenvalues:
 [1] 63255498 59533713 56828169 55259564 54862849 53599530 51904267 51385857
 [9] 50949594 50448282

Smallest eigenvalues:
 [1]  0.63734119  0.57445111  0.52384105  0.42092156  0.38533863  0.37679104
 [7]  0.33042094  0.29810122  0.23653938 -0.02378385

Largest  eigenvalues:
 [1] 63600365 60051132 57470063 55396019 55391954 53784579 52302689 51889047
 [9] 51544347 51095898

Smallest eigenvalues:
 [1]  0.51994774  0.51639376  0.47663901  0.46760953  0.32900118  0.31842745
 [7]  0.30924047  0.26801878 -0.03818643 -1.16756900

Largest  eigenvalues:
 [1] 63662271 60485632 57527631 56326118 55614006 54584158 52731053 52344902
 [9] 51634205 51146867

Smallest eigenvalues:
 [1]  0.48328920  0.42787750  0.36987557  0.30745724  0.30352216  0.27737620
 [7]  0.26770761  0.04073542 -1.48947386 -2.50340650

Largest  eigenvalues:
 [1] 64167773 59543924 56578038 56000180 54821535 53184462 52002393 51735733
 [9] 51597789 50581031

Smallest eigenvalues:
 [1]  0.3837986  0.3189130  0.2606605  0.2598902  0.2277843  0.2170432
 [7]  0.1256639 -0.1040040 -0.8911664 -1.0151174

Largest  eigenvalues:
 [1] 64005904 61156880 58089652 56573854 55502220 54837168 52846203 52639711
 [9] 51865067 51440816

Smallest eigenvalues:
 [1]  0.35742058  0.34568332  0.33108576  0.29742645  0.21909574  0.17427533
 [7]  0.12305939  0.06227753 -0.13489715 -0.76433901

Largest  eigenvalues:
 [1] 63232132 60131839 57142035 55517821 55100759 53803981 52586383 52193985
 [9] 51617067 51315934

Smallest eigenvalues:
 [1]  0.5466208  0.4967246  0.3807028  0.3712237  0.2574054  0.2535420
 [7]  0.2340367  0.2301929  0.1325831 -0.1254779

Largest  eigenvalues:
 [1] 64052832 60691122 57469384 56026900 55660761 53956005 52736235 52131179
 [9] 52114103 51282560

Smallest eigenvalues:
 [1]  0.4037012  0.3521072  0.3280791  0.2550376  0.2417018  0.2400799
 [7]  0.2278215  0.1771234 -0.7800077 -6.1343407

Largest  eigenvalues:
 [1] 62133088 59409572 56274144 54916464 54198771 53182483 51833913 50767242
 [9] 50291487 50061494

Smallest eigenvalues:
 [1]  0.53718516  0.48817502  0.40652090  0.40084619  0.37524395  0.34283589
 [7]  0.32066116  0.25596458  0.16594763 -0.03977973

Largest  eigenvalues:
 [1] 64666573 59813277 56967995 55927469 54979719 53237422 52018191 51599059
 [9] 51411081 50654344

Smallest eigenvalues:
 [1]  0.5863206  0.5540619  0.3660004  0.3357883  0.3308424  0.3035866
 [7]  0.2564905  0.1926957  0.1348714 -0.6011687

Largest  eigenvalues:
 [1] 64549217 60455773 57580895 55754282 55281208 53622331 52292144 51778729
 [9] 51761486 51282293

Smallest eigenvalues:
 [1]  0.4233936  0.3923690  0.3565185  0.3522399  0.2706483  0.1992710
 [7]  0.1937219  0.1574523 -0.4014794 -0.7171172

Largest  eigenvalues:
 [1] 64772814 60561956 57355931 56220468 55725827 53578165 53198393 52350586
 [9] 52340102 51879462

Smallest eigenvalues:
 [1]   0.06490486  -1.80228086  -2.69572036  -3.52033941  -3.55069947
 [6]  -3.84548309  -5.71278350 -31.46560668 -35.47167959 -63.46264795

Largest  eigenvalues:
 [1] 64997748 59963960 57058946 56641242 54610984 53009910 52891822 52115119
 [9] 51965522 51151556

Smallest eigenvalues:
 [1]  0.4831236  0.4593811  0.4016475  0.3778138  0.3434826  0.3240533
 [7]  0.2739518 -0.2593484 -0.3011723 -1.0297635

Largest  eigenvalues:
 [1] 65545649 60161552 57590318 56614626 55251940 53558575 52815210 52746128
 [9] 51984869 51710529

Smallest eigenvalues:
 [1]  0.5499005  0.4761912  0.4751196  0.3409258  0.2214093  0.1936841
 [7]  0.1374441 -0.2217093 -0.2720919 -0.4819296

Largest  eigenvalues:
 [1] 64653491 59996375 57353618 56287928 54929199 53304119 52242095 52139553
 [9] 51892960 51162272

Smallest eigenvalues:
 [1]  0.482074080  0.460566062  0.385325015  0.228719676  0.204170119
 [6]  0.203174929  0.196435913  0.055128857 -0.005558804 -0.326605294

Largest  eigenvalues:
 [1] 62768595 60424613 57366627 56084040 54315705 54177786 52396494 51857246
 [9] 50831455 50780357

Smallest eigenvalues:
 [1]  0.33616348  0.30931887  0.24539654  0.21218479  0.19538602  0.16675887
 [7] -0.04329842 -0.69152847 -3.69108248 -3.70084264

Largest  eigenvalues:
 [1] 66730562 60734822 58651687 56911715 55320015 53843097 52873511 52833433
 [9] 52210005 52131775

Smallest eigenvalues:
 [1]  0.3611995  0.3274914  0.3050859  0.3032461  0.2313873  0.1929277
 [7] -0.6057555 -1.7203846 -6.0100409 -6.2851009

Largest  eigenvalues:
 [1] 65276626 60435392 57738273 56471316 55756719 54336068 52382170 52308816
 [9] 52272510 51459525

Smallest eigenvalues:
 [1]  0.4335927  0.3927939  0.3713157  0.3186559  0.2776129  0.2157777
 [7]  0.1130594 -0.1613570 -0.4355709 -0.7732010

Largest  eigenvalues:
 [1] 63031142 60317934 57502074 55434523 54969485 53726933 52281038 52160996
 [9] 51554053 51441035

Smallest eigenvalues:
 [1]  0.5193983  0.4570162  0.3336109  0.2595471  0.2309372  0.1836258
 [7]  0.1728076  0.1150490 -0.1525138 -0.9321288

Largest  eigenvalues:
 [1] 65418361 61047491 58192914 56319833 56028300 54807647 53364910 52520563
 [9] 52260960 52038206

Smallest eigenvalues:
 [1]  0.4268365  0.3927026  0.3802362  0.2556951  0.2540186  0.1327133
 [7] -0.1691681 -0.1740369 -0.7788713 -7.8781130

Largest  eigenvalues:
 [1] 62830070 60802078 56983708 55954913 55551738 53578210 52451131 51827853
 [9] 51608119 50635326

Smallest eigenvalues:
 [1]  0.53814031  0.43750791  0.42313005  0.34093855  0.32466209  0.23680186
 [7]  0.17705006  0.11334663  0.01340931 -0.08469750

Largest  eigenvalues:
 [1] 63555464 60490871 57430637 55738280 54921299 53881775 52456179 52068906
 [9] 51293499 51061757

Smallest eigenvalues:
 [1]  0.4333640  0.4317225  0.3928476  0.3572899  0.2367908  0.1986234
 [7]  0.1922412  0.1784152  0.1477908 -1.9821548

Largest  eigenvalues:
 [1] 65152205 59676858 57135198 56774622 54493271 53259100 52539180 51869170
 [9] 51610097 51147730

Smallest eigenvalues:
 [1]  0.48435633  0.40264210  0.36446977  0.36301620  0.32316294  0.24950164
 [7]  0.19704065  0.09462268 -0.96091428 -1.29952398

Largest  eigenvalues:
 [1] 64065666 59934080 56998028 55770122 55225703 53370099 52637581 51871130
 [9] 51796019 51531562

Smallest eigenvalues:
 [1]  0.4106107  0.3917283  0.3747283  0.2766745  0.2655919  0.2452429
 [7]  0.1711048 -0.1104001 -0.5303969 -0.6167583

Largest  eigenvalues:
 [1] 66347962 59627369 57501559 56844415 54610971 53257406 52851364 51812852
 [9] 51751618 51205624

Smallest eigenvalues:
 [1]  0.3818560  0.3622534  0.3585395  0.3434945  0.3060358  0.2726398
 [7]  0.1727128  0.1078282 -1.1614511 -6.9716373

Largest  eigenvalues:
 [1] 65220544 60027510 57054620 55816913 55283493 53766530 51961272 51960431
 [9] 51725012 50968240

Smallest eigenvalues:
 [1]  0.4059022  0.3530834  0.3361140  0.3195295  0.2869012  0.2324727
 [7]  0.1811697  0.1787874  0.1682798 -1.3636802

Largest  eigenvalues:
 [1] 62953397 60254564 57754141 55633894 55078550 53966077 51886474 51805769
 [9] 51118635 50921819

Smallest eigenvalues:
 [1]  0.619214797  0.616442213  0.584535630  0.460510220  0.435279445
 [6]  0.345675152  0.303333379  0.246263739  0.167528658 -0.002613377

Largest  eigenvalues:
 [1] 63338416 60494701 57078485 55733066 54895248 53254074 52016268 51831658
 [9] 51710907 51100720

Smallest eigenvalues:
 [1]  0.4716803  0.3844930  0.3749503  0.3587162  0.3251543  0.3150077
 [7]  0.2847899  0.2483912  0.1770407 -2.3884923

Largest  eigenvalues:
 [1] 65042623 60892258 57715940 56646422 56036754 54388616 52892757 52558994
 [9] 52485842 51851005

Smallest eigenvalues:
 [1]  0.4895471  0.4573535  0.4067461  0.4025775  0.3292774  0.3281108
 [7]  0.3122810  0.1748698  0.1436429 -2.3075010

Largest  eigenvalues:
 [1] 64436462 60550646 57432767 56493112 55535528 53834227 52602911 52405994
 [9] 52347225 51596706

Smallest eigenvalues:
 [1]  0.4855649  0.4806738  0.4493792  0.4257337  0.4082319  0.3735515
 [7]  0.3304049  0.2607255  0.1915591 -0.9385318

Largest  eigenvalues:
 [1] 64387570 59921530 57110558 55931866 55157099 53491320 51791941 51746275
 [9] 51692209 50844819

Smallest eigenvalues:
 [1]  0.40843473  0.32427276  0.31404083  0.28269195  0.25819740  0.20088638
 [7]  0.15872948 -0.05990638 -0.40760688 -1.56795718

Largest  eigenvalues:
 [1] 61387319 59136736 56580228 54256121 54200180 52605164 51293670 51223159
 [9] 50441478 50253623

Smallest eigenvalues:
 [1]   0.28950387   0.21357170   0.19234762   0.17185247   0.03154836
 [6]  -2.17331564  -4.86923620 -13.51039474 -20.12396804 -21.59833755

Largest  eigenvalues:
 [1] 65245542 60127559 57761262 56001396 55146296 53612514 52432609 52082065
 [9] 51579811 51486569

Smallest eigenvalues:
 [1]  0.39205837  0.31352983  0.30824127  0.18453919  0.13212866  0.12475500
 [7] -0.03321208 -0.43045756 -1.82916584 -6.20041403

Largest  eigenvalues:
 [1] 63583849 59890614 56364157 55975814 54306776 52795132 51825314 51663233
 [9] 51222232 50367169

Smallest eigenvalues:
 [1]   0.4417341   0.4038176   0.2764126   0.2090916   0.1918436   0.1719696
 [7]   0.1196186  -1.2944904  -3.1554940 -10.6048038

Largest  eigenvalues:
 [1] 64910314 59780734 56499646 55538812 54685551 53039032 51768858 51550473
 [9] 51236687 51055376

Smallest eigenvalues:
 [1]  0.49598739  0.47153020  0.38643072  0.32012031  0.29891131  0.28403887
 [7]  0.19823060  0.10982614 -0.07062857 -1.37500070

Largest  eigenvalues:
 [1] 64122822 60164936 57021753 56138603 54995170 53078490 52399287 52108555
 [9] 51936459 51337943

Smallest eigenvalues:
 [1]  0.43790307  0.42965487  0.42093261  0.39689484  0.32490137  0.29326572
 [7]  0.18560769  0.14404229  0.08376391 -5.96082852

Largest  eigenvalues:
 [1] 62395166 59918541 56974262 55364335 54878954 53654648 52038522 52011692
 [9] 51105441 50938925

Smallest eigenvalues:
 [1]  0.58033472  0.55348785  0.55319654  0.46123111  0.39062386  0.33984309
 [7]  0.33279145  0.26923419  0.26738863 -0.02851748

Largest  eigenvalues:
 [1] 63921647 60853449 57697019 56174340 55496605 53631706 52174747 52131082
 [9] 52016515 50972321

Smallest eigenvalues:
 [1]  0.44672618  0.42344827  0.28009525  0.21728263  0.04270283 -0.24956196
 [7] -0.38973148 -0.65082647 -1.04833091 -1.20644654

Largest  eigenvalues:
 [1] 64033331 60440040 57434177 55940394 55471909 53570874 52698263 52079971
 [9] 51945936 51654200

Smallest eigenvalues:
 [1]  5.229017e-01  4.872134e-01  4.091669e-01  3.871437e-01  3.374349e-01
 [6]  2.724708e-01  2.646559e-02  4.953285e-05 -2.159932e-01 -1.022007e+01

Largest  eigenvalues:
 [1] 64585766 60772815 57768232 55733029 55649730 54203728 52804990 52194973
 [9] 51786908 51641055

Smallest eigenvalues:
 [1]   0.39485902   0.35743264   0.29258255   0.26565283   0.21072465
 [6]   0.05240952  -0.52427941  -1.78479060  -3.69658365 -13.50641203

Largest  eigenvalues:
 [1] 65252481 60701004 58545524 56854701 55362679 54052209 52863939 52717160
 [9] 52422373 51850961

Smallest eigenvalues:
 [1]   0.4260388   0.3843881   0.3199751   0.2957491   0.2919985   0.2727853
 [7]   0.2296530   0.1868074  -0.2691620 -33.6905296

Largest  eigenvalues:
 [1] 64659464 60283454 57135113 56598090 54910010 53312651 52638118 51763427
 [9] 51735213 50828911

Smallest eigenvalues:
 [1]  0.45245959  0.43137403  0.42789055  0.41377461  0.27000240  0.15589950
 [7]  0.06469077  0.02853310 -0.55176870 -4.58658188

Largest  eigenvalues:
 [1] 65043370 60333388 57283807 56284134 55269108 53172234 52410858 52087600
 [9] 51866501 51260698

Smallest eigenvalues:
 [1]  0.39484097  0.32028836  0.28356366  0.26924378  0.16560932  0.02345127
 [7] -0.29873418 -0.54655779 -1.30287880 -3.55914105

Largest  eigenvalues:
 [1] 63300354 59384292 56769794 55386602 54802349 53057496 51936379 51613263
 [9] 51292005 50570245

Smallest eigenvalues:
 [1]  0.5090463  0.4855877  0.4854849  0.4402381  0.3986666  0.3634851
 [7]  0.3071932  0.2615275  0.1640894 -0.4264008

Largest  eigenvalues:
 [1] 63605236 59899879 56995324 55933483 54689395 53049682 51927081 51768912
 [9] 51065334 50474857

Smallest eigenvalues:
 [1]  0.4426110  0.3924150  0.3596015  0.3576191  0.2842544  0.2478722
 [7]  0.2419023  0.2189636 -0.6422768 -1.0990688

Largest  eigenvalues:
 [1] 65854651 60392332 58206567 57219409 54917368 53739538 53203900 51959474
 [9] 51769853 51272527

Smallest eigenvalues:
 [1]  0.4949781  0.4140768  0.3787345  0.3448595  0.3333660  0.3259888
 [7]  0.2844763  0.2524878  0.1310555 -1.6280998

Largest  eigenvalues:
 [1] 64238811 60040281 57171062 56542604 54825437 53367394 52436649 52229641
 [9] 51998420 51034604

Smallest eigenvalues:
 [1]  0.35386660  0.31129898  0.27713572  0.26879827  0.25843558  0.23912535
 [7]  0.17438173  0.06320406 -0.12203291 -1.33315029

Largest  eigenvalues:
 [1] 66317305 60312688 58051522 56936628 55235273 53884129 52940023 52699727
 [9] 51739837 51548984

Smallest eigenvalues:
 [1]  0.5510319  0.5161116  0.5037409  0.4154655  0.4120026  0.3990238
 [7]  0.3271287  0.2679941  0.2270957 -0.1703969

Largest  eigenvalues:
 [1] 64154331 60503779 57492130 55541542 55345073 53710495 51905311 51791781
 [9] 51718372 51017918

Smallest eigenvalues:
 [1]   0.4462222   0.4413162   0.3764029   0.3592977   0.2907381   0.2880201
 [7]   0.2393497   0.1297328  -4.4514676 -15.6981149

Largest  eigenvalues:
 [1] 63816159 60564082 57121921 55900641 55222074 54073102 51895720 51650771
 [9] 51268021 50550616

Smallest eigenvalues:
 [1]  0.581633838  0.494953119  0.465368073  0.406638838  0.325886603
 [6]  0.313158887  0.306838249  0.268819250  0.207593516 -0.009696508

Largest  eigenvalues:
 [1] 65146062 60099226 56879229 56228445 54718501 52981955 52338662 51812001
 [9] 51147366 51014058

Smallest eigenvalues:
 [1]   0.398131529   0.381355802   0.364193841   0.321923968   0.318962823
 [6]   0.287641207   0.199177536   0.175516353   0.008682012 -13.697321706

Largest  eigenvalues:
 [1] 62586258 59671900 56939990 55172669 54620691 53391229 51834535 51496248
 [9] 50957699 50791267

Smallest eigenvalues:
 [1]  0.5373549  0.3872080  0.3834492  0.3232014  0.3185726  0.3099545
 [7]  0.2930033 -0.3948456 -0.6872954 -0.7143613

Largest  eigenvalues:
 [1] 65016429 60373698 57780454 56620777 55399207 53834880 52838026 52743138
 [9] 52149093 51270082

Smallest eigenvalues:
 [1]   0.4628780   0.3568853   0.3260001   0.2822877   0.2800484   0.2474752
 [7]   0.2427732   0.2266537   0.2103802 -46.3683064

Largest  eigenvalues:
 [1] 63598151 59883891 57031902 55800920 54973653 53321992 51884066 51850233
 [9] 51779028 51005041

Smallest eigenvalues:
 [1]  0.5545398  0.5217730  0.5112008  0.4545997  0.4518587  0.3429025
 [7]  0.2798084  0.2561103  0.1991687 -0.1232933

Largest  eigenvalues:
 [1] 64484433 60315178 57468264 55982883 54868379 53522754 52060384 52016813
 [9] 51755214 51244827

Smallest eigenvalues:
 [1]  0.58673801  0.56720582  0.50854628  0.40485383  0.39769796  0.35089211
 [7]  0.25830660  0.22392965  0.01674273 -0.93324220

Largest  eigenvalues:
 [1] 63886977 60729946 57621728 55869068 55771665 54311748 52564797 52165203
 [9] 51889929 51282359

Smallest eigenvalues:
 [1]   0.34698327   0.24479120   0.21234660   0.19986008   0.17859472
 [6]   0.09196713   0.06446403  -0.22413795 -14.59909836 -21.32771476

Largest  eigenvalues:
 [1] 64865361 60133172 56897101 56342744 55436304 53807472 52311100 52247735
 [9] 51796752 51360835

Smallest eigenvalues:
 [1]  0.37312771  0.37184272  0.36667553  0.32592863  0.02734883  0.02222577
 [7] -0.06980914 -0.16022570 -0.81788154 -1.96318679

Largest  eigenvalues:
 [1] 64687280 59339129 56755609 55437233 53972644 52396293 51836459 51311588
 [9] 50960750 50905212

Smallest eigenvalues:
 [1]  0.5897315  0.5828536  0.5721948  0.5049707  0.4852852  0.3320432
 [7]  0.3168799  0.2096651  0.1794736 -0.9524993

Largest  eigenvalues:
 [1] 64715781 60298513 56894736 56242623 55206968 53365362 52215443 52039307
 [9] 51799506 50854229

Smallest eigenvalues:
 [1]  0.4642808  0.4515403  0.4476178  0.3966770  0.3521420  0.2985550
 [7]  0.2366061  0.1849280  0.1127254 -0.6650059

Largest  eigenvalues:
 [1] 65738517 60204478 57370096 56469144 55383243 53559289 52556160 52479965
 [9] 51578968 51266802

Smallest eigenvalues:
 [1]  0.5572239  0.4581508  0.4485191  0.3912046  0.3837334  0.2791748
 [7]  0.2131950  0.1473619  0.1430001 -0.2701492

Largest  eigenvalues:
 [1] 65247883 60923462 57981055 56172890 56056063 54551032 52922420 52639435
 [9] 52234702 51988180

Smallest eigenvalues:
 [1]  0.4278794  0.3476179  0.3183024  0.2369793  0.2132186  0.1871104
 [7] -0.1011245 -0.2236885 -5.7885355 -5.9580871

Largest  eigenvalues:
 [1] 64286370 60488102 57529748 55757762 55600341 54161487 52751630 52529613
 [9] 51838513 51656311

Smallest eigenvalues:
 [1]  0.46965636  0.38818181  0.23838787  0.21927810  0.12616960  0.02622104
 [7] -0.49254969 -0.58047406 -0.61184724 -0.66725288

Largest  eigenvalues:
 [1] 62967702 59133922 56397725 55423130 54243728 52665853 51389320 51213887
 [9] 51164835 50103864

Smallest eigenvalues:
 [1]   0.42825641   0.39942765   0.36942551   0.33032954   0.26166593
 [6]   0.23420744   0.23011344   0.11908614  -0.09278426 -26.28260262

Largest  eigenvalues:
 [1] 62750030 59768004 56684393 55236055 55054427 53387009 52023520 51215090
 [9] 51066586 50587866

Smallest eigenvalues:
 [1]  0.4816451  0.4668635  0.2941645  0.2504987  0.2145759  0.1991994
 [7]  0.1981649  0.1351890  0.1006855 -0.8509431

Largest  eigenvalues:
 [1] 63257582 60351017 57108991 55608188 55059808 53621656 51913832 51618678
 [9] 50875572 50648289

Smallest eigenvalues:
 [1]  0.54546501  0.51450324  0.48724536  0.45671083  0.39243157  0.36990241
 [7]  0.34163215  0.05913585 -0.11125103 -0.11468128

Largest  eigenvalues:
 [1] 64991354 59947584 57046232 56478948 54597889 53066801 52412655 51765989
 [9] 51355717 50773118

Smallest eigenvalues:
 [1]  0.44728753  0.35795645  0.33933782  0.32804442  0.21225882  0.21049584
 [7]  0.15980083  0.14846945 -0.06079634 -0.18078756

Largest  eigenvalues:
 [1] 67266219 60669648 57623456 56922178 55185723 53488630 53024284 52573740
 [9] 52055097 51973084

Smallest eigenvalues:
 [1]  0.4866668  0.4786676  0.4489369  0.3615731  0.3022249  0.2778196
 [7]  0.2182407 -0.1331183 -0.2604480 -0.8549073

Largest  eigenvalues:
 [1] 64523437 59928819 57432788 55326168 55255790 53452493 52103472 51758429
 [9] 51592691 50858343

Smallest eigenvalues:
 [1]   0.43850409   0.38427917   0.25357374   0.24798042  -0.05440934
 [6]  -0.24140800  -0.71673711  -4.93092252  -8.02792029 -20.90923070

Largest  eigenvalues:
 [1] 65249773 60106396 57294159 56064667 54739048 53252048 52352397 51677287
 [9] 51463083 50458460

Smallest eigenvalues:
 [1]  0.5991883  0.5281029  0.5178836  0.4622291  0.4454491  0.4059809
 [7]  0.2962903  0.1331650 -0.1296811 -1.1521993

Largest  eigenvalues:
 [1] 64526084 60285005 57265766 56190777 55278706 53471709 52690261 52267597
 [9] 51623127 51275306

Smallest eigenvalues:
 [1]  0.4188800  0.3487356  0.3279679  0.3269908  0.3075070  0.2495696
 [7]  0.2208671  0.2091194 -1.3076344 -4.1788323

Largest  eigenvalues:
 [1] 64366927 60693923 57820655 55579550 55544610 54149107 52438327 51997257
 [9] 51667113 51598606

Smallest eigenvalues:
 [1]   0.4661149   0.4407696   0.3560121   0.3428487   0.3228056   0.2507656
 [7]   0.1896730   0.1462090  -2.6825332 -28.2155618

Largest  eigenvalues:
 [1] 61986590 59683254 56485676 55499970 54402611 53489888 51767450 51112500
 [9] 50399418 50229598

Smallest eigenvalues:
 [1]  0.5329010  0.4513208  0.4414890  0.3713458  0.3555911  0.3053348
 [7]  0.2269964 -0.2588324 -0.3180586 -0.4310804

Largest  eigenvalues:
 [1] 65358608 60603954 58086456 56869578 55079701 53290685 52894107 52768550
 [9] 51954210 51784438

Smallest eigenvalues:
 [1]  0.5617092  0.5354533  0.4306728  0.4148428  0.3158316  0.3071711
 [7]  0.2266957  0.2207708  0.2206010 -0.5619875

Largest  eigenvalues:
 [1] 64734970 60953231 57507971 56017674 55625522 54040222 52357535 52323881
 [9] 52120162 51547714

Smallest eigenvalues:
 [1]   0.4700373   0.4265857   0.4048073   0.3963303   0.3359164   0.3233833
 [7]   0.2706780   0.2436359  -0.2125806 -10.2950976

Largest  eigenvalues:
 [1] 64422931 60170357 57548662 56342241 55244688 53709279 52339785 51944408
 [9] 51928136 50815782

Smallest eigenvalues:
 [1]  0.596600063  0.580191868  0.541670645  0.530609083  0.497916460
 [6]  0.436080669  0.306870086  0.241490864  0.169635234 -0.001726538

Largest  eigenvalues:
 [1] 64294945 60516733 57663696 55909461 55163800 53264149 52199414 52112162
 [9] 51571047 51089777

Smallest eigenvalues:
 [1]  0.4961910  0.4902026  0.4806140  0.4553746  0.4390719  0.2595080
 [7]  0.1791196 -0.2440164 -0.6227254 -3.0845770

Largest  eigenvalues:
 [1] 64387207 60315566 57771970 55909323 55112907 53611629 52287926 52091550
 [9] 51807467 51117083

Smallest eigenvalues:
 [1]   0.3165348   0.2868056   0.2435300   0.2355389   0.1478802   0.1392101
 [7]   0.1313882  -1.8590454  -7.4206405 -12.6158730

Largest  eigenvalues:
 [1] 64169161 60745713 57632644 55876968 55282915 54205999 52662057 52153117
 [9] 51798160 51468295

Smallest eigenvalues:
 [1]   0.4425852   0.4177886   0.3940021   0.2782246   0.1765252  -0.2251043
 [7]  -1.3219801  -2.1602911  -7.2638773 -16.2835269

Largest  eigenvalues:
 [1] 65463398 59849089 57004151 56818991 54575699 52753964 52405633 51836765
 [9] 51404133 50852713

Smallest eigenvalues:
 [1]  0.595002753  0.499714627  0.496328368  0.429235879  0.405218161
 [6]  0.382180088  0.262937485  0.200909666  0.002652293 -0.499905603

Largest  eigenvalues:
 [1] 64468475 60624678 57449008 55784301 55496268 53769662 52911557 51938199
 [9] 51561082 51431505

Smallest eigenvalues:
 [1]   0.402866174   0.391950759   0.326876034   0.280944028   0.274173956
 [6]   0.182973124  -0.005183514  -0.534444484  -1.481506686 -21.430849617

Largest  eigenvalues:
 [1] 64859279 60681333 57672223 55802533 55648619 54313291 52602615 52348499
 [9] 51829606 51524747

Smallest eigenvalues:
 [1]  0.4119543  0.4046272  0.3730116  0.3507124  0.3311649  0.2710863
 [7]  0.1903433  0.1051565 -0.1564091 -0.1932710

Largest  eigenvalues:
 [1] 65973088 60914917 57724318 56058834 55645614 53826329 52704344 52195036
 [9] 51983071 51843962

Smallest eigenvalues:
 [1]  0.47219064  0.38574298  0.37339287  0.34166300  0.33395930  0.27276534
 [7]  0.24513438  0.22089711  0.03058645 -1.93180410

Largest  eigenvalues:
 [1] 65625374 60427104 57648340 56737618 55186455 53755204 52605260 52450966
 [9] 51990118 51601657

Smallest eigenvalues:
 [1]  0.5020374  0.4191968  0.3869501  0.2561177  0.2272818  0.2118193
 [7] -0.2205335 -0.3867581 -1.6421047 -2.6228899

Largest  eigenvalues:
 [1] 66398218 61009272 58434454 56750705 55942717 54161086 53024288 52873617
 [9] 52418817 52080028

Smallest eigenvalues:
 [1]  0.38320997  0.36041026  0.32108723  0.31321878  0.24711360  0.23687529
 [7]  0.18993739  0.09900609 -0.11287443 -7.11540963

Largest  eigenvalues:
 [1] 65209274 59383444 56863153 56030463 54684419 53108447 51999627 51305003
 [9] 51194510 50584511

Smallest eigenvalues:
 [1]  0.44748223  0.41966422  0.40973741  0.29212575  0.24848101  0.24345831
 [7]  0.20466526  0.09570455 -0.10115300 -0.28204296

Largest  eigenvalues:
 [1] 66835808 61391501 58492227 56927542 55580044 53831180 53109222 52908205
 [9] 52086839 52022214

Smallest eigenvalues:
 [1]  0.55870135  0.52577165  0.47899852  0.46535595  0.46441455  0.44421676
 [7]  0.23913658  0.23565963  0.04982777 -0.05214577

Largest  eigenvalues:
 [1] 62705148 60130743 56777315 55465905 55262063 53405581 52249528 51664529
 [9] 51217419 50464234

Smallest eigenvalues:
 [1]  0.6335170  0.6058209  0.5532983  0.5524656  0.4573758  0.4543889
 [7]  0.3424434  0.2313038  0.2235777 -0.8873691

Largest  eigenvalues:
 [1] 64776839 60419149 57624121 56267497 55176198 53743129 52237618 52009423
 [9] 51825588 50989582

Smallest eigenvalues:
 [1]  0.4809460  0.4000531  0.3643749  0.3633007  0.3445975  0.3377922
 [7]  0.2070527  0.1865913 -0.5667321 -2.3734881

Largest  eigenvalues:
 [1] 64019446 59980557 57263975 56189248 54889406 53251221 52132000 52064996
 [9] 51700317 50635496

Smallest eigenvalues:
 [1]  0.6369606  0.5302138  0.5200224  0.4815634  0.4375574  0.3863850
 [7]  0.3701213  0.3085190  0.2146247 -0.1748042

Largest  eigenvalues:
 [1] 65155071 61211659 58338330 56544796 56325039 54708452 53472067 52642735
 [9] 52528081 51940575

Smallest eigenvalues:
 [1]  0.4785571  0.4746846  0.4410983  0.4118512  0.3841887  0.3668965
 [7]  0.3277161  0.1811739  0.1408216 -0.6609918

Largest  eigenvalues:
 [1] 64909126 61115423 58179149 56212328 56057032 54498844 52544017 52510847
 [9] 52190004 51690883

Smallest eigenvalues:
 [1]  0.47117178  0.46469081  0.41250110  0.34659523  0.34399625  0.32194163
 [7]  0.31081005  0.12085568  0.06078797 -2.71815573

Largest  eigenvalues:
 [1] 64350075 59518803 56663317 55984812 54508994 52817657 51998067 51519314
 [9] 51497351 50560359

Smallest eigenvalues:
 [1]  0.4346896  0.3733635  0.3646124  0.3505277  0.2973378  0.2606022
 [7]  0.2281173  0.1832396 -1.3018144 -6.9913078

Largest  eigenvalues:
 [1] 64948744 60146340 57352168 56005045 55060614 53669277 52084438 51805155
 [9] 51760344 50830627

Smallest eigenvalues:
 [1]   0.40427683   0.34842963   0.30804670   0.24481902   0.15717935
 [6]   0.05892585  -0.00211258  -0.78667016  -1.56359745 -12.26724365

Largest  eigenvalues:
 [1] 65621086 60871049 58196565 56339127 55622847 54115936 52829808 52349538
 [9] 52103273 51605139

Smallest eigenvalues:
 [1]  0.51651388  0.48494782  0.46418786  0.46389734  0.44118384  0.41089926
 [7]  0.40272391  0.30869897  0.09280225 -0.11407244

Largest  eigenvalues:
 [1] 63662340 59634720 57365275 55432102 54967724 53265366 51598050 51544271
 [9] 51452041 50482966

Smallest eigenvalues:
 [1]  0.32354642  0.32169932  0.26056856  0.25879940  0.21499204  0.11053373
 [7] -0.08515092 -0.54543152 -1.41498525 -2.72793053

Largest  eigenvalues:
 [1] 65450136 59518139 57091560 56065267 54313443 52782946 52178448 51804085
 [9] 51517405 51122820

Smallest eigenvalues:
 [1]  0.4367802  0.3624695  0.3374817  0.3349788  0.2379174  0.2035338
 [7] -1.1352942 -1.7838715 -3.0375818 -8.8461238

Largest  eigenvalues:
 [1] 65747952 60107712 57451055 57318072 54778518 53192069 53168751 52449707
 [9] 52265871 51682659

Smallest eigenvalues:
 [1]   0.37074622   0.32964236   0.25232790   0.23409043   0.14494076
 [6]   0.13759617   0.11152770   0.07757987  -0.57253582 -13.93100786

Largest  eigenvalues:
 [1] 65781897 59924479 57497598 56680141 54718461 53090438 52722620 51923643
 [9] 51659170 51122536

Smallest eigenvalues:
 [1]  0.5831168  0.5639826  0.3837977  0.3826191  0.3035591  0.2863617
 [7]  0.2745112  0.2731092  0.2431454 -1.4086800

Largest  eigenvalues:
 [1] 65137463 60643966 57849733 56184126 55552678 54203133 52339115 52319215
 [9] 52256902 51332130

Smallest eigenvalues:
 [1]  0.3683887  0.3512420  0.3408925  0.3232900  0.2787079  0.2724606
 [7]  0.2245215  0.1846142 -0.2622792 -1.5402836

Largest  eigenvalues:
 [1] 64623202 60783323 57881613 56446604 55995575 54235915 52386160 52236666
 [9] 52109384 51197995

Smallest eigenvalues:
 [1]  0.46198582  0.45573780  0.43610679  0.36581319  0.35699677  0.34375384
 [7]  0.25456610  0.14674583  0.08096377 -0.26255144

Largest  eigenvalues:
 [1] 64448147 61161415 57735874 56329391 55854340 54270310 52482906 52143619
 [9] 52012443 51288637

Smallest eigenvalues:
 [1]  0.4454687  0.4390658  0.4226786  0.3351076  0.3039356  0.2955374
 [7]  0.2863432  0.2531215  0.1173429 -0.3254932

Largest  eigenvalues:
 [1] 63319878 59730634 56756909 55304533 54739660 53105694 51500323 51455907
 [9] 51228466 50587355

Smallest eigenvalues:
 [1]  0.50226669  0.45125814  0.41137682  0.33723767  0.33328902  0.21965764
 [7]  0.12710130  0.04384981 -0.12613060 -1.86189819

Largest  eigenvalues:
 [1] 61730491 59517124 56837496 54670470 54418834 52959528 51681618 51557314
 [9] 50819779 50630242

Smallest eigenvalues:
 [1]  0.4082084  0.3809722  0.3175078  0.3117375  0.3034126  0.2684511
 [7]  0.2369499  0.2207037 -0.3627658 -0.9675033

Largest  eigenvalues:
 [1] 64127099 60297681 57598985 55669821 55220419 53732401 51926088 51745300
 [9] 51737051 51057534

Smallest eigenvalues:
 [1]  0.472090059  0.457929953  0.372775765  0.320080079  0.255523639
 [6]  0.234289583  0.228135878  0.005882272 -0.007653789 -0.180203494

Largest  eigenvalues:
 [1] 65302765 60951090 58156776 55806616 55607269 54387828 52698923 52422608
 [9] 51864350 51707824

Smallest eigenvalues:
 [1]  0.5217158  0.4826237  0.3938609  0.3764443  0.3246314  0.2812599
 [7]  0.2804431  0.2751018 -0.8850331 -1.4925676

Largest  eigenvalues:
 [1] 64889062 59795307 57211664 55956867 54999276 53616969 52016384 51972910
 [9] 51716295 51143142

Smallest eigenvalues:
 [1]  0.42296270  0.41268900  0.40888269  0.37646961  0.31108342  0.27795950
 [7]  0.19224440  0.16648144  0.15671339 -0.09273714

Largest  eigenvalues:
 [1] 64267331 60084489 57393624 55524141 55430005 53850331 52270825 52006573
 [9] 51570610 51225934

Smallest eigenvalues:
 [1]  3.193495e-01  2.013858e-01  9.200554e-02  8.926988e-02  9.936771e-04
 [6] -2.215423e-02 -1.101043e-01 -8.727731e-01 -1.565285e+01 -1.840693e+01

Largest  eigenvalues:
 [1] 62460189 60161864 56292925 55248765 55189474 53442812 51989511 51885954
 [9] 50976871 50455187

Smallest eigenvalues:
 [1]  0.5385928  0.4965616  0.4868131  0.4751368  0.4265040  0.4066629
 [7]  0.3680893  0.3539590  0.2986524 -0.9663422

Largest  eigenvalues:
 [1] 65287550 60627157 57758124 56718238 55491871 53974496 52592540 52320014
 [9] 51865157 51279229

Smallest eigenvalues:
 [1]  0.56935255  0.56354283  0.54377823  0.53103914  0.47037046  0.37939205
 [7]  0.36660544  0.33274338  0.31475206 -0.05407509

Largest  eigenvalues:
 [1] 65572468 61072960 58293329 57137740 55616490 53992113 53098514 52812922
 [9] 52335700 51810663

Smallest eigenvalues:
 [1]  0.39771853  0.36605174  0.35853521  0.28550846  0.22965467 -0.06847966
 [7] -0.30470030 -1.54637995 -2.25399036 -9.44133852

Largest  eigenvalues:
 [1] 63105488 60083343 57030489 55284656 55239587 53482165 52226953 51869946
 [9] 51269099 51061421

Smallest eigenvalues:
 [1]  0.5171361  0.4865891  0.4518466  0.4104234  0.3556949  0.2574824
 [7]  0.2164616  0.1135890 -0.4051819 -0.4166858

Largest  eigenvalues:
 [1] 64173327 60655314 58378402 55888399 55454987 54630121 52780321 52214480
 [9] 51606673 51422334

Smallest eigenvalues:
 [1]  0.4029243  0.4018202  0.3899124  0.3105355  0.2693868  0.2628813
 [7]  0.2519655  0.2371773  0.2353172 -0.7939161

Largest  eigenvalues:
 [1] 64607546 60727005 57790348 55740800 55681926 54315022 52456711 52037329
 [9] 51845447 51196923

Smallest eigenvalues:
 [1]  0.366884917  0.275665985  0.218540002  0.007691799 -0.006153075
 [6] -0.191619157 -0.672055184 -0.864089060 -0.901121715 -1.334254853

Largest  eigenvalues:
 [1] 62099733 60216656 56901223 55598598 55188973 53763432 52376058 51891639
 [9] 50930336 50819007

Smallest eigenvalues:
 [1]  0.42610577  0.33129939  0.32683798  0.26952448  0.25144868  0.24254517
 [7]  0.11172515  0.07045316 -2.62996106 -6.92126661

Largest  eigenvalues:
 [1] 63799434 60628491 57881872 55808186 55791607 54155629 52676672 52200287
 [9] 51794047 51657184

Smallest eigenvalues:
 [1]  0.5487412  0.4565224  0.4462112  0.4244772  0.4183680  0.3785733
 [7]  0.3549216  0.3367931  0.3349219 -0.4078569

Largest  eigenvalues:
 [1] 63489102 59887664 56903379 55705661 54786918 53210919 51700762 51474477
 [9] 51185618 50363963

Smallest eigenvalues:
 [1]  0.5405838  0.4536518  0.4077796  0.3958012  0.3701455  0.3227531
 [7]  0.2808164  0.2673987  0.1986518 -1.3182308

Largest  eigenvalues:
 [1] 64164268 60062226 56977050 56058612 55020514 53400863 52003669 51861822
 [9] 51733894 51039032

Smallest eigenvalues:
 [1]  0.4270398  0.2864364  0.2571402  0.2373492  0.2039900  0.1876548
 [7]  0.1817205 -2.1896355 -3.1294113 -6.5270451

Largest  eigenvalues:
 [1] 64892434 59937071 56962640 56583702 54665060 53176919 52351480 52247487
 [9] 51744908 51006328

Smallest eigenvalues:
 [1]   0.5341144   0.4107927   0.4005878   0.3090971   0.2481083   0.2461680
 [7]  -0.1281613  -0.2992312  -0.6081750 -19.7901473

Largest  eigenvalues:
 [1] 65382267 60099102 57087956 55870202 54976591 53418825 52080401 52032896
 [9] 51658714 51250411

Smallest eigenvalues:
 [1]  0.51259405  0.50985427  0.46812844  0.38045732  0.36816855  0.36809214
 [7]  0.27374988  0.23827465 -0.02485813 -0.38040892

Largest  eigenvalues:
 [1] 62650980 59780044 56743963 55194066 54722693 53315350 51948454 51735596
 [9] 50874021 50628503

Smallest eigenvalues:
 [1]  0.50521696  0.46510991  0.43458252  0.39244545  0.38267005  0.35211441
 [7]  0.34020312  0.09802594  0.04738960 -0.02482130

Largest  eigenvalues:
 [1] 63739581 60305508 57361615 55468862 54863352 53439318 51993580 51522328
 [9] 51517327 51152138

Smallest eigenvalues:
 [1]  0.46761774  0.42545473  0.42043402  0.38920906  0.30095922  0.27767208
 [7]  0.25500262  0.17357523  0.17339234 -0.07817236

Largest  eigenvalues:
 [1] 64608709 61206609 58213748 56061023 55700191 54158954 52831963 52208762
 [9] 52180561 51948289

Smallest eigenvalues:
 [1]  0.4989402  0.4619286  0.3987685  0.3691881  0.3585004  0.2764301
 [7]  0.2401817 -0.1596020 -0.2613991 -0.5504757

Largest  eigenvalues:
 [1] 63736179 59813801 57434454 55337619 54933574 53661507 51936093 51500664
 [9] 51226749 50693658

Smallest eigenvalues:
 [1]  0.48503699  0.43655895  0.40992494  0.38106473  0.34250827  0.32877577
 [7]  0.28788444  0.21054488  0.16162259 -0.03885352

Largest  eigenvalues:
 [1] 64206663 59447133 57262210 55571173 54493701 53059324 51848335 51729715
 [9] 51275121 50839147

Smallest eigenvalues:
 [1]   0.4441993   0.4173982   0.4049454   0.3850415   0.3815862   0.3424496
 [7]   0.3171507   0.2675028  -0.3561928 -33.5318669

Largest  eigenvalues:
 [1] 66225916 60488782 57869109 57080502 55102329 53714415 53090096 51956956
 [9] 51913401 51097694

Smallest eigenvalues:
 [1]  0.4457368  0.3469112  0.3111173  0.2777945  0.2741597  0.2596741
 [7] -0.1852783 -0.4284197 -3.5392829 -4.9668615

Largest  eigenvalues:
 [1] 65313613 59957328 57855888 56466579 55224343 54015896 52719527 52402783
 [9] 52395980 51834450

Smallest eigenvalues:
 [1]  0.3377719  0.3016237  0.2998872  0.2683010  0.2435994  0.2341296
 [7] -0.6551704 -0.7253914 -1.4010014 -9.6362314

Largest  eigenvalues:
 [1] 62368185 59927158 57522380 55937590 54214348 54102724 52385871 52107340
 [9] 51047245 50735455

Smallest eigenvalues:
 [1]   0.260392160   0.246198173   0.186251639   0.137679517   0.081803619
 [6]   0.044102629   0.018894230   0.005853617  -0.990973008 -17.603513577

Largest  eigenvalues:
 [1] 62908863 60733371 57767519 55569707 55207542 53982085 52193411 51845545
 [9] 51372746 51224998

Smallest eigenvalues:
 [1]  0.6131991  0.5135985  0.5011057  0.4633477  0.3946598  0.3463550
 [7]  0.3091917  0.2928958  0.2560634 -1.0221547

Largest  eigenvalues:
 [1] 65238470 61076332 57875594 56809465 55393005 53901856 52814122 52722993
 [9] 52182180 51926616

Smallest eigenvalues:
 [1]  0.5355943  0.4957699  0.4848498  0.4499409  0.4378068  0.3363424
 [7]  0.2886285  0.2509242  0.2167049 -0.1989357

Largest  eigenvalues:
 [1] 65458743 60026275 57834345 56593570 54697921 53062377 52831881 51795006
 [9] 51477791 50890314

Smallest eigenvalues:
 [1]   0.4387782   0.4277284   0.4100086   0.3495594   0.3489280   0.2971214
 [7]   0.1925726   0.1919807  -0.5387739 -21.0813380

Largest  eigenvalues:
 [1] 65004417 60376581 57702056 56532773 55130848 53414412 52714241 52001861
 [9] 51906824 50990053

Smallest eigenvalues:
 [1]  0.5256431  0.4572065  0.4491234  0.4113677  0.3850087  0.3790004
 [7]  0.3171255  0.1960669  0.1807790 -1.9247137

Largest  eigenvalues:
 [1] 62940405 60269618 57575250 55412373 54921097 53843621 51914001 51808395
 [9] 51081605 50929350

Smallest eigenvalues:
 [1]  0.6205814  0.5906973  0.5541414  0.5475933  0.4521749  0.3755399
 [7]  0.2649637  0.2049598  0.1841806 -0.8680196

Largest  eigenvalues:
 [1] 64353659 60059015 56872269 55844029 55007882 53352383 51725673 51651644
 [9] 51422861 50519991

Smallest eigenvalues:
 [1]   0.12920234   0.07653261   0.06371167  -0.04779952  -0.34083850
 [6]  -1.92409911  -9.72468340 -27.61676598 -33.29934368 -44.89290360

Largest  eigenvalues:
 [1] 65180621 60207937 56484016 56340252 55208204 53330429 52327657 52303894
 [9] 52194607 51147638

Smallest eigenvalues:
 [1]  0.37429053  0.34924468  0.34516069  0.34213494  0.28880090  0.09359304
 [7]  0.07296078  0.05012915 -1.28637025 -3.38288881

Largest  eigenvalues:
 [1] 62689806 59049125 56601700 55003811 54732128 53093561 51879078 51489399
 [9] 50876470 50486287

Smallest eigenvalues:
 [1]  0.47232773  0.45977329  0.43119076  0.36240963  0.32969283  0.25910272
 [7]  0.23378894  0.02993916 -0.18171418 -0.24359475

Largest  eigenvalues:
 [1] 62234920 59332481 56892529 54813651 54477956 52900682 51874847 51266706
 [9] 50945506 50799773

Smallest eigenvalues:
 [1]  0.4153222  0.3721074  0.3648583  0.3597596  0.3279138  0.2510410
 [7]  0.2327371  0.1508180  0.1263878 -0.7126174

Largest  eigenvalues:
 [1] 63577332 60097602 57111281 55502187 55245232 53909106 52332234 51916698
 [9] 51393220 51173762

Smallest eigenvalues:
 [1]  0.5033041  0.5028158  0.3602542  0.3423207  0.3097934  0.2378690
 [7]  0.2302833  0.1502926 -1.0370043 -5.8579513

Largest  eigenvalues:
 [1] 64680500 60901910 57293572 56249877 55814252 54005386 52474461 52274526
 [9] 51954039 51479185

Smallest eigenvalues:
 [1]  0.4363476  0.4250772  0.3885742  0.3249050  0.2703968  0.2699337
 [7]  0.2582783 -0.1438690 -0.3453970 -0.7135927

Largest  eigenvalues:
 [1] 64614830 60386060 57820301 56550732 55390296 53923850 52997069 52582632
 [9] 52169874 51713304

Smallest eigenvalues:
 [1]  0.4570453  0.4069215  0.3449191  0.3265189  0.3156249  0.2754068
 [7]  0.2434499  0.1960337 -0.2192655 -2.0999734

Largest  eigenvalues:
 [1] 64012457 60461494 57354408 56073168 55690807 54014159 52241063 52112263
 [9] 52017083 50998877

Smallest eigenvalues:
 [1]  0.4798902  0.4523935  0.3724019  0.3239674  0.2783808  0.2624360
 [7]  0.2622589  0.1560630  0.1261194 -0.1911510

Largest  eigenvalues:
 [1] 63582006 60115770 57810428 55284706 55250052 53883565 52254894 52162502
 [9] 51444836 51278298

Smallest eigenvalues:
 [1]  0.473308256  0.401127285  0.334910641  0.322614510  0.286410878
 [6]  0.283300887  0.194000008  0.047672795 -0.004845634 -0.292629510

Largest  eigenvalues:
 [1] 64558938 61130217 57782812 56540130 55437595 53800198 52441661 52407814
 [9] 51749690 51345857

Smallest eigenvalues:
 [1]  0.4848754  0.4563133  0.4359468  0.3283973  0.3072911  0.2526044
 [7]  0.1913358 -0.1546851 -0.2407034 -4.5787521

Largest  eigenvalues:
 [1] 61991750 60031365 56568428 55263409 54337442 53486483 52057173 51534840
 [9] 50573657 50333762

Smallest eigenvalues:
 [1]  0.4570738  0.3474239  0.3350057  0.2766244  0.2600711  0.2315790
 [7]  0.2209667  0.1974956 -1.7134918 -5.2846710

Largest  eigenvalues:
 [1] 64274292 60140438 57252366 56165528 54930888 53579782 52358009 52237435
 [9] 52197215 51365213

Smallest eigenvalues:
 [1]  0.49670168  0.49394717  0.44829228  0.36448408  0.32831097  0.31792781
 [7]  0.10269757  0.07532116 -0.15397033 -0.20599405

Largest  eigenvalues:
 [1] 64363426 59878684 57104908 56088550 54249504 52786876 52087835 51823916
 [9] 51434253 50963480

Smallest eigenvalues:
 [1]  0.5167286  0.4824251  0.3597968  0.3111099  0.2555201  0.2021249
 [7]  0.1219693 -0.1239433 -0.8158369 -6.6270137

Largest  eigenvalues:
 [1] 63320238 60817045 57641719 56159222 55196536 54326377 52965386 52316766
 [9] 51996043 51352786

Smallest eigenvalues:
 [1]  0.50290442  0.47585084  0.47098028  0.40679262  0.33466914  0.31840766
 [7]  0.30616957  0.25841052  0.02244975 -1.47613820

Largest  eigenvalues:
 [1] 65447523 60485006 57435826 56876586 55352013 53730149 52920697 52447010
 [9] 51860555 51438062

Smallest eigenvalues:
 [1]  0.3383644  0.2979536  0.2618785  0.2103490  0.2046308  0.1647281
 [7] -0.2224727 -4.2857895 -6.4515612 -8.6066024

Largest  eigenvalues:
 [1] 66507608 61108059 58847356 57035193 55712819 54346549 53014014 52925881
 [9] 52581974 52269794

Smallest eigenvalues:
 [1]  0.4252840  0.3423662  0.3336869  0.3323679  0.2306571  0.2033730
 [7]  0.1020442 -0.2578452 -1.5659658 -5.8674456

Largest  eigenvalues:
 [1] 66077594 59809813 56904559 56805066 54488160 52998364 52539768 51375897
 [9] 51336507 50597457

Smallest eigenvalues:
 [1]  0.63793933  0.52631474  0.43413163  0.41457364  0.32760467  0.32722992
 [7]  0.29616832  0.17152286  0.05353258 -0.46194262

Largest  eigenvalues:
 [1] 63828026 60126248 57351873 55447429 54739545 53282513 51977171 51636795
 [9] 51497797 50927279

Smallest eigenvalues:
 [1]  0.5222351  0.4562282  0.4485056  0.4196149  0.4015466  0.3842206
 [7]  0.3312612  0.2452085  0.2279085 -0.7680761

Largest  eigenvalues:
 [1] 64024180 61105254 57827067 56250724 55873003 54252140 52567359 52415834
 [9] 52111082 51355014

Smallest eigenvalues:
 [1]  0.5519751  0.4872064  0.4747355  0.4578739  0.4470574  0.4217565
 [7]  0.2450505  0.1807670  0.0219168 -4.1126368

Largest  eigenvalues:
 [1] 63577667 59716110 57128273 55359317 55340230 53770377 52120032 52087750
 [9] 51340085 51059569

Smallest eigenvalues:
 [1]   0.1186554   0.0825284   0.0529728  -0.0372975  -0.1339336  -0.5006408
 [7]  -0.6340608  -5.3942508  -9.0506397 -10.7815102

Largest  eigenvalues:
 [1] 60197593 59660633 57177402 55554625 53771355 53535568 51798011 51774512
 [9] 50876604 50181561

Smallest eigenvalues:
 [1]  0.6035463  0.5954294  0.5759948  0.5109591  0.4127615  0.2858684
 [7]  0.2626945  0.2203413 -0.7094681 -0.9064164

Largest  eigenvalues:
 [1] 65283980 60389947 57340141 56593202 55224555 53487125 52489125 52288459
 [9] 52051476 51226028

Smallest eigenvalues:
 [1]   0.33051335   0.32947440   0.32208165   0.28144278   0.20115887
 [6]   0.10026024   0.02786063  -1.57545617  -5.72180767 -13.01099703

Largest  eigenvalues:
 [1] 66766159 60644655 58073269 57145833 55261515 53464085 53400369 52299392
 [9] 52034857 51386274

Smallest eigenvalues:
 [1]   0.1787263   0.1694780  -0.1508300  -0.1618422  -0.2092064  -2.6735940
 [7] -10.8811268 -13.9918489 -16.1152760 -45.2920170

Largest  eigenvalues:
 [1] 64181573 60385359 57681995 55624559 55139120 53978694 52483650 52397406
 [9] 51458610 51359352

Smallest eigenvalues:
 [1]   0.55709940   0.44304761   0.43967077   0.24651467   0.21007720
 [6]   0.07587060   0.03942532  -0.06699987  -1.22521144 -13.42529864

Largest  eigenvalues:
 [1] 63738121 60120180 57069934 55617674 55327418 53629248 52393111 52082738
 [9] 51650625 51243038

Smallest eigenvalues:
 [1]  0.31741735  0.29445243  0.26649249  0.15290198  0.14590069  0.01748872
 [7] -0.02409168 -0.97643113 -2.48616229 -2.69990715

Largest  eigenvalues:
 [1] 64645061 60039385 56551220 56093698 54579275 52924085 52139720 51588420
 [9] 51466508 50635687

Smallest eigenvalues:
 [1]   0.1898011   0.1779258  -0.2048827  -0.3105301  -0.3244568  -0.6612220
 [7]  -0.7574761  -9.0586112 -12.3224468 -45.5009116

Largest  eigenvalues:
 [1] 63169532 61208265 57581156 56074674 55009955 54392361 52306164 52170824
 [9] 51041471 50923017

Smallest eigenvalues:
 [1]  0.4469115  0.4369492  0.3852842  0.3410604  0.2868728  0.2702469
 [7]  0.1745803 -0.0855023 -0.3849818 -0.9510035

Largest  eigenvalues:
 [1] 65252960 60425611 58126205 56877061 54898749 53225959 52740829 52410286
 [9] 51893976 51624976

Smallest eigenvalues:
 [1]  0.5096993  0.4690237  0.3976463  0.3880216  0.3637760  0.3054254
 [7]  0.2829234  0.2599532  0.1933149 -0.7891419

Largest  eigenvalues:
 [1] 65924624 59684389 56611975 56340959 54443394 52705533 52350657 51798634
 [9] 51530241 51042740

Smallest eigenvalues:
 [1]  -0.1306257  -0.2182491  -0.4359008  -0.5852863  -1.1135423  -1.6209949
 [7]  -1.8196521  -2.2606164  -2.4056539 -11.1826519

Largest  eigenvalues:
 [1] 63929336 60765465 57684461 56001098 55794429 54214258 52600603 52521789
 [9] 51943063 51675518

Smallest eigenvalues:
 [1]  0.3996114  0.3851469  0.3834856  0.3747796  0.3739012  0.2204755
 [7] -0.6547359 -0.7969780 -3.7007032 -4.6063026

Largest  eigenvalues:
 [1] 65111569 59930882 57508501 56327488 54775501 53097587 52410190 52366181
 [9] 51636071 51499959

Smallest eigenvalues:
 [1]  0.49717037  0.44398068  0.33357902  0.32290876  0.16551153  0.11560995
 [7]  0.01621756 -0.31879867 -0.43762964 -6.27493168

Largest  eigenvalues:
 [1] 64756233 59566271 57041714 55570610 54146153 52653235 52048032 51750849
 [9] 51214058 51075972

Smallest eigenvalues:
 [1]  0.5280886  0.5229860  0.5163932  0.4758649  0.4746665  0.4543488
 [7]  0.3745868  0.2968540  0.2602990 -0.5961865

Largest  eigenvalues:
 [1] 64009321 60606589 57143668 56323018 55377409 53661104 52287254 52082333
 [9] 52009968 51226181

Smallest eigenvalues:
 [1]  0.42972082  0.37327617  0.32616719  0.25645898  0.25346892  0.20537717
 [7]  0.07521011 -0.02827733 -0.11018006 -0.51743350

Largest  eigenvalues:
 [1] 61290100 60031369 57133066 55819832 53867922 53851609 52174240 51635254
 [9] 50746817 50707498

Smallest eigenvalues:
 [1]   0.4838751   0.4833004   0.4393723   0.3841969   0.2933796   0.2815018
 [7]   0.2175510   0.1997441  -1.7149451 -28.3217400

Largest  eigenvalues:
 [1] 63829585 59968574 57081574 55657127 55174927 53322796 52153221 51690406
 [9] 51555364 51042939

Smallest eigenvalues:
 [1]  0.46707631  0.46191817  0.36168906  0.29191823  0.28113160  0.27180736
 [7]  0.19479707  0.04415995 -0.18954797 -1.97918844

Largest  eigenvalues:
 [1] 64718511 59452673 56622443 55988099 54291841 52823758 52016166 51700274
 [9] 51213750 50847463

Smallest eigenvalues:
 [1]  0.4660506  0.4599969  0.4131064  0.3923726  0.3892344  0.3143654
 [7]  0.2647937  0.2221240 -0.1185449 -3.4275015

Largest  eigenvalues:
 [1] 63537445 60421480 57546608 55664746 55451003 54147554 52344905 52314703
 [9] 51575202 51251961

Smallest eigenvalues:
 [1]  0.4056294  0.3800859  0.3677871  0.3472109  0.2619507  0.2334085
 [7]  0.1778901  0.1465146 -0.3718325 -0.6810458

Largest  eigenvalues:
 [1] 65145399 61156549 58473966 56551354 55873371 54296463 53116771 52557560
 [9] 52053291 51930585

Smallest eigenvalues:
 [1]  0.4047533  0.3961447  0.3761853  0.3121273  0.3105423  0.2957181
 [7]  0.2280731  0.2215193 -0.7267893 -1.1710817

Largest  eigenvalues:
 [1] 64978227 59900672 57844393 56155312 55024515 53940857 52191911 52158163
 [9] 51779626 51200255

Smallest eigenvalues:
 [1]  0.5094213  0.4887179  0.4350756  0.3718631  0.3454801  0.3173984
 [7]  0.2981974  0.2455020  0.1727210 -1.0740660

Largest  eigenvalues:
 [1] 64660658 59901449 57277046 55567244 54947603 53478410 52105215 51708121
 [9] 51680084 51284710

Smallest eigenvalues:
 [1]   0.23666775   0.19696834   0.16535025   0.13610663   0.07894434
 [6]  -0.06924628  -0.15111873  -2.95676465 -12.11895385 -12.66048797

Largest  eigenvalues:
 [1] 63078323 58732346 56016653 55248847 53883715 52688534 51431821 51127713
 [9] 50889641 50050161

Smallest eigenvalues:
 [1]  0.4052114  0.3977633  0.3518903  0.3464258  0.3031983  0.2768000
 [7]  0.2580313  0.2407707  0.1873606 -2.9965878

Largest  eigenvalues:
 [1] 65124315 60438801 57102924 57043930 54950138 53450674 52805348 52546452
 [9] 52017693 51660801

Smallest eigenvalues:
 [1]  0.5477875  0.4588957  0.4520199  0.3379817  0.2525528  0.2217774
 [7]  0.1773967  0.1738130  0.1545247 -0.2604269

Largest  eigenvalues:
 [1] 63736110 60366337 57321776 55295173 55274215 53485717 52936781 51827820
 [9] 51765377 51497498

Smallest eigenvalues:
 [1]  0.4816732  0.4739031  0.4259841  0.4072189  0.3362325  0.2803447
 [7]  0.1677723  0.1128676 -0.6205316 -1.3516641

Largest  eigenvalues:
 [1] 65095020 59765952 57366970 56114894 54864578 53368385 52159709 52067841
 [9] 51932334 51221450

Smallest eigenvalues:
 [1]   0.29010428   0.24140761   0.20818745   0.11323732   0.02074865
 [6]  -0.33961604 -13.07879631 -16.28979150 -56.76642877 -70.64630226

Largest  eigenvalues:
 [1] 63027284 59421479 56231444 54706048 54562277 53028310 51814327 51507339
 [9] 50830466 50597701

Smallest eigenvalues:
 [1]  0.5647435  0.3920006  0.3366998  0.2980104  0.2973342  0.2718065
 [7]  0.2709506 -0.1080825 -1.0100542 -1.1747386

Largest  eigenvalues:
 [1] 62408256 59614678 57393694 55353284 54565459 53588408 52406147 51886748
 [9] 50863848 50740281

Smallest eigenvalues:
 [1]  0.57144900  0.52921040  0.52911305  0.50753726  0.48910617  0.45276255
 [7]  0.37900531  0.07620250  0.05655370 -0.01034054

Largest  eigenvalues:
 [1] 65419041 59907847 57169638 56226242 54652356 52926350 52404559 51574323
 [9] 51552065 50761521

Smallest eigenvalues:
 [1]  0.371271890  0.330851213  0.307232654  0.281531137  0.256668163
 [6]  0.232274056  0.193993701  0.182034178 -0.005417974 -0.302951598

Largest  eigenvalues:
 [1] 63789800 59241096 57039615 55103653 54506807 53149607 51400099 51336439
 [9] 51092612 50372391

Smallest eigenvalues:
 [1]  0.4909831  0.4549253  0.4099944  0.3741369  0.3719137  0.2222549
 [7]  0.1747840 -0.3199870 -4.0824018 -4.3992507

Largest  eigenvalues:
 [1] 63554601 60075734 56807171 55074291 54931844 53146499 51787747 51057811
 [9] 51009623 50725826

Smallest eigenvalues:
 [1]  0.57592619  0.54454884  0.50724665  0.36937398  0.36003625  0.31825666
 [7]  0.25611902  0.23308721  0.22615272 -0.04615426

Largest  eigenvalues:
 [1] 63053855 60229365 56868888 55576619 55183520 53737069 52080177 51891840
 [9] 51300620 50879257

Smallest eigenvalues:
 [1]  0.5589331  0.4863285  0.4112946  0.3783604  0.3362585  0.2128650
 [7]  0.1215538 -0.2453996 -0.4138166 -1.0953834

Largest  eigenvalues:
 [1] 64953052 60249766 57455140 56518763 55019934 53460661 52457286 52097709
 [9] 51611383 50985717

Smallest eigenvalues:
 [1]  0.5972178  0.5456131  0.4455389  0.4226966  0.3205695  0.3148668
 [7]  0.2679887  0.2527282  0.1654921 -0.5227497

Largest  eigenvalues:
 [1] 65243761 60006447 56832069 56368450 54727375 53024001 52441960 51826070
 [9] 51778153 51063630

Smallest eigenvalues:
 [1]   0.38359621   0.36222014   0.35961793   0.26874270   0.20798768
 [6]   0.08574142  -0.41520101  -5.17263069 -11.23711291 -38.95989049

Largest  eigenvalues:
 [1] 62789801 59712578 56427323 54950722 54868390 52852027 51819028 51118818
 [9] 50854511 50411281

Smallest eigenvalues:
 [1]  0.4909796  0.4570228  0.4066567  0.3032244  0.2554636  0.2424323
 [7]  0.2384851 -0.4434140 -0.8030490 -2.3378398

Largest  eigenvalues:
 [1] 67150421 60669272 58591803 57408161 55274280 53620116 53564825 52896289
 [9] 52227571 52064083

Smallest eigenvalues:
 [1]  0.5579982  0.5051204  0.3622174  0.3388242  0.2910276  0.2906055
 [7]  0.2526001  0.1288093  0.1058786 -0.9665361

Largest  eigenvalues:
 [1] 65983704 60976055 58410422 57315994 55543214 54136413 53258475 52768257
 [9] 52473207 51747584

Smallest eigenvalues:
 [1]  0.4335797  0.4310832  0.3973678  0.3264764  0.2949178  0.2167845
 [7]  0.1722916  0.1245493  0.1232390 -0.3697616

Largest  eigenvalues:
 [1] 63363120 60481686 57178352 55545719 55256142 53928166 52441585 52338007
 [9] 51405894 51281093

Smallest eigenvalues:
 [1]  0.5092447  0.4580002  0.4432456  0.3791556  0.2967002  0.2387923
 [7]  0.2172654  0.1813795 -0.1203716 -0.3629448

Largest  eigenvalues:
 [1] 63005277 59507447 56539402 54936544 54658541 52937044 51505806 51095008
 [9] 50982621 50339473

Smallest eigenvalues:
 [1]  0.46291563  0.38719190  0.31786026  0.29318455  0.19211782  0.16450483
 [7] -0.04082186 -0.12421561 -0.83118975 -2.12806154

Largest  eigenvalues:
 [1] 65394117 60275985 57693786 56521421 55051914 53605746 52458415 52410567
 [9] 52337765 51609474

Smallest eigenvalues:
 [1]  0.44524083  0.33245889  0.32462086  0.25437299  0.24604660  0.23578911
 [7]  0.17555370  0.09603666 -0.01507374 -0.19263204

Largest  eigenvalues:
 [1] 64906064 59519019 57160557 55722279 54727460 53363251 51797701 51737353
 [9] 51250806 50731940

Smallest eigenvalues:
 [1]  0.41492594  0.29416226  0.28393718  0.28006142  0.18150681  0.14976376
 [7]  0.14608236  0.07471617 -0.77893733 -1.07189272

Largest  eigenvalues:
 [1] 64983449 60648684 57972259 55649599 55561426 54057784 53003278 52137233
 [9] 52052877 51781663

Smallest eigenvalues:
 [1]   0.4577545   0.4522391   0.4027851   0.3863218   0.3476765   0.3327155
 [7]   0.2706671   0.2129754  -1.0122043 -20.5550455

Largest  eigenvalues:
 [1] 63515113 60002132 57141020 55851145 55311790 53615514 51988878 51967686
 [9] 51778499 50941847

Smallest eigenvalues:
 [1]  0.54853294  0.50670621  0.43630769  0.42127703  0.39077436  0.28047300
 [7]  0.27437091  0.27193397  0.25827140 -0.09679595

Largest  eigenvalues:
 [1] 65329281 60762509 57832429 56852817 55367283 53742499 52927568 52432303
 [9] 52172398 51360320

Smallest eigenvalues:
 [1]  0.5483294  0.5379973  0.5170185  0.3726293  0.3230770  0.3121718
 [7]  0.2450974  0.2203398  0.0599361 -5.3187898

Largest  eigenvalues:
 [1] 62669562 60249016 56921224 55580776 54825988 53797765 52224272 51661710
 [9] 51005158 50788887

Smallest eigenvalues:
 [1]   0.30186246   0.25588873   0.22552097   0.17886503   0.04501903
 [6]  -0.17855591  -0.48106412 -10.43718676 -13.43292393 -24.39000393

Largest  eigenvalues:
 [1] 62345266 59068683 56452822 54424568 54355514 52693592 51603877 51499862
 [9] 50607549 50361774

Smallest eigenvalues:
 [1]  0.5029969  0.4924368  0.4343908  0.4127689  0.3936988  0.3684727
 [7]  0.3423737  0.2358618 -0.1057755 -0.2538911

Largest  eigenvalues:
 [1] 64414116 60106720 57646132 56283123 54645963 53203514 52327673 51834114
 [9] 51693769 51057981

Smallest eigenvalues:
 [1]  0.5258422  0.4687241  0.4557539  0.4278174  0.3596955  0.3399936
 [7]  0.3066862  0.1886756 -0.2935807 -0.4541939

Largest  eigenvalues:
 [1] 65254733 60385691 57041037 56303551 55570412 53723274 52300271 52221783
 [9] 51738451 51113930

Smallest eigenvalues:
 [1]   0.238454453   0.095073277  -0.007738026  -0.161267824  -0.368006568
 [6]  -1.702313950  -6.342835540 -18.344036839 -23.197898678 -95.354781700

Largest  eigenvalues:
 [1] 65296510 60911543 57177145 57000834 55917603 53967696 53321942 52893030
 [9] 51963347 51883159

Smallest eigenvalues:
 [1]  0.4991829  0.4818742  0.3902265  0.3703390  0.3133894  0.2937669
 [7]  0.1900952  0.1659271  0.1239934 -0.5915255

Largest  eigenvalues:
 [1] 64302211 60716873 57685295 56023991 55870578 54208739 52796191 52538021
 [9] 52020759 51807013

Smallest eigenvalues:
 [1]  0.429156932  0.368938493  0.325209364  0.241678838  0.226363620
 [6]  0.153614750 -0.003838937 -0.130597834 -1.006863253 -2.150462474

Largest  eigenvalues:
 [1] 62477984 59853835 57105826 55674597 54204036 53824487 52107679 51568295
 [9] 50698970 50496817

Smallest eigenvalues:
 [1]    0.2789917    0.2225079    0.1954517    0.1855275   -0.2659694
 [6]   -0.6825136   -0.7343493   -1.7496139   -6.4743192 -100.3148702

Largest  eigenvalues:
 [1] 66884428 60727530 57939227 56612360 55508821 53538982 52925127 52178014
 [9] 52109953 51010463

Smallest eigenvalues:
 [1]  0.5461506  0.4823923  0.4672295  0.3512405  0.3175798  0.2802527
 [7]  0.2663688  0.2644027  0.2258517 -0.4020982

Largest  eigenvalues:
 [1] 62906218 60603242 57310859 55776414 55097754 54178427 52751712 51888506
 [9] 51265792 50969062

Smallest eigenvalues:
 [1]  0.4625740  0.4010580  0.3619648  0.3291956  0.3288281  0.2895016
 [7]  0.2553185  0.2263961  0.2109011 -3.3883164

Largest  eigenvalues:
 [1] 64932886 60317744 57475822 56630719 55104380 53516737 52474525 52437673
 [9] 52419629 51452034

Smallest eigenvalues:
 [1]  0.52715344  0.43580318  0.38113151  0.32608084  0.31390926  0.19302616
 [7] -0.05792133 -0.93230301 -1.91622521 -6.09469851

Largest  eigenvalues:
 [1] 64517255 60109472 57331116 56545376 54876978 53172348 52340385 52301442
 [9] 51780712 51186017

Smallest eigenvalues:
 [1]  0.44887669  0.42603683  0.41961486  0.41196201  0.37011495  0.17941008
 [7]  0.14942029  0.14904827  0.05206293 -1.94679354

Largest  eigenvalues:
 [1] 64203103 60492865 57359657 56044722 55344547 53440895 52741323 52071351
 [9] 51698724 51591883

Smallest eigenvalues:
 [1]  0.3892820  0.3487393  0.3113848  0.2719389  0.2204615  0.0496663
 [7] -0.2384710 -0.5021606 -0.5821858 -3.1487417

Largest  eigenvalues:
 [1] 65609042 60671337 58168512 56122139 55410158 53825258 52993446 52289341
 [9] 52052802 51959624

Smallest eigenvalues:
 [1]  0.3921902  0.3769315  0.3519380  0.3496981  0.2686873  0.2389682
 [7]  0.1381529  0.1366931 -0.9824289 -1.0151289

Largest  eigenvalues:
 [1] 65782954 60798656 58210469 56374832 55633437 54264241 52434761 52415451
 [9] 52353673 51677285

Smallest eigenvalues:
 [1]  0.59710702  0.54076646  0.52405931  0.49091527  0.42684775  0.39801605
 [7]  0.27760095  0.14651228  0.11536004 -0.02958352

Largest  eigenvalues:
 [1] 64891688 60407884 57291069 55306151 55149069 53551103 52079719 51520547
 [9] 51514934 51198273

Smallest eigenvalues:
 [1]  0.53794929  0.42607518  0.30905173  0.26351827  0.21458911  0.02477885
 [7] -0.02717911 -0.16207734 -1.02056580 -2.80488081

Largest  eigenvalues:
 [1] 63291348 59431319 56748974 55163999 54910435 53023954 51818178 51532302
 [9] 51263653 50697319

Smallest eigenvalues:
 [1]  0.5318254  0.4674420  0.3899673  0.3229714  0.2784848  0.2699827
 [7]  0.1655744 -0.1108428 -0.1673049 -1.1428309

Largest  eigenvalues:
 [1] 64448618 60730551 57304818 56627205 55459424 53505813 52740090 52501294
 [9] 51901187 51070646

Smallest eigenvalues:
 [1]  0.25243659  0.21358580  0.19323473  0.18336026  0.09014207 -0.71495101
 [7] -1.16325950 -2.01383008 -4.18354226 -5.26476507

Largest  eigenvalues:
 [1] 65518080 59796194 57316053 56510531 55031019 53501384 52611474 52060676
 [9] 51870141 50819031

Smallest eigenvalues:
 [1]  0.4910755  0.4891466  0.4774769  0.4365560  0.4104876  0.3207398
 [7]  0.3188411  0.3007056  0.2665099 -0.2975243

Largest  eigenvalues:
 [1] 64208698 59919816 57112887 55732158 55158474 53411081 52265271 51740662
 [9] 51638936 50902639

Smallest eigenvalues:
 [1]  0.5101966  0.4951504  0.4665691  0.3619481  0.3521903  0.3331943
 [7]  0.2803387 -0.3407573 -1.5429698 -2.1064550

Largest  eigenvalues:
 [1] 67419690 60898653 58684381 57775396 55279604 53791756 53763943 52741421
 [9] 52232406 51983087

Smallest eigenvalues:
 [1]  0.5696144  0.5590046  0.4389156  0.3974480  0.3645191  0.3583544
 [7]  0.3416514  0.2737678  0.1813640 -1.8833488

Largest  eigenvalues:
 [1] 64871755 60282387 57177814 56218951 55325217 53843399 52221401 52102718
 [9] 52018948 50934637

Smallest eigenvalues:
 [1]  0.4693469  0.4518112  0.3918816  0.3859981  0.3344764  0.3247012
 [7]  0.2740529  0.2253304  0.1303382 -0.0675637

Largest  eigenvalues:
 [1] 65381241 59405266 56627087 56373903 54257151 52803392 52403884 51544328
 [9] 51286517 50622072

Smallest eigenvalues:
 [1]  0.5149883  0.4299325  0.4092290  0.3678656  0.3144539  0.2852062
 [7]  0.2502052 -0.2123847 -0.5578747 -1.5390840

Largest  eigenvalues:
 [1] 64785318 60554602 57631317 56480150 55190970 53384658 52500148 52281630
 [9] 52105357 51159596

Smallest eigenvalues:
 [1]  0.4722795  0.4650883  0.4566886  0.4523340  0.4111263  0.4048655
 [7]  0.3561046  0.3181576  0.3020069 -0.2281016

Largest  eigenvalues:
 [1] 64963433 60252594 57667626 56279449 55156992 53719120 52367111 52129632
 [9] 51905101 51220596

Smallest eigenvalues:
 [1]  0.4813249  0.4633643  0.4425030  0.3960609  0.3827651  0.3703349
 [7]  0.3567444  0.3300237 -0.2133325 -3.0614927

Largest  eigenvalues:
 [1] 63039208 59986948 57170072 55602980 55163735 53530057 51909456 51679701
 [9] 51416241 50544673

Smallest eigenvalues:
 [1]  0.33992788  0.33117354  0.24444898  0.16244912  0.16041558  0.02198482
 [7] -0.03019142 -0.04202999 -0.69409640 -4.92509489

Largest  eigenvalues:
 [1] 64303371 60012434 57103694 55855808 55827790 53966460 52150433 51788493
 [9] 51760883 50690858

Smallest eigenvalues:
 [1]  0.3739392  0.3400950  0.3374348  0.2752155  0.2492474  0.2432026
 [7]  0.2187203  0.2043097 -3.0246086 -9.9196261

Largest  eigenvalues:
 [1] 64510963 60626035 57711355 55719739 55574296 54148691 52370501 52177869
 [9] 51655977 51564711

Smallest eigenvalues:
 [1]  0.5550998  0.4613133  0.3985648  0.3393245  0.3329940  0.3010023
 [7]  0.2456954  0.1834303 -0.5305284 -2.3738032

Largest  eigenvalues:
 [1] 66580830 59676158 57142087 56878847 54361913 53231395 52558753 51759258
 [9] 51380248 51058168

Smallest eigenvalues:
 [1]  0.4774911  0.4439654  0.4332345  0.3126872  0.3014802  0.2551789
 [7]  0.1868672  0.1186505 -2.1765488 -4.3838795

Largest  eigenvalues:
 [1] 63389818 59813482 57254308 55899256 54896559 53372822 52739198 52192275
 [9] 51700891 51484188

Smallest eigenvalues:
 [1]   0.43328845   0.38719455   0.37674980   0.27752984   0.12302446
 [6]  -0.07760758  -0.11254720  -0.41678797  -3.89305747 -14.39757724

Largest  eigenvalues:
 [1] 63721875 59221417 56626464 55014390 54261307 52626148 51366186 51048924
 [9] 51001995 50472366

Smallest eigenvalues:
 [1]  0.5049877  0.4139814  0.3794518  0.3507782  0.3320662  0.2714831
 [7]  0.2431447  0.2112054  0.1881777 -0.2357201

Largest  eigenvalues:
 [1] 63363523 59721126 57030640 55540033 54812756 53299844 51787395 51676671
 [9] 51585476 50791837

Smallest eigenvalues:
 [1]  0.4198794  0.3204345  0.3035517  0.2641293  0.2438497  0.2095091
 [7]  0.1592699  0.1364110 -1.1454457 -4.0666950

Largest  eigenvalues:
 [1] 65093158 59097482 56547614 56075054 53901870 52596559 52102653 51245021
 [9] 51099102 50486599

Smallest eigenvalues:
 [1]  0.5227194  0.5059859  0.4981923  0.4457535  0.3767528  0.3616820
 [7]  0.2974851  0.2890158 -0.4473132 -2.1675098

Largest  eigenvalues:
 [1] 66617715 61003702 58140449 57788429 55209434 53823945 53382298 52434736
 [9] 52113933 51524019

Smallest eigenvalues:
 [1]  0.445328417  0.385286421  0.364609395  0.315363511  0.273160561
 [6]  0.261115992  0.254419890  0.203082302 -0.004028773 -1.052138807

Largest  eigenvalues:
 [1] 65084793 60246996 57372672 56263051 55367276 53722296 52323883 52022610
 [9] 51834624 51014821

Smallest eigenvalues:
 [1]  0.4341606  0.3577792  0.3255446  0.3157514  0.2818044  0.2334308
 [7]  0.2146404 -0.4799234 -1.6754531 -4.5124258

Largest  eigenvalues:
 [1] 63383427 60232910 57210838 55661666 55578067 53675023 51953631 51771568
 [9] 51471919 51237151

Smallest eigenvalues:
 [1]  0.42093704  0.37580775  0.31111732  0.29431373  0.27486582  0.24140553
 [7]  0.19546482  0.03669958 -0.14103699 -5.23249640

Largest  eigenvalues:
 [1] 65359462 60576357 57823392 56572610 56182118 54262181 52595117 52410399
 [9] 51955369 51251053

Smallest eigenvalues:
 [1]   0.2729783   0.2706867   0.2384592   0.2278426   0.1235578  -0.4504019
 [7]  -0.5971150  -1.4395688 -16.3249884 -34.0914851

Largest  eigenvalues:
 [1] 64901160 59759172 56958042 56667693 54905439 53217128 52489484 51370122
 [9] 51198887 50426340

Smallest eigenvalues:
 [1]  0.4554501  0.3550554  0.3425412  0.3238883  0.2681186  0.2454067
 [7] -0.1319494 -0.3589444 -1.5479449 -8.7067886

Largest  eigenvalues:
 [1] 63402451 59613515 56936391 54913542 54746845 52954454 51685464 51163980
 [9] 51013426 50560135

Smallest eigenvalues:
 [1]  0.50499464  0.50237240  0.46944764  0.45110610  0.28366685  0.26981990
 [7]  0.12573600 -0.01493711 -0.43155697 -9.48172877

Largest  eigenvalues:
 [1] 64984141 60068182 57095392 55869088 54885385 53134114 52120017 51964467
 [9] 51894852 51237814

Smallest eigenvalues:
 [1]  0.43274085  0.40635116  0.39121924  0.38072803  0.33036984  0.28694404
 [7]  0.21678863  0.20260673  0.06202214 -1.07354130

Largest  eigenvalues:
 [1] 64923661 61194443 58218019 56469070 56263877 54855320 53132086 52796651
 [9] 52185622 51983742

Smallest eigenvalues:
 [1]   0.48516217   0.36710366   0.29781240   0.20398797  -0.07905503
 [6]  -0.36319719  -0.37410108  -1.24833610  -2.03155426 -24.59923755

Largest  eigenvalues:
 [1] 65748158 60418040 57699642 56553541 55557636 53669555 52679027 52323301
 [9] 52193404 51390377

Smallest eigenvalues:
 [1]  0.5499865  0.4208013  0.4102624  0.3910351  0.3840838  0.2929361
 [7]  0.2620767  0.1673236  0.1459602 -1.1357819

Largest  eigenvalues:
 [1] 65232715 60516047 57818024 56383629 55534259 54121014 52830329 52455888
 [9] 52364252 51829765

Smallest eigenvalues:
 [1]  0.24334952  0.22008136  0.20946134  0.20289071  0.19768708 -0.01684957
 [7] -0.05938816 -0.07341618 -1.40394549 -3.74934048

Largest  eigenvalues:
 [1] 68040001 60681448 58564870 57737275 54968708 53959572 53753965 52351765
 [9] 51793378 51688121

Smallest eigenvalues:
 [1]  0.4822019  0.4618066  0.3679673  0.3482136  0.3172875  0.3096675
 [7]  0.2920842  0.2557456  0.2378626 -0.1069289

Largest  eigenvalues:
 [1] 64715112 60386260 57290028 56280337 54909910 53360729 52496448 51746698
 [9] 51714526 50854797

Smallest eigenvalues:
 [1]  0.40366129  0.35584743  0.34893782  0.26607788  0.25617216  0.24545336
 [7]  0.23088991  0.07835972 -0.06808716 -0.71303065

Largest  eigenvalues:
 [1] 64418227 60272024 57538448 55416779 55135472 53764506 52055857 51945465
 [9] 51643290 51106653

Smallest eigenvalues:
 [1]  0.6458670  0.5290819  0.4215005  0.3536802  0.3200041  0.2503895
 [7]  0.2296752  0.1531097 -0.1155864 -0.5435428

Largest  eigenvalues:
 [1] 63183821 59985908 57502172 55322395 55038142 53752840 52348876 51810737
 [9] 51198202 50840139

Smallest eigenvalues:
 [1]   0.4640593   0.4377243   0.3644144   0.3194029   0.3104610   0.2795312
 [7]   0.2055138   0.1923308  -1.2375955 -12.4058702

Largest  eigenvalues:
 [1] 64573106 59936877 56722379 55809260 55104462 53406175 52353098 51918984
 [9] 51852662 51219078

Smallest eigenvalues:
 [1]  0.45384324  0.37035798  0.35794837  0.32435794  0.25690769  0.25328091
 [7]  0.24230546  0.05948428 -0.75149526 -1.32151493

Largest  eigenvalues:
 [1] 64449102 60377059 57220185 55480173 55462660 53830333 52192780 51873629
 [9] 51413374 51156962

Smallest eigenvalues:
 [1]  0.49027024  0.44953124  0.42905935  0.42731675  0.36738142  0.30615057
 [7]  0.24320575  0.21787247  0.16608311 -0.08800963

Largest  eigenvalues:
 [1] 63324737 59538915 56864243 55083026 55073825 53210917 51888727 51500722
 [9] 51158414 50660139

Smallest eigenvalues:
 [1]  0.5442891  0.5004407  0.4789799  0.4641114  0.3300991  0.3097456
 [7]  0.3088163  0.2767147  0.2209505 -0.8225658

Largest  eigenvalues:
 [1] 64463616 59933708 57098043 55853022 54863078 53391108 52313894 51896564
 [9] 51627284 51003963

Smallest eigenvalues:
 [1]  0.4654656  0.4138306  0.3295331  0.2914700  0.2825199  0.2504557
 [7]  0.2406395  0.2264968  0.1826636 -4.7170459

Largest  eigenvalues:
 [1] 66806578 60182174 57652106 57160939 54902998 53537384 53148556 52223214
 [9] 52068645 51477767

Smallest eigenvalues:
 [1]  0.49404084  0.43808708  0.37417089  0.35002741  0.34270305  0.30349633
 [7]  0.28832401  0.18733932 -0.04115719 -0.38155206

Largest  eigenvalues:
 [1] 65596407 60748616 57948171 56464715 55692419 54062004 53442958 52657923
 [9] 52140380 51994919

Smallest eigenvalues:
 [1]  0.43767714  0.41360798  0.29450200  0.26490822  0.24130288  0.20592951
 [7]  0.16103586  0.07000476 -0.41737411 -0.50971827

Largest  eigenvalues:
 [1] 67168498 60566866 57849403 57404401 54764190 53469202 53123933 52272941
 [9] 51948122 51711059

Smallest eigenvalues:
 [1]  0.4287099  0.4282514  0.3973804  0.3892213  0.3123146  0.2358853
 [7]  0.1612999  0.1605497 -0.2688335 -5.8299995

Largest  eigenvalues:
 [1] 65084274 59743409 56896469 56346631 54535488 52725316 52411718 51643999
 [9] 51561855 50930849

Smallest eigenvalues:
 [1]  0.3082562  0.3047844  0.2716003  0.2579050  0.1788843 -0.2576115
 [7] -0.3452661 -0.9506603 -2.0562081 -2.6868315

Largest  eigenvalues:
 [1] 65264885 60778802 57708336 56415326 55899069 54367923 52810124 52405618
 [9] 52093863 51653800

Smallest eigenvalues:
 [1]  0.59600416  0.53213548  0.51288707  0.47686931  0.46248450  0.38031461
 [7]  0.30797385  0.30478171  0.20292123 -0.01065626

Largest  eigenvalues:
 [1] 65765198 60987537 58210608 56764277 55471310 53732148 52709991 52519562
 [9] 52020629 51685092

Smallest eigenvalues:
 [1]  0.6034738  0.5556320  0.5199809  0.4999030  0.4861337  0.4641957
 [7]  0.4211815  0.3063336  0.2672209 -0.2760835

Largest  eigenvalues:
 [1] 64124588 59773195 56768950 55984895 54821312 53177997 51973039 51811308
 [9] 51628959 50833276

Smallest eigenvalues:
 [1]   0.4404908   0.4034500   0.3996555   0.3893506   0.3052125   0.2917697
 [7]   0.1438516  -0.3118468  -9.3989921 -18.2183983

Largest  eigenvalues:
 [1] 65500943 60219216 57519340 56635008 54742896 53386022 52744574 51496580
 [9] 51475777 50514245

Smallest eigenvalues:
 [1]  0.46474102  0.37507310  0.36475399  0.28321383  0.23768977  0.23375274
 [7]  0.19428444  0.05959832  0.04432313 -6.34832757

Largest  eigenvalues:
 [1] 61708688 59864826 57140470 56000404 54333436 53803108 52122637 51134929
 [9] 50551509 50525734

Smallest eigenvalues:
 [1]  0.4706150  0.4617676  0.4283637  0.4041858  0.3622399  0.3478138
 [7]  0.2470418  0.2353118 -0.6615252 -1.0302431

Largest  eigenvalues:
 [1] 65180634 60288309 58247009 56440038 55256285 54039406 52539085 52509700
 [9] 52187060 51768085

Smallest eigenvalues:
 [1]  0.47066771  0.38953935  0.35319067  0.29865405  0.04963312  0.01243067
 [7] -0.12960261 -0.13251663 -1.29890621 -2.15787959

Largest  eigenvalues:
 [1] 65055322 59994988 56704071 56240372 54695048 53018451 52309600 52188075
 [9] 51422350 51171086

Smallest eigenvalues:
 [1]  0.42271475  0.37708931  0.36209363  0.33430741  0.28253021  0.24862574
 [7]  0.20156792  0.15752430  0.08164249 -3.32906415

Largest  eigenvalues:
 [1] 61367940 59582945 56825009 55424000 53504078 53409756 51673331 50917345
 [9] 50245675 50109295

Smallest eigenvalues:
 [1]   0.28327777   0.27753930   0.10578123   0.07314426  -0.16387648
 [6]  -0.88582894  -1.55372743  -2.32373572  -2.52625439 -27.40042386

Largest  eigenvalues:
 [1] 63004957 60612180 57156802 55952653 55483519 54309703 52438970 52367865
 [9] 51399196 51253812

Smallest eigenvalues:
 [1]  0.47750982  0.46956939  0.44915818  0.42281053  0.35592319  0.19446157
 [7]  0.18962537  0.16803872  0.08330244 -0.32227640

Largest  eigenvalues:
 [1] 65523492 60063624 56901120 56376583 55001407 53157168 52437940 52200364
 [9] 51999228 51485916

Smallest eigenvalues:
 [1]   0.4571964   0.3238459   0.2648202   0.2493922   0.2049719   0.2019953
 [7]   0.1837542  -0.5546926  -2.1066588 -21.2173276

Largest  eigenvalues:
 [1] 65229683 60393280 57768877 56105495 54799568 53196929 52388765 52113475
 [9] 51972804 51710292

Smallest eigenvalues:
 [1]   0.41078896   0.35949319   0.34406070   0.32722415   0.31474933
 [6]   0.29921865   0.27754639   0.09137449  -0.02184615 -29.39202358

Largest  eigenvalues:
 [1] 63022377 59484776 57100237 55226959 55194210 53428889 51724593 51475606
 [9] 51288230 50596320

Smallest eigenvalues:
 [1]  0.36847322  0.34207286  0.33981044  0.27570306  0.25959508  0.22660283
 [7]  0.17982102  0.03736938 -0.33792894 -2.94218894

Largest  eigenvalues:
 [1] 64995722 60254030 57290980 55896512 55322786 53625187 51823965 51548462
 [9] 51526877 50883196

Smallest eigenvalues:
 [1]  0.4955103  0.4726134  0.4609949  0.3370033  0.3052478  0.3018187
 [7]  0.2919358  0.2790933  0.2225502 -0.4303885

Largest  eigenvalues:
 [1] 61920249 59872713 56871954 55567620 54250349 53663278 52162575 51672359
 [9] 50790756 50459394

Smallest eigenvalues:
 [1]  0.48895418  0.46394416  0.45855480  0.42888069  0.41184146  0.31492873
 [7]  0.28350104  0.27625885  0.09075314 -3.54530943

Largest  eigenvalues:
 [1] 64043044 60509385 57318820 55474611 55434749 53804844 52156129 51656538
 [9] 51607360 50997015

Smallest eigenvalues:
 [1]  0.452059327  0.450230083  0.399109587  0.240694255  0.173602166
 [6]  0.154327437  0.066358713 -0.008891906 -1.682021539 -3.384752104

Largest  eigenvalues:
 [1] 63903868 60786594 57278680 56008697 55397039 53990673 52489251 52194596
 [9] 51931905 51254613

Smallest eigenvalues:
 [1]   0.3655935   0.3329792   0.2606046   0.2589456   0.2511102   0.2165988
 [7]   0.2043469  -0.6491771  -8.5410615 -16.9960753

Largest  eigenvalues:
 [1] 64497420 61351850 57931601 56981107 56359736 55256138 53113711 52663058
 [9] 52255885 51664821

Smallest eigenvalues:
 [1]  0.46277828  0.45676796  0.44092611  0.43662052  0.35244114  0.28151719
 [7]  0.23070772  0.19887279  0.04933185 -1.02341151

Largest  eigenvalues:
 [1] 65890518 59920846 57251140 57034471 54819032 53363671 52921575 52189240
 [9] 52064594 51554353

Smallest eigenvalues:
 [1]   0.11801268   0.09489184   0.08466386   0.07295297  -0.22823110
 [6]  -0.63592599  -1.93349065  -6.46042397 -17.86811655 -67.45496709

Largest  eigenvalues:
 [1] 63867038 59435600 56543078 54968586 54542654 52832065 51947736 51299224
 [9] 51285669 51006173

Smallest eigenvalues:
 [1]  0.5278092  0.4939030  0.4748969  0.4338467  0.4239038  0.4017272
 [7]  0.3793102  0.3614124  0.3346325 -0.5934390

Largest  eigenvalues:
 [1] 63959375 60847791 57545913 56281084 55855382 54118737 52261688 52190027
 [9] 52085476 51105563

Smallest eigenvalues:
 [1]  0.6247623  0.5476715  0.4598102  0.4455974  0.4411331  0.4318708
 [7]  0.3728331  0.2579648 -0.1275022 -0.1724734

Largest  eigenvalues:
 [1] 64797134 60195553 57625071 56073197 55273474 53481629 52518988 52242795
 [9] 51812093 51410050

Smallest eigenvalues:
 [1]  0.5584616  0.5545359  0.4930952  0.4839450  0.3540002  0.3452527
 [7]  0.3301492  0.3117685  0.2383850 -0.1593142

Largest  eigenvalues:
 [1] 63363949 59670131 57190772 55369679 55204815 53698423 52031428 51669022
 [9] 51246827 50811008

Smallest eigenvalues:
 [1]  0.47844117  0.41895707  0.40023332  0.39309687  0.35261705  0.33232005
 [7]  0.05061357  0.01728149 -0.14966521 -4.74192526

Largest  eigenvalues:
 [1] 64413604 59608540 56700461 56022953 54331782 52694243 52069234 51614090
 [9] 51250684 50674572

Smallest eigenvalues:
 [1]  0.5676876  0.5214993  0.4597463  0.3925009  0.3615232  0.3507187
 [7]  0.2664203  0.1855388  0.1679822 -0.6563396

Largest  eigenvalues:
 [1] 65042474 60765130 57521496 56683838 55783312 53960441 52919359 52613443
 [9] 52462212 51773650

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	4.344984	0.7528672	126.3173	0.04	2.611653	2.863883

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

EDA ~ alt + n + acc + PM1

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- EDA_fd
covariates <- list(altitude = altitude_fd, 
                   noise = noise_fd,
                   acceleration = acceleration_fd,
                   pollution = pollution1_fd)
path_plot <- 'figures/model_EDA_alt_noise_acc_PM1_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 80, norder = 4, lambda = 1e4),
                     noise = list(nbetabasis = 80, norder = 4, lambda = 1e4),
                     acceleration = list(nbetabasis = 80, norder = 4, lambda = 1e4),
                     pollution = list(nbetabasis = 80, norder = 4, lambda = 1e4))

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, HR = HR,
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 19.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 606 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Smallest eigenvalues:
 [1]  0.3603906  0.3206480  0.2860769  0.2596945  0.2094575  0.1474205
 [7]  0.1147731 -0.1408713 -0.1589878 -3.8942672

Largest  eigenvalues:
 [1] 64042812 60125820 57559805 55670773 55051760 53392896 52138209 51717479
 [9] 51678901 51142828

Smallest eigenvalues:
 [1]  0.19308764  0.17015664  0.10711512  0.02288223 -0.01647957 -0.01698404
 [7] -0.02461813 -0.18648999 -0.18929676 -2.45392676

Largest  eigenvalues:
 [1] 63355450 61056600 57701327 55871095 55332918 53938763 52739427 52427972
 [9] 51869486 51615887

Smallest eigenvalues:
 [1]  0.313184927  0.299904415  0.297226800  0.272611956  0.223798356
 [6]  0.129874123  0.067220822 -0.005984975 -0.153001156 -0.633852607

Largest  eigenvalues:
 [1] 64140129 61112687 58366275 55856481 55741450 54327511 53206043 52322060
 [9] 52089966 51897926

Smallest eigenvalues:
 [1]  0.486435822  0.484210632  0.414051726  0.353098383  0.346720503
 [6]  0.259123560  0.251768800 -0.006308419 -0.043910305 -0.102562167

Largest  eigenvalues:
 [1] 61984148 60501986 57601754 55831981 54968196 54066883 52461370 52415988
 [9] 51222636 51000972

Smallest eigenvalues:
 [1]  0.3567004  0.3285938  0.2976389  0.2334785  0.2046435  0.1983599
 [7]  0.1705519  0.1184595 -0.1281541 -3.2064522

Largest  eigenvalues:
 [1] 65163173 59818161 57293665 56025018 54719041 53144375 52121514 51967281
 [9] 51426274 51120415

Smallest eigenvalues:
 [1]  0.41800093  0.41103957  0.37141810  0.28186811  0.27306749  0.14039522
 [7]  0.05665045 -0.02675393 -0.10474338 -0.33093004

Largest  eigenvalues:
 [1] 64358283 60638162 57254916 56045643 55652612 53846201 52740030 52017768
 [9] 51714901 51420528

Smallest eigenvalues:
 [1]  0.2635689  0.1968254  0.1840918  0.1463388  0.1367938  0.0774332
 [7] -0.1700209 -0.1777492 -0.3643735 -0.4571581

Largest  eigenvalues:
 [1] 65013751 60998681 57648795 56151025 55480723 53867210 52962816 52135892
 [9] 52042929 51761050

Smallest eigenvalues:
 [1]  0.34805612  0.31317840  0.23050060  0.22377275  0.18881466 -0.05365539
 [7] -0.12786940 -0.30029511 -0.38798873 -0.65147113

Largest  eigenvalues:
 [1] 64870413 59853259 56521056 56464943 54495022 52690414 52475124 52167009
 [9] 51688408 51233785

Smallest eigenvalues:
 [1]  0.4924669167  0.4224823921  0.4110749524  0.3006899051  0.2739084512
 [6]  0.2118511766  0.2073970513  0.0566545630  0.0004435585 -1.9697097632

Largest  eigenvalues:
 [1] 63897554 59811350 57221227 55815994 54681379 53175611 52229504 51781375
 [9] 51653218 51043701

Smallest eigenvalues:
 [1]  0.37594417  0.35853443  0.33685754  0.32689900  0.23091090  0.22691332
 [7]  0.22173925  0.10436881  0.06168631 -0.03016414

Largest  eigenvalues:
 [1] 64507451 60409949 58002489 55634486 55321207 54073815 52718494 52110591
 [9] 51872357 51712245

Smallest eigenvalues:
 [1]  0.44564453  0.40144457  0.35814751  0.33064016  0.20256703  0.06430269
 [7] -0.43919089 -0.45225889 -1.04595515 -3.72937176

Largest  eigenvalues:
 [1] 64699010 60039590 57230094 55798586 55200344 52971868 52186125 51956598
 [9] 51697452 51235547

Smallest eigenvalues:
 [1]  0.3637690  0.3179382  0.2953825  0.2815649  0.2708426  0.1716318
 [7]  0.1256518  0.0709207 -0.2944240 -1.8981729

Largest  eigenvalues:
 [1] 63315355 59864465 57107461 55193265 54822933 53603761 52141302 52028246
 [9] 51338200 51002270

Smallest eigenvalues:
 [1]  0.38703956  0.38204369  0.35914554  0.27981298  0.27351546  0.21683480
 [7]  0.20852930 -0.05007726 -0.21218630 -1.18122172

Largest  eigenvalues:
 [1] 64864962 59719156 57151947 56535418 54774457 53303421 52543399 52172525
 [9] 51483342 50767655

Smallest eigenvalues:
 [1]  0.5666210  0.5128652  0.5047648  0.4344818  0.3820561  0.3682778
 [7]  0.2593738  0.2163635  0.1474606 -0.0161257

Largest  eigenvalues:
 [1] 65018802 59485575 56759327 55961013 54888526 53236899 52142138 51950984
 [9] 51851831 51205014

Smallest eigenvalues:
 [1]  0.49674605  0.38986244  0.36977487  0.32981922  0.22408674  0.21679872
 [7]  0.14659607  0.09302246 -0.08805735 -0.11807157

Largest  eigenvalues:
 [1] 66291866 59307802 57238030 56639429 54034094 53259521 52543575 51326778
 [9] 51117772 50519245

Smallest eigenvalues:
 [1]  0.5048780  0.5018486  0.4783975  0.4409971  0.4168265  0.3654423
 [7]  0.2558727  0.1582258 -0.1423267 -0.2183561

Largest  eigenvalues:
 [1] 63345416 60087174 56783771 55243839 54976033 53456167 51999856 51371631
 [9] 50839683 50520652

Smallest eigenvalues:
 [1]  0.3680907  0.2673715  0.2556593  0.2264717  0.2032561  0.1806324
 [7]  0.1578470  0.1348485 -0.1274604 -0.5267096

Largest  eigenvalues:
 [1] 66512102 60534115 57855623 57260735 55043218 53384080 53184007 52933113
 [9] 51654632 51496812

Smallest eigenvalues:
 [1]  0.46250142  0.40812451  0.38320941  0.23381370  0.21528419  0.12381999
 [7]  0.10875845  0.07737656  0.06233337 -0.79995766

Largest  eigenvalues:
 [1] 65753544 60501423 56960768 56753694 55112839 53464936 52724815 52234591
 [9] 52020426 51263068

Smallest eigenvalues:
 [1]  0.48720891  0.47571582  0.45112471  0.39529391  0.33727289  0.27785494
 [7]  0.15250768  0.02060553 -0.07968460 -0.71683640

Largest  eigenvalues:
 [1] 63421109 59880816 57059970 55351813 54886550 53781939 52421157 51800205
 [9] 50989232 50887761

Smallest eigenvalues:
 [1]  0.39905433  0.36072808  0.34246557  0.30407559  0.29587872  0.27107999
 [7]  0.24143192  0.11505289  0.11430622 -0.06455022

Largest  eigenvalues:
 [1] 64281762 61489955 58090710 56617451 55655382 54025692 52788376 52530737
 [9] 52474244 51781334

Smallest eigenvalues:
 [1]  0.4524249  0.4297710  0.3758639  0.3483349  0.3256069  0.2992669
 [7]  0.2661505  0.2370527  0.1072519 -0.1315416

Largest  eigenvalues:
 [1] 64822507 61097914 58013734 56414784 56408389 54708214 53058937 52587644
 [9] 52315629 51706456

Smallest eigenvalues:
 [1]  0.30172964  0.25823254  0.15310404  0.09629276  0.09252563  0.01557363
 [7] -0.06069795 -0.11263539 -0.43452943 -1.44370508

Largest  eigenvalues:
 [1] 64743454 60218965 56999694 55926177 54883767 53329324 51982796 51929633
 [9] 51562484 50890426

Smallest eigenvalues:
 [1]  0.49313171  0.43804805  0.40373882  0.32104682  0.27865145  0.26023728
 [7]  0.18798723  0.16612590  0.07420535 -0.06207839

Largest  eigenvalues:
 [1] 63228762 60339728 57141445 55692928 54834423 53103843 51918880 51757665
 [9] 51683771 50766304

Smallest eigenvalues:
 [1]  0.3815686  0.2937906  0.2934616  0.2672913  0.2637593  0.2198001
 [7]  0.2107763  0.1004381 -0.4090973 -0.5188172

Largest  eigenvalues:
 [1] 63894586 59758694 57239506 55185835 54421974 52959164 51919518 51354950
 [9] 51113528 51070084

Smallest eigenvalues:
 [1]  0.34347383  0.27432736  0.26188890  0.23710049  0.22722438  0.21810667
 [7]  0.19475320  0.01777969 -0.18448097 -0.26251265

Largest  eigenvalues:
 [1] 65754532 60415101 57841584 56729040 55100359 53409275 52978023 52750692
 [9] 51987324 51898316

Smallest eigenvalues:
 [1]  0.4341985  0.3725930  0.3666928  0.3291824  0.2923235  0.2614658
 [7]  0.1960324  0.1268017  0.1227838 -1.4700311

Largest  eigenvalues:
 [1] 64976715 59836961 57158468 56027573 55025189 53202778 52093152 52054413
 [9] 51493984 51140531

Smallest eigenvalues:
 [1]  0.49515698  0.44302564  0.35624174  0.34921851  0.33763801  0.29688016
 [7]  0.26949354  0.14490958 -0.08477671 -1.05720891

Largest  eigenvalues:
 [1] 63539838 59124913 56986340 55537837 54439466 52891167 51600459 51493504
 [9] 51429997 50568226

Smallest eigenvalues:
 [1]  0.43287209  0.39230530  0.33789149  0.31164282  0.26393407  0.19947962
 [7] -0.03676008 -0.07383353 -0.08369749 -0.22410323

Largest  eigenvalues:
 [1] 61127531 59035791 56117928 54820812 54126598 52912263 51797545 50841255
 [9] 50128339 49932966

Smallest eigenvalues:
 [1] -0.2460616 -0.3330930 -0.3729782 -0.3737812 -0.4331279 -0.5176597
 [7] -0.5487857 -0.9669094 -1.1436436 -1.2282288

Largest  eigenvalues:
 [1] 64858128 61061489 58209202 55631681 55550754 54216186 52454133 51974642
 [9] 51671098 51419047

Smallest eigenvalues:
 [1]  0.27058774  0.23880427  0.23389710  0.20867380  0.17934001  0.02470653
 [7] -0.01126291 -0.21387908 -0.34756716 -0.76965295

Largest  eigenvalues:
 [1] 64842719 61059995 57733046 56630744 55598746 54004868 52775192 52599737
 [9] 52376831 51802623

Smallest eigenvalues:
 [1]  0.39886268  0.30092224  0.25846460  0.24828442  0.21635403  0.11846062
 [7]  0.09696379 -0.05399715 -1.18493062 -1.22707519

Largest  eigenvalues:
 [1] 64505280 60140247 56638533 56268165 55292871 53292063 52537867 52240039
 [9] 52193336 51205387

Smallest eigenvalues:
 [1]  0.468809909  0.374803091  0.341744479  0.286649767  0.249555276
 [6]  0.189182536  0.142985110 -0.009777275 -0.622729528 -1.012807441

Largest  eigenvalues:
 [1] 64029117 58805802 56461250 55821379 53978132 52250512 51751027 51256342
 [9] 51020191 49960559

Smallest eigenvalues:
 [1]  0.424019349  0.324891136  0.238578223  0.228276122  0.226693893
 [6]  0.206355120  0.186955433  0.149452847  0.003521582 -7.045044203

Largest  eigenvalues:
 [1] 61832975 59825418 56886563 55066069 54669400 53472166 52120498 51468919
 [9] 50728614 50525906

Smallest eigenvalues:
 [1]  0.26833906  0.22044811  0.21640131  0.21348019  0.07544258  0.04953039
 [7] -0.12830040 -0.17947132 -1.00590867 -2.90901045

Largest  eigenvalues:
 [1] 66492448 60572966 57389874 56426197 55331903 53686182 52545385 52417101
 [9] 51793282 51658011

Smallest eigenvalues:
 [1]  0.43086981  0.35695808  0.34527069  0.34409043  0.25809766  0.24956918
 [7]  0.22633378  0.18869623  0.04441534 -0.06619720

Largest  eigenvalues:
 [1] 64569776 60746734 58209546 55780995 55604053 54234904 52757165 52437905
 [9] 51782170 51522448

Smallest eigenvalues:
 [1]  0.3199920  0.3085092  0.2815040  0.2192651  0.2166413  0.1703417
 [7]  0.1068566 -0.1781967 -0.2262937 -2.1929220

Largest  eigenvalues:
 [1] 65075273 60567053 57749733 55895980 55826053 54154201 52434478 52240629
 [9] 52204402 51355481

Smallest eigenvalues:
 [1]  0.36679593  0.36204198  0.30321159  0.27852106  0.20601523  0.09675696
 [7]  0.02474611 -0.08693992 -0.22011251 -1.60236497

Largest  eigenvalues:
 [1] 63877916 59888506 57013986 55192226 55033924 53438740 52166670 51471107
 [9] 51344018 51183333

Smallest eigenvalues:
 [1]  0.474959591  0.388621819  0.357229674  0.342993411  0.324167216
 [6]  0.310567632  0.241170437  0.013774104 -0.006679943 -0.073915400

Largest  eigenvalues:
 [1] 65237018 60365372 57467544 56411339 54843198 53060364 52541326 52121609
 [9] 51296529 50886352

Smallest eigenvalues:
 [1]  0.34471929  0.32909510  0.30661962  0.25509392  0.24737358  0.20364714
 [7]  0.06887637  0.05206281 -0.10369626 -2.43385066

Largest  eigenvalues:
 [1] 63171106 59821566 56965008 55146968 54994103 53372462 51709603 51671283
 [9] 51149930 50895599

Smallest eigenvalues:
 [1]  0.48916970  0.39957389  0.38312140  0.35914591  0.25344685  0.21311593
 [7]  0.18543280  0.12980339  0.03028597 -0.77720909

Largest  eigenvalues:
 [1] 65238373 59942593 57167130 57130370 54517661 53085943 52858254 52016865
 [9] 51906367 51073233

Smallest eigenvalues:
 [1]  0.37306304  0.32342526  0.32011327  0.17822441  0.14853715  0.14105478
 [7] -0.06471892 -0.22865453 -0.57631561 -0.71568892

Largest  eigenvalues:
 [1] 65070191 60984772 58054948 56780020 55345357 53402084 53005991 52656621
 [9] 51832038 51704852

Smallest eigenvalues:
 [1]  0.28908031  0.24141226  0.22387002  0.15346420  0.10963183  0.07682236
 [7] -0.03741547 -0.04481323 -0.79968007 -0.82843491

Largest  eigenvalues:
 [1] 64853322 60580673 58070284 56409408 55069526 53499647 52708025 52469870
 [9] 52087559 51785470

Smallest eigenvalues:
 [1]  0.33057720  0.28530559  0.27569552  0.22232186  0.13690152  0.02835007
 [7] -0.10745943 -0.36032917 -0.40872622 -1.11880970

Largest  eigenvalues:
 [1] 64155923 59585147 56853874 54875791 54761907 53058820 51286058 51238972
 [9] 51113988 50490770

Smallest eigenvalues:
 [1]  0.39960852  0.23095879  0.21918600  0.16759046  0.08511106  0.06018156
 [7] -0.03117794 -0.05202401 -0.09417116 -1.33545675

Largest  eigenvalues:
 [1] 63335509 59835216 56962529 55206734 54747277 53152608 51682359 51488730
 [9] 51309686 50888761

Smallest eigenvalues:
 [1]  0.5364285  0.5353717  0.4451344  0.4384927  0.4352319  0.3925692
 [7]  0.3231796  0.2993528  0.2874640 -0.2740327

Largest  eigenvalues:
 [1] 64168402 60433535 57581693 55838796 55364991 53658423 51735558 51697195
 [9] 51564242 50652737

Smallest eigenvalues:
 [1]  0.54477934  0.53961058  0.46571162  0.40663906  0.37828691  0.34767162
 [7]  0.20242885  0.10694160  0.01386924 -0.32716346

Largest  eigenvalues:
 [1] 62134351 59525841 56632421 55230589 54338034 53394068 51681453 51589397
 [9] 50455817 50289707

Smallest eigenvalues:
 [1]  0.44576428  0.32286257  0.31535376  0.25187381  0.14262545  0.12887404
 [7]  0.06061520  0.04429567 -0.05580773 -2.15177198

Largest  eigenvalues:
 [1] 63505411 59554332 56760102 55289636 55039486 53369357 52378995 51839392
 [9] 51441216 51216217

Smallest eigenvalues:
 [1]  0.5205121  0.5028372  0.4369018  0.3663844  0.3630000  0.3339224
 [7]  0.3291279  0.2937270  0.2668510 -0.4076816

Largest  eigenvalues:
 [1] 63812606 59626039 57210590 55512293 54681728 52916285 51692881 51525854
 [9] 51044999 50389901

Smallest eigenvalues:
 [1]  0.37353636  0.31628203  0.24671127  0.23271970  0.21987027  0.12945540
 [7] -0.01279438 -0.20582004 -0.29160393 -0.86838223

Largest  eigenvalues:
 [1] 64246167 60069298 57089796 56026719 55078598 53558221 52425139 51965156
 [9] 51934191 51448378

Smallest eigenvalues:
 [1]  0.387618700  0.350842220  0.313729781  0.274074025  0.230364909
 [6]  0.201045632  0.191965046  0.005931078 -0.145759565 -0.261922357

Largest  eigenvalues:
 [1] 64812748 61049897 58348316 56108538 55789309 54391289 52461537 52307812
 [9] 52019069 51537906

Smallest eigenvalues:
 [1]  0.35843234  0.35473116  0.33890849  0.32846012  0.31521429  0.28887962
 [7]  0.22239760  0.01641749 -0.23299799 -0.32896698

Largest  eigenvalues:
 [1] 65476519 60479513 57689154 56575188 55216963 53689845 52491133 52169096
 [9] 51982746 51247026

Smallest eigenvalues:
 [1]  0.46052563  0.43961626  0.41741332  0.40072946  0.30383083  0.25091436
 [7]  0.19061881  0.16642050  0.07783223 -0.13221950

Largest  eigenvalues:
 [1] 65440331 60869551 57965413 56422599 55596541 54095370 52633987 52530999
 [9] 52022117 51526187

Smallest eigenvalues:
 [1]  0.48360484  0.47577667  0.42888151  0.42256623  0.34681360  0.34478007
 [7]  0.27721432  0.25140540  0.22366972 -0.03321141

Largest  eigenvalues:
 [1] 65390979 60730666 57959144 56619766 56027558 54435551 52608311 52367810
 [9] 52286101 51354269

Smallest eigenvalues:
 [1]  0.3373224  0.3266732  0.2598420  0.2295445  0.2081416  0.1724380
 [7]  0.1444689 -0.5320565 -0.6962719 -0.7924707

Largest  eigenvalues:
 [1] 66333537 60712971 57981165 57139470 55098263 53523924 53274765 52331288
 [9] 51896990 51522859

Smallest eigenvalues:
 [1]  0.358128201  0.321289787  0.306916866  0.273582428  0.264583667
 [6]  0.191468149  0.163286958 -0.005859051 -0.391608586 -0.424768896

Largest  eigenvalues:
 [1] 63886544 60503146 57149465 55781985 55736539 54049574 52905981 52206455
 [9] 51954925 51687018

Smallest eigenvalues:
 [1]  0.48178954  0.40723983  0.39895801  0.38145384  0.31096653  0.25125948
 [7]  0.23717507  0.19727587  0.06835951 -0.09234222

Largest  eigenvalues:
 [1] 64917614 59570925 57013438 56450765 54200155 52678059 52445773 51409487
 [9] 51177865 50346307

Smallest eigenvalues:
 [1]  0.49139837  0.47513540  0.44025141  0.42538513  0.36614629  0.30053951
 [7]  0.28887771  0.07024903 -0.02697186 -0.46653374

Largest  eigenvalues:
 [1] 65266549 60192459 57627485 56337903 55479689 53456239 52604307 52102947
 [9] 51738313 51063413

Smallest eigenvalues:
 [1]  0.28076112  0.22395012  0.22355702  0.21288323  0.15382624  0.03527388
 [7] -0.13569635 -0.42121597 -0.59959270 -5.43688229

Largest  eigenvalues:
 [1] 66269055 60853321 57240954 57222216 55622334 53782052 53247162 52414815
 [9] 52221674 51469603

Smallest eigenvalues:
 [1]  0.27821730  0.19862006  0.19819928  0.13485490  0.07339599 -0.13500070
 [7] -0.28586167 -0.40306937 -0.99114765 -1.90357430

Largest  eigenvalues:
 [1] 64427041 60545555 57908962 56640833 55541517 53868869 52600700 52428444
 [9] 52259322 51271379

Smallest eigenvalues:
 [1]  0.14068416  0.09121334 -0.02220390 -0.06431161 -0.21434716 -0.26956082
 [7] -0.60929578 -1.21714060 -1.34764833 -1.48726618

Largest  eigenvalues:
 [1] 66219887 60093450 57918014 55880813 54851939 53048982 52343802 51705149
 [9] 51278967 50943662

Smallest eigenvalues:
 [1]  0.46875744  0.43413460  0.37802219  0.37219335  0.27783285  0.23231523
 [7]  0.17196609  0.15705356  0.05810619 -0.18960095

Largest  eigenvalues:
 [1] 65498045 61244736 58057107 56841727 55886177 54275404 53471337 52840763
 [9] 52377361 52076991

Smallest eigenvalues:
 [1]  0.30065156  0.28012827  0.24835356  0.24701815  0.13455353  0.12902444
 [7]  0.12729337  0.03730063 -0.78035003 -2.06242905

Largest  eigenvalues:
 [1] 63508021 59788113 56961370 55547485 54800061 53196096 51960334 51743953
 [9] 51524377 50954353

Smallest eigenvalues:
 [1]  0.29180419  0.27555984  0.24628449  0.22956510  0.20239016  0.18006428
 [7]  0.11235817  0.09156804 -0.04272696 -5.83561262

Largest  eigenvalues:
 [1] 63345500 60597202 57177419 55826058 54903460 53904659 51950536 51776875
 [9] 51023165 50725203

Smallest eigenvalues:
 [1]  0.51898108  0.51190742  0.49346421  0.45000858  0.44590826  0.40245592
 [7]  0.26890601  0.17226099  0.01089595 -0.01735811

Largest  eigenvalues:
 [1] 65450490 60164291 57661918 56539077 54888937 53282850 52370456 52311259
 [9] 51956350 51530022

Smallest eigenvalues:
 [1]  0.3058265  0.2989377  0.2661292  0.1974696  0.1739128  0.1180772
 [7]  0.1179815  0.1047524 -0.0267872 -1.6321315

Largest  eigenvalues:
 [1] 65868486 60961942 58268142 56642964 55654836 53985039 53045952 52600567
 [9] 52474029 52195419

Smallest eigenvalues:
 [1]  0.29353112  0.26421254  0.24069880  0.21331116  0.14220334  0.13595383
 [7]  0.08201721 -0.02624704 -1.37526050 -1.59779590

Largest  eigenvalues:
 [1] 66324597 60409218 57749827 56802431 55062561 53910980 52636040 52490835
 [9] 52366116 51812154

Smallest eigenvalues:
 [1]  0.3238356  0.2496848  0.2159286  0.1849888  0.1712111  0.1618124
 [7] -0.1586719 -0.2831307 -0.3315398 -0.9900699

Largest  eigenvalues:
 [1] 66198155 59954691 57371542 56871274 54652198 53037627 52860533 52456301
 [9] 51650825 51589338

Smallest eigenvalues:
 [1]  0.28030410  0.23164345  0.16569131  0.14974950  0.07352849 -0.04166859
 [7] -0.04956359 -0.38941178 -0.44200870 -0.53847499

Largest  eigenvalues:
 [1] 63973941 60192981 57661301 55427909 54774789 53571659 51624257 51540728
 [9] 51529087 50945402

Smallest eigenvalues:
 [1]  0.42430077  0.37351528  0.36916465  0.33133912  0.22922266  0.22083748
 [7]  0.14874419  0.08477195  0.06912904 -0.16018647

Largest  eigenvalues:
 [1] 64611572 60355340 57490467 56329037 55303275 53826454 52384693 52383575
 [9] 52180474 51306512

Smallest eigenvalues:
 [1]  0.50171588  0.46687751  0.45267226  0.39188347  0.34826348  0.32061463
 [7]  0.31232823  0.12021224  0.09798791 -0.13610437

Largest  eigenvalues:
 [1] 64772381 59660125 57134377 55753136 54904515 53502594 51926088 51854032
 [9] 51320852 50429195

Smallest eigenvalues:
 [1]  0.38531642  0.34042368  0.23556259  0.20364124  0.17823409 -0.04027302
 [7] -0.04702928 -0.05179629 -0.07915303 -1.30598756

Largest  eigenvalues:
 [1] 64284780 60462140 57269798 55685606 55474462 53795416 52884626 51973386
 [9] 51892705 51644598

Smallest eigenvalues:
 [1]  0.4215706  0.4121962  0.3736347  0.3310153  0.2855394  0.2404173
 [7]  0.2231569  0.2040454  0.1198840 -0.1835219

Largest  eigenvalues:
 [1] 62627336 60759937 57180116 55433331 55365360 53677334 52273855 52176674
 [9] 51348637 51157193

Smallest eigenvalues:
 [1]  0.4916969  0.4845972  0.4465242  0.4170723  0.3137256  0.3047418
 [7]  0.2508813  0.2288577  0.2121150 -0.0672257

Largest  eigenvalues:
 [1] 64235432 59578502 57258443 55447346 54628133 53072705 51695272 51402215
 [9] 51306666 50653162

Smallest eigenvalues:
 [1]  0.3842260  0.3788244  0.3093946  0.2491844  0.2410652  0.1990001
 [7]  0.1674324 -0.4061881 -0.6413068 -1.5163069

Largest  eigenvalues:
 [1] 62641300 59213911 56765481 55065029 54852673 53142059 51877363 51746645
 [9] 50950153 50613542

Smallest eigenvalues:
 [1]  0.60627072  0.59890510  0.54791023  0.44315392  0.38616628  0.35894897
 [7]  0.26408105  0.22032031  0.12442103 -0.01300647

Largest  eigenvalues:
 [1] 62810815 60171645 57072618 55771058 54808337 54115070 52447664 52203238
 [9] 51068261 50844478

Smallest eigenvalues:
 [1]  0.28762597  0.27535851  0.27197888  0.24981564  0.22488444  0.15031248
 [7]  0.02205735 -0.64347616 -0.90645808 -1.62884934

Largest  eigenvalues:
 [1] 64811016 60261258 57815952 56154256 55134026 53305000 52437683 52147419
 [9] 52080975 51590695

Smallest eigenvalues:
 [1]  0.43939866  0.38067198  0.30842538  0.29381131  0.25166320  0.14475968
 [7]  0.10947469  0.08465491 -0.13708031 -1.16591922

Largest  eigenvalues:
 [1] 65503611 60526228 57455322 56213183 55119027 53370079 52370235 52310403
 [9] 51914938 51329582

Smallest eigenvalues:
 [1]  0.114355585 -0.004635647 -0.008848434 -0.159913929 -0.164976422
 [6] -0.246746159 -0.336428536 -0.475751998 -0.693432413 -1.421451540

Largest  eigenvalues:
 [1] 63031583 59916935 57118657 55164654 54726760 53107658 52182645 51350157
 [9] 51156730 50926974

Smallest eigenvalues:
 [1]  0.45998872  0.41580810  0.39184842  0.33953891  0.33800481  0.33182469
 [7]  0.27681551  0.25551057  0.21870749 -0.02127224

Largest  eigenvalues:
 [1] 61723181 59132596 56775358 54843397 54310412 53083041 51443760 51092701
 [9] 50398566 50087078

Smallest eigenvalues:
 [1]  0.4124039  0.3006569  0.2514511  0.2511782  0.2249729  0.2143911
 [7]  0.1778251  0.1097218 -0.1895180 -0.2528983

Largest  eigenvalues:
 [1] 64547811 60215328 57630273 56368777 54897717 53369060 52518681 51626623
 [9] 51478585 50467374

Smallest eigenvalues:
 [1]  0.3579867  0.3538659  0.3065763  0.2799404  0.2398964  0.2322097
 [7]  0.1360400  0.1043339 -0.4957799 -1.1937904

Largest  eigenvalues:
 [1] 65307097 60270620 58356998 55588030 55510642 54424149 52858980 52693364
 [9] 51851792 51550041

Smallest eigenvalues:
 [1]  0.4043210  0.3438279  0.3292763  0.3054532  0.2274421  0.1681585
 [7]  0.1507635  0.1159263 -0.2828722 -0.4291482

Largest  eigenvalues:
 [1] 63682380 59316459 57318296 55877214 54162732 52832241 51785944 51713349
 [9] 51387607 50693001

Smallest eigenvalues:
 [1]  0.431394797  0.420844315  0.360916333  0.359955744  0.346086671
 [6]  0.339005585  0.285401444  0.257995076 -0.002866243 -5.545150798

Largest  eigenvalues:
 [1] 64216750 60061595 57117564 55598064 55108613 53333083 52120494 51716823
 [9] 51626127 50854276

Smallest eigenvalues:
 [1]  0.4608246  0.3841535  0.3712152  0.3627737  0.2946871  0.2719265
 [7]  0.2047346  0.1746251  0.1477002 -0.1509604

Largest  eigenvalues:
 [1] 64045586 59697654 57065280 55967590 54704728 53200363 52078906 51823622
 [9] 51804903 50923302

Smallest eigenvalues:
 [1]  0.522567142  0.508919326  0.412642972  0.352535295  0.307459818
 [6]  0.302199698  0.158631452  0.134830209  0.024603845 -0.002993484

Largest  eigenvalues:
 [1] 63177302 59624004 57131831 54773680 54626686 53134592 51864442 51348919
 [9] 50898124 50539322

Smallest eigenvalues:
 [1]  0.51385050  0.45614854  0.42400424  0.35775865  0.33238024  0.28848757
 [7]  0.24921755  0.16494337  0.02533496 -0.02961978

Largest  eigenvalues:
 [1] 61446744 59820695 56948255 56035796 54095329 53944818 52733495 51624963
 [9] 50741235 50665946

Smallest eigenvalues:
 [1]  0.46139118  0.44187490  0.39909965  0.33792925  0.31125959  0.29159161
 [7]  0.27961396  0.17456575  0.14171066 -0.03839334

Largest  eigenvalues:
 [1] 63714964 60702691 57312911 55907357 55824463 54108635 52535897 52011540
 [9] 51875612 51479550

Smallest eigenvalues:
 [1]  0.42639968  0.39559155  0.36525013  0.34761243  0.34320671  0.28718473
 [7]  0.26210578  0.21108925  0.05909535 -0.14595074

Largest  eigenvalues:
 [1] 61834668 60856656 57519513 55647639 55020232 53877479 52142949 52131096
 [9] 51248404 50990330

Smallest eigenvalues:
 [1]  0.30001491  0.29098047  0.26735308  0.20674120  0.16650157  0.12895381
 [7]  0.08717612 -0.13805674 -0.42287786 -0.51276924

Largest  eigenvalues:
 [1] 64617957 61378016 58295062 56594013 55839873 54005981 53775110 52832017
 [9] 52238143 52083503

Smallest eigenvalues:
 [1]  0.4068207  0.4065248  0.3910243  0.3167281  0.2799650  0.2734857
 [7]  0.2637625  0.2035177 -0.1255357 -4.0310711

Largest  eigenvalues:
 [1] 64923755 60501512 57783306 56311142 55204456 53720725 52398973 52116895
 [9] 52065385 51204325

Smallest eigenvalues:
 [1]  0.284458278  0.239570607  0.161864226  0.078653164  0.001354026
 [6] -0.049783775 -0.107340000 -0.436127485 -0.590370738 -1.137575036

Largest  eigenvalues:
 [1] 64891547 59770522 56935810 55457870 54649439 52996751 51960321 51644092
 [9] 51297891 51122953

Smallest eigenvalues:
 [1]  0.3988811  0.3785343  0.3597117  0.3264402  0.3187563  0.3079406
 [7]  0.2994325  0.1886132  0.1358960 -0.1118437

Largest  eigenvalues:
 [1] 65289964 60791535 57433230 57124862 55243598 53653674 52871165 52665504
 [9] 52329115 51409997

Smallest eigenvalues:
 [1]  0.42503823  0.39471310  0.26896249  0.23419675  0.23267573  0.19209878
 [7]  0.18739692 -0.06811077 -0.54508634 -0.63416543

Largest  eigenvalues:
 [1] 65320022 61025858 57394836 56222003 56006665 54116520 53056581 52540694
 [9] 52208895 51664922

Smallest eigenvalues:
 [1]  0.5547804  0.4796298  0.4590903  0.4184093  0.3740510  0.3720161
 [7]  0.3422207  0.3344018  0.2337584 -0.2264861

Largest  eigenvalues:
 [1] 64118028 60212374 57337982 56028139 55373081 53506169 52063641 51965326
 [9] 51773277 50799994

Smallest eigenvalues:
 [1]  0.29195785  0.26514031  0.22143992  0.21376256  0.16918389  0.15121911
 [7]  0.12781814  0.05062987 -0.04063535 -0.26847746

Largest  eigenvalues:
 [1] 62134203 58916993 56411820 54813421 54712013 53001419 51976627 51491648
 [9] 50715303 50466484

Smallest eigenvalues:
 [1]  0.57420020  0.53871151  0.48216025  0.44775400  0.39620996  0.39488092
 [7]  0.36739665  0.22070880  0.13224398 -0.06623388

Largest  eigenvalues:
 [1] 63968624 60037365 56660136 55413056 55287549 53582239 52220309 51450455
 [9] 51410823 50580619

Smallest eigenvalues:
 [1]  0.352742067  0.337433782  0.334528432  0.270141273  0.265758769
 [6]  0.173941368  0.162504619  0.062101215  0.006925509 -0.129423609

Largest  eigenvalues:
 [1] 64924472 59172526 56684532 56374077 54581068 53022179 52416933 51606833
 [9] 50762362 50190823

Smallest eigenvalues:
 [1]  0.397795416  0.375662603  0.335943325  0.311856821  0.294155796
 [6]  0.204684635  0.003725602 -0.216922536 -0.242593855 -2.926670356

Largest  eigenvalues:
 [1] 65461585 60376823 57493288 56042344 55495960 53954256 52660679 52163290
 [9] 51972204 51782551

Smallest eigenvalues:
 [1]  0.18194292  0.08483852 -0.06535354 -0.23098375 -0.23570552 -0.29365374
 [7] -0.43288915 -0.71670623 -0.83823223 -4.91196316

Largest  eigenvalues:
 [1] 62451671 59615497 56787975 55366325 54455170 53447420 52074444 51802714
 [9] 51036027 50681459

Smallest eigenvalues:
 [1]  0.637143917  0.538830483  0.513684301  0.504624488  0.431139853
 [6]  0.386743562  0.303686175  0.217925661  0.156696251 -0.001484799

Largest  eigenvalues:
 [1] 65111852 60550941 57706261 56389305 55355203 53864406 52454220 52406028
 [9] 52019443 51352038

Smallest eigenvalues:
 [1]  0.4381370  0.4163145  0.3968833  0.3435968  0.2781574  0.2569211
 [7]  0.1466814  0.1412468  0.1271378 -1.8012059

Largest  eigenvalues:
 [1] 63956777 60373091 57520828 55380189 55318216 53820383 52203252 52113608
 [9] 51522971 51319108

Smallest eigenvalues:
 [1]  0.4074957  0.3736822  0.3610401  0.3152661  0.2545363  0.2487171
 [7]  0.1374125  0.1346574 -0.3316199 -0.4561040

Largest  eigenvalues:
 [1] 63134456 60483048 56862999 55826770 54949694 53260382 52170498 51709374
 [9] 51536848 50733833

Smallest eigenvalues:
 [1]  0.3730152  0.3535112  0.3378832  0.3305521  0.2481641  0.2221549
 [7]  0.1935049  0.1100101 -0.1051907 -1.9676151

Largest  eigenvalues:
 [1] 61936147 59599615 56855775 54932905 54400927 53029978 51361980 51207151
 [9] 50618151 50410146

Smallest eigenvalues:
 [1]  0.46423913  0.40073847  0.36553243  0.34260564  0.32537861  0.29811718
 [7]  0.28135759  0.18887851  0.12339765 -0.04777045

Largest  eigenvalues:
 [1] 64927043 59830651 57435423 56049643 54706435 53080973 52191417 51846698
 [9] 51758212 51008885

Smallest eigenvalues:
 [1]  0.53378569  0.52429601  0.48888533  0.48028643  0.44036744  0.33179848
 [7]  0.18613807  0.11911690  0.06998202 -0.11580793

Largest  eigenvalues:
 [1] 63563802 60240938 57434281 55583602 55165952 53637103 52165471 51917817
 [9] 51678109 51046726

Smallest eigenvalues:
 [1]  0.4625514  0.4098466  0.3950050  0.3897157  0.3592403  0.1428243
 [7]  0.1260283  0.1138990 -0.1988930 -1.3626917

Largest  eigenvalues:
 [1] 64519744 59214123 56732450 54844362 54837469 53120083 52147075 51286113
 [9] 51212950 50596867

Smallest eigenvalues:
 [1]  0.44985555  0.43340665  0.39665318  0.37379911  0.29793721  0.17104380
 [7]  0.16079471  0.10643018  0.06518246 -1.59781987

Largest  eigenvalues:
 [1] 64446842 60147472 56881250 55975115 55313850 53315808 52367494 52052142
 [9] 51597967 51215915

Smallest eigenvalues:
 [1]  0.269956889  0.168703941  0.128518350  0.045044792  0.039120644
 [6]  0.003191129 -0.116530282 -0.330270907 -0.590093810 -0.851078350

Largest  eigenvalues:
 [1] 64240755 60878508 57548537 55651574 55272276 53572096 52107573 51850581
 [9] 51539419 51213731

Smallest eigenvalues:
 [1]  0.41871591  0.38195318  0.35698294  0.32602633  0.29134595  0.24158548
 [7]  0.22386232  0.19775791 -0.05521472 -2.23561446

Largest  eigenvalues:
 [1] 63191346 60076232 57326240 55869687 54709059 53356190 52177186 51715577
 [9] 51652003 51200595

Smallest eigenvalues:
 [1]  0.39243812  0.37778438  0.29793035  0.25610061  0.22433754  0.22185230
 [7]  0.01741347 -0.03202508 -0.08575769 -5.24342707

Largest  eigenvalues:
 [1] 63363168 59695982 56724347 55117036 54980511 52899753 51465013 51446686
 [9] 51224826 50449030

Smallest eigenvalues:
 [1]  0.49175672  0.40112003  0.36323426  0.29570560  0.27596625  0.23047658
 [7]  0.19690478  0.17238320  0.04136418 -0.98022697

Largest  eigenvalues:
 [1] 64944767 59798967 57647056 55922501 54627372 53456253 52215664 51699038
 [9] 51483015 50796357

Smallest eigenvalues:
 [1]  0.35680785  0.33378388  0.25902892  0.23487622  0.23211194  0.21514133
 [7]  0.16171935  0.09826078 -0.22083617 -0.80487036

Largest  eigenvalues:
 [1] 62464811 60246060 57279819 55640718 55052970 53486891 52297287 52177961
 [9] 51454446 50813074

Smallest eigenvalues:
 [1]  0.21809328  0.17766232  0.17054201  0.16118970  0.07402816  0.07078496
 [7] -0.10071888 -0.28095705 -1.46274409 -1.55358804

Largest  eigenvalues:
 [1] 63606322 59473104 56973373 54813005 54695710 53216161 51599122 51123121
 [9] 50987209 50443197

Smallest eigenvalues:
 [1]  0.36202829  0.35079600  0.24234965  0.20275350  0.16940017  0.10203958
 [7]  0.02006566 -0.04535303 -0.23270112 -3.57495525

Largest  eigenvalues:
 [1] 64980942 59705304 56925347 56302661 54872859 53152064 52460402 52262021
 [9] 51759935 51262943

Smallest eigenvalues:
 [1]  0.31840516  0.20177103  0.15939058  0.13932871 -0.02069221 -0.03142577
 [7] -0.11038247 -0.22070981 -1.09169964 -2.05762710

Largest  eigenvalues:
 [1] 65888465 59784264 57060916 56618711 54568943 53057364 52664335 52188248
 [9] 51414871 51391962

Smallest eigenvalues:
 [1]  0.46273726  0.36205484  0.22338922  0.19390587  0.18597176  0.15130079
 [7]  0.11961507 -0.06721433 -0.36030320 -1.67870313

Largest  eigenvalues:
 [1] 63818053 59417184 56343085 55084596 54632459 52934193 51713555 51286134
 [9] 51128063 50371408

Smallest eigenvalues:
 [1]  0.416692834  0.364815114  0.240203085  0.191391103  0.118741762
 [6]  0.063732697  0.004530815 -0.015170372 -0.077513604 -0.632270320

Largest  eigenvalues:
 [1] 63359283 59430167 56752892 54791207 54516702 53005746 51683104 51252831
 [9] 51073236 50643275

Smallest eigenvalues:
 [1]  0.48314931  0.39699723  0.38656114  0.36852205  0.31081783  0.29669520
 [7]  0.28052225 -0.03951312 -0.04482099 -2.32612212

Largest  eigenvalues:
 [1] 64308431 60612838 56984282 55689644 55565238 53620448 52189609 51984478
 [9] 51817341 51126469

Smallest eigenvalues:
 [1]  0.255893637  0.255496711  0.222270377  0.034376715 -0.009442275
 [6] -0.140263386 -0.433526406 -0.723518822 -1.077376241 -1.454730069

Largest  eigenvalues:
 [1] 65895119 59530534 56850827 56252136 54400012 52998113 52314320 51750849
 [9] 51363202 50943201

Smallest eigenvalues:
 [1]  0.31448537  0.31089953  0.24469739  0.18495554  0.12219551  0.02676088
 [7] -0.30076956 -0.85848804 -1.58658861 -1.85757015

Largest  eigenvalues:
 [1] 66457410 60426487 58459040 56947635 55141540 53193619 52890811 52219571
 [9] 51797093 51481297

Smallest eigenvalues:
 [1]  0.39882907  0.36988662  0.34962567  0.34640457  0.32618712  0.30297334
 [7]  0.25496569  0.19267631  0.18536449 -0.01011802

Largest  eigenvalues:
 [1] 64526635 60723027 58150356 55814539 55688479 54371589 52435290 52057851
 [9] 51923014 51186804

Smallest eigenvalues:
 [1]  0.10331314  0.09411901 -0.05479243 -0.10662159 -0.12199998 -0.31617443
 [7] -0.32968892 -0.38409834 -0.74752024 -1.24051087

Largest  eigenvalues:
 [1] 66153630 60398999 57972392 57252778 54850598 53367460 53112243 52797847
 [9] 51888651 51518140

Smallest eigenvalues:
 [1]  0.38241794  0.35423516  0.33731761  0.30472545  0.30069783  0.20922189
 [7]  0.10869108 -0.08314438 -0.15020855 -1.32186369

Largest  eigenvalues:
 [1] 63638549 60277715 57401201 56276972 55013923 53339215 52519683 52066540
 [9] 51829671 51332714

Smallest eigenvalues:
 [1]  0.49799915  0.44928913  0.44581410  0.41499356  0.33121849  0.27941617
 [7]  0.23813911  0.20386552  0.05577655 -0.06201129

Largest  eigenvalues:
 [1] 66259222 60049795 57766631 57093564 54859826 53569324 53193417 51933343
 [9] 51746823 50986621

Smallest eigenvalues:
 [1]  0.38344711  0.33708112  0.33666557  0.27678748  0.26551530  0.21773843
 [7]  0.20135358  0.05200353 -0.02940766 -0.41362848

Largest  eigenvalues:
 [1] 64948306 60119483 57028828 56571925 54897534 53300319 52546207 52486640
 [9] 51982007 51535200

Smallest eigenvalues:
 [1]  0.20179198  0.19685450  0.18101021  0.13777247 -0.03113217 -0.23597599
 [7] -0.51116234 -1.00738849 -1.38620527 -1.51914677

Largest  eigenvalues:
 [1] 65295663 60301423 57699408 56512384 54765000 53432575 52643772 52164124
 [9] 51620770 51354129

Smallest eigenvalues:
 [1]  0.5354128  0.5036787  0.4995127  0.4318419  0.3589464  0.3519149
 [7]  0.1788749  0.1578994  0.1156847 -0.2320354

Largest  eigenvalues:
 [1] 64203162 59266658 56591366 55558831 54351875 52286714 51617249 51118063
 [9] 51098441 50270800

Smallest eigenvalues:
 [1]  0.5313828  0.4991924  0.4406278  0.4039710  0.3529575  0.2939176
 [7]  0.2645401  0.0338451 -0.3570618 -4.0684087

Largest  eigenvalues:
 [1] 65487650 59825436 56828623 56436953 54550995 52546916 52259940 51470609
 [9] 51418905 50639626

Smallest eigenvalues:
 [1]  0.21519902  0.15399032  0.10489712 -0.02301297 -0.05059752 -0.12224821
 [7] -0.13170798 -0.77349678 -1.06153459 -1.88610184

Largest  eigenvalues:
 [1] 66332553 60411304 57380203 57188388 54998345 53277662 53126460 52821210
 [9] 51854920 51802795

Smallest eigenvalues:
 [1]  0.3746854  0.3275190  0.3178091  0.2250618  0.1771928  0.1572432
 [7]  0.1093535 -0.1651058 -0.3501318 -0.9610655

Largest  eigenvalues:
 [1] 64128097 59864698 56886956 55135106 54682539 53092378 51768006 51661962
 [9] 51289161 51044492

Smallest eigenvalues:
 [1]  0.39885408  0.37649569  0.36196943  0.28037889  0.26043615  0.20837866
 [7]  0.18578268  0.05003467  0.04163188 -1.45146658

Largest  eigenvalues:
 [1] 64616076 60324247 56857436 56039624 55398832 53639036 51908081 51784943
 [9] 51716899 50874203

Smallest eigenvalues:
 [1]  0.376280719  0.307968800  0.270685000  0.171366752  0.160953665
 [6]  0.108070901  0.072151884  0.020834484  0.002786508 -1.987170405

Largest  eigenvalues:
 [1] 63983121 60170079 57266457 55482300 55072229 53896826 52008947 51582188
 [9] 51111977 50789597

Smallest eigenvalues:
 [1]  0.24094082  0.16113435  0.07831721  0.04222213 -0.03530437 -0.04026649
 [7] -0.07239794 -0.12900239 -0.35897698 -0.82937782

Largest  eigenvalues:
 [1] 66149144 60763201 58175050 56352719 55258555 53761435 52584161 52274386
 [9] 51911871 51441598

Smallest eigenvalues:
 [1]  0.45072375  0.44930617  0.42707307  0.33227141  0.27608788  0.25176901
 [7]  0.05342844  0.04366002 -0.05559960 -2.35706928

Largest  eigenvalues:
 [1] 65316235 60092150 57101572 56471027 55207253 53717852 52384138 52138233
 [9] 51965542 51267309

Smallest eigenvalues:
 [1]  0.46426041  0.43155913  0.39258429  0.37299448  0.36460008  0.30936865
 [7]  0.28669020  0.17339815  0.13165021 -0.07712913

Largest  eigenvalues:
 [1] 64447110 59828114 56546209 55860706 54700493 53110423 51915110 51875719
 [9] 51444778 50799338

Smallest eigenvalues:
 [1]  0.32180708  0.30948438  0.28262209  0.22483686  0.19245215 -0.05613209
 [7] -0.09511850 -0.17865712 -0.56782904 -2.91985104

Largest  eigenvalues:
 [1] 65494462 60770984 57409712 55881813 55367889 53448261 51999398 51898515
 [9] 51631644 51150789

Smallest eigenvalues:
 [1]  0.4215955  0.3830922  0.3608919  0.3411174  0.3170894  0.3020075
 [7]  0.2732070  0.2585327  0.2136132 -0.0904391

Largest  eigenvalues:
 [1] 64170768 60128314 57281690 55445678 55411005 53774799 51903407 51567664
 [9] 51325856 50429510

Smallest eigenvalues:
 [1]  0.41027462  0.34991550  0.33201372  0.28719242  0.23969036  0.17322448
 [7]  0.08775426 -0.03237588 -0.07105975 -0.25147471

Largest  eigenvalues:
 [1] 65732569 60345982 57423459 56437619 55366065 53937114 52478352 51988905
 [9] 51832965 50614801

Smallest eigenvalues:
 [1]  0.30067100  0.25692767  0.17869120  0.14802603  0.13641694  0.11662896
 [7]  0.02789947 -0.76134603 -0.96719689 -1.04722745

Largest  eigenvalues:
 [1] 65316550 59817144 57643068 55937888 55004182 53727770 52529449 52012799
 [9] 52006955 51646610

Smallest eigenvalues:
 [1]  0.4718204  0.3725984  0.3688057  0.3619263  0.3417680  0.2895856
 [7]  0.2668145  0.2288515  0.1696846 -0.0419761

Largest  eigenvalues:
 [1] 65430252 60186549 57902544 56708130 54799905 53182629 52727318 51983730
 [9] 51787673 51207025

Smallest eigenvalues:
 [1]  0.16163110  0.10226022  0.07016115  0.01021784 -0.01938875 -0.15511759
 [7] -0.20201882 -0.28235975 -0.83649657 -1.41196324

Largest  eigenvalues:
 [1] 63589651 60474192 57779315 55120910 54979755 53748396 51942201 51879761
 [9] 51166026 50946444

Smallest eigenvalues:
 [1]  0.43652355  0.42026365  0.39998526  0.39097169  0.31227609  0.27948034
 [7]  0.26460260  0.19855633  0.06991435 -0.03640425

Largest  eigenvalues:
 [1] 65120762 60300018 58019377 55737396 55382700 53653209 52427660 52078487
 [9] 51952404 51482757

Smallest eigenvalues:
 [1]  0.365817485  0.253268375  0.245423941  0.174328665  0.139668327
 [6]  0.035727625  0.009370155 -0.049486401 -0.160140997 -0.538150752

Largest  eigenvalues:
 [1] 66174484 60557071 57955294 56600992 54988746 53595055 52667171 52608848
 [9] 51925991 51758373

Smallest eigenvalues:
 [1]  0.37421177  0.37286524  0.36146869  0.27574148  0.24273759  0.16643424
 [7]  0.16437171  0.10164275  0.03150259 -0.41895148

Largest  eigenvalues:
 [1] 66555193 61015849 57875134 57278162 56051532 54362047 53313086 53219235
 [9] 52404952 52003054

Smallest eigenvalues:
 [1]  0.42999126  0.39400374  0.32997726  0.30741752  0.29716140  0.24433894
 [7]  0.17649854  0.13992982  0.09912456 -0.68463267

Largest  eigenvalues:
 [1] 65480565 59535569 57271541 56789497 54602543 53325300 52731957 51867612
 [9] 51482190 50987039

Smallest eigenvalues:
 [1]  0.56084345  0.49043668  0.48142433  0.41932512  0.36428754  0.26911925
 [7]  0.25576346  0.21769094 -0.04888047 -3.80561657

Largest  eigenvalues:
 [1] 64832032 60105255 57402449 56089024 55128969 53440947 52201383 51955887
 [9] 51932038 50968290

Smallest eigenvalues:
 [1]  0.43845323  0.42975066  0.39989268  0.38468818  0.34356178  0.22839252
 [7]  0.20607929  0.08697602  0.07640505 -5.50472005

Largest  eigenvalues:
 [1] 63794133 60633576 57902608 56019595 55698928 54404253 52707114 52662581
 [9] 51882010 51585602

Smallest eigenvalues:
 [1]  0.4624995  0.3755231  0.3703261  0.3592630  0.3440499  0.3248258
 [7]  0.2752419  0.2409431  0.1158476 -0.7668570

Largest  eigenvalues:
 [1] 64221205 60318583 57709171 55619533 55531237 54156202 52544302 52282630
 [9] 51618503 51105844

Smallest eigenvalues:
 [1]  0.45448890  0.42029267  0.39848239  0.29456969  0.20575790  0.15607533
 [7]  0.13126174  0.08395056  0.01181098 -1.42544809

Largest  eigenvalues:
 [1] 63006324 60062214 56941706 55361428 54650641 53614751 51778485 51688758
 [9] 50917214 50820470

Smallest eigenvalues:
 [1]  0.51249200  0.45822914  0.40281296  0.39870987  0.36076613  0.35794471
 [7]  0.34564490  0.14319905  0.10718640 -0.07663943

Largest  eigenvalues:
 [1] 65176484 61281441 57663689 56588514 56289128 54564393 53434200 52573449
 [9] 52280838 51819554

Smallest eigenvalues:
 [1]  0.42829448  0.41753283  0.38087157  0.36199592  0.33765541  0.29052853
 [7]  0.26068976  0.01377166 -0.20060367 -0.87768029

Largest  eigenvalues:
 [1] 64144509 60444007 57639448 56127475 55400155 53856133 52361648 52171013
 [9] 51806209 51182076

Smallest eigenvalues:
 [1]   0.308025995   0.206761619   0.203216503   0.186286851   0.113052555
 [6]   0.076307466   0.006604131  -0.181839664  -0.291542576 -21.811795757

Largest  eigenvalues:
 [1] 65871585 59810854 57759104 56107180 54956920 53792945 52488773 52300045
 [9] 51995030 51435775

Smallest eigenvalues:
 [1]  0.4434678  0.3933192  0.3548960  0.2414716  0.2047585  0.1569187
 [7]  0.1048188 -0.1947996 -0.3046727 -0.7510127

Largest  eigenvalues:
 [1] 65753249 60422185 57651871 56907886 54849631 52897648 52848862 52433092
 [9] 51726218 51532197

Smallest eigenvalues:
 [1]  0.5779033  0.5601017  0.4521349  0.4358426  0.3057825  0.2802577
 [7]  0.2698895  0.2403582 -0.2231736 -0.2502104

Largest  eigenvalues:
 [1] 65495792 60740763 57667770 56644212 55475239 53738347 52781202 52599364
 [9] 51953171 51400325

Smallest eigenvalues:
 [1]  0.39276884  0.35729847  0.34816612  0.30998125  0.27557320  0.22853905
 [7]  0.14775489  0.11577115  0.08818914 -3.10563628

Largest  eigenvalues:
 [1] 63716726 59893907 57517720 55575251 54941132 53477474 51870779 51750287
 [9] 51570194 50904700

Smallest eigenvalues:
 [1]  0.34195849  0.24133060  0.21694165  0.19503112  0.10672832  0.02787603
 [7] -0.10118311 -0.21591306 -0.67050739 -1.28075896

Largest  eigenvalues:
 [1] 65171880 60592546 57871300 56212817 55299538 53882689 52342246 52080007
 [9] 51797614 51116417

Smallest eigenvalues:
 [1]  0.40662046  0.38647370  0.33170701  0.33162997  0.30318397  0.22392881
 [7]  0.20000899  0.08068127  0.05883845 -0.39544448

Largest  eigenvalues:
 [1] 65145845 60237238 57688219 56369463 55097132 53466215 53217061 52567880
 [9] 51852069 51605759

Smallest eigenvalues:
 [1]  0.4959148  0.4117465  0.3925934  0.3892781  0.2854885  0.2722464
 [7]  0.1915873  0.1864380 -0.1529678 -0.1771534

Largest  eigenvalues:
 [1] 64485225 60417703 57274239 55921359 55124532 53399009 51904648 51825347
 [9] 51797969 50898568

Smallest eigenvalues:
 [1]  0.6139020  0.5804288  0.5208425  0.5147206  0.4563544  0.3409322
 [7]  0.2962343  0.2506831  0.2447080 -0.6830423

Largest  eigenvalues:
 [1] 64533801 59843461 57051366 55700044 55026546 53588815 52152621 51836739
 [9] 51632093 50798520

Smallest eigenvalues:
 [1]  0.38089860  0.36074590  0.30022144  0.28137132  0.27443576  0.18334242
 [7]  0.17583582  0.16014067  0.13095374 -0.07063696

Largest  eigenvalues:
 [1] 65799156 60657443 58331932 56359963 55470306 53900753 52569202 52415561
 [9] 52330166 51790033

Smallest eigenvalues:
 [1]  0.3616097  0.3286228  0.3181877  0.3007739  0.2525987  0.2037673
 [7]  0.1977944  0.1026287 -0.5029078 -3.1767412

Largest  eigenvalues:
 [1] 65431182 59830413 57109716 56758413 54850195 52841188 52646603 52424251
 [9] 51838168 51478743

Smallest eigenvalues:
 [1]  0.4471657  0.4327267  0.3227875  0.2972009  0.2606796  0.2331267
 [7]  0.2251395  0.1442445  0.1034761 -0.6873129

Largest  eigenvalues:
 [1] 61983548 59479073 56151308 54809728 54805144 53062109 51964424 51953472
 [9] 50874982 50679640

Smallest eigenvalues:
 [1]  0.38179778  0.29670344  0.26829412  0.21802983  0.15912084  0.07662484
 [7] -0.02784264 -0.12456120 -0.57823318 -0.78838126

Largest  eigenvalues:
 [1] 65278982 61455893 58255280 57242291 55362965 53669651 53381839 52675368
 [9] 52285646 51440846

Smallest eigenvalues:
 [1]  0.4701700  0.4498259  0.4130603  0.3694225  0.3263399  0.2567731
 [7]  0.2288796  0.1915548  0.1630194 -0.6071124

Largest  eigenvalues:
 [1] 62909426 59399446 56885421 54818310 54707668 53234116 51921570 51200939
 [9] 50850083 50466636

Smallest eigenvalues:
 [1]  0.24025026  0.23284841  0.21419365  0.18911631  0.13054411  0.01454168
 [7] -0.13678224 -0.19889759 -0.32694998 -1.22316880

Largest  eigenvalues:
 [1] 64079599 59956866 57537982 55733631 54838047 53561966 51793740 51766962
 [9] 51707695 50824179

Smallest eigenvalues:
 [1]  0.41558011  0.37971485  0.23767634  0.07841913  0.07488108  0.04916357
 [7] -0.02906305 -0.08548154 -0.30606844 -2.11074582

Largest  eigenvalues:
 [1] 63827165 60265287 57422937 55607886 55498858 53761653 52625950 51818676
 [9] 51735138 51284014

Smallest eigenvalues:
 [1]  0.206281423  0.186940906  0.184822632  0.164652584  0.156494196
 [6]  0.147955263  0.058202108 -0.007530551 -0.279125147 -0.352152164

Largest  eigenvalues:
 [1] 63593910 59314045 56383037 55532901 54778798 53085053 51773136 51495649
 [9] 50830776 50198942

Smallest eigenvalues:
 [1]  0.47735267  0.38922739  0.38311668  0.37983251  0.34968656  0.28385840
 [7]  0.19040160  0.16099142 -0.08795911 -0.44315592

Largest  eigenvalues:
 [1] 64537503 60757877 57781254 55942695 55358972 53760801 52792436 52172156
 [9] 52105396 51884014

Smallest eigenvalues:
 [1]  0.36681956  0.33198055  0.33129214  0.32368534  0.24858332  0.21126190
 [7]  0.20711594  0.19122726 -0.08568089 -1.58808715

Largest  eigenvalues:
 [1] 64961779 60717350 58030721 55773400 55687200 54230392 52235425 52002581
 [9] 51934151 51336714

Smallest eigenvalues:
 [1]  0.23151387  0.16549267  0.15482562  0.08237195  0.03596431 -0.06702173
 [7] -0.37048212 -0.38894702 -1.34481634 -1.70611943

Largest  eigenvalues:
 [1] 64597605 59563841 56882993 55986066 54643173 53036149 52238462 51993337
 [9] 51601370 51022888

Smallest eigenvalues:
 [1]  0.43433141  0.41408769  0.29875081  0.29814096  0.23928795  0.23167230
 [7]  0.18174241  0.16648653 -0.06203392 -1.23436719

Largest  eigenvalues:
 [1] 64440736 60560603 57212631 56259889 55598767 53962329 52232686 52090257
 [9] 51934081 51051546

Smallest eigenvalues:
 [1]  0.3042010065  0.2028350908  0.1740175163  0.1612815640  0.1369131970
 [6]  0.0001836193 -0.0677540862 -0.2490146759 -0.4799055444 -1.0698131028

Largest  eigenvalues:
 [1] 64993726 60428037 57374522 56547352 54849189 53550509 52484664 52412518
 [9] 51789101 51646571

Smallest eigenvalues:
 [1]  0.27330582  0.23265980  0.20692219  0.12274527  0.07847066 -0.19807447
 [7] -0.25987368 -0.30761489 -0.51152650 -1.38724883

Largest  eigenvalues:
 [1] 64121480 59235452 57025321 55467561 54263155 53170667 51844510 51643615
 [9] 51464198 50938521

Smallest eigenvalues:
 [1]  0.22199018  0.21752864  0.17762979  0.16634727  0.12907103 -0.04799962
 [7] -0.09461652 -0.13949955 -0.17537962 -1.50600064

Largest  eigenvalues:
 [1] 64803510 60825577 57752098 56073264 55661494 54323780 52679780 52602585
 [9] 52017695 51827638

Smallest eigenvalues:
 [1]  0.529283596  0.519283179  0.490264063  0.434428678  0.422483895
 [6]  0.342396511  0.313743248  0.261834375  0.078963518 -0.009048804

Largest  eigenvalues:
 [1] 62319757 59863546 56791761 54995234 54701300 53307653 51698147 51593220
 [9] 50666779 50490874

Smallest eigenvalues:
 [1]   0.37679206   0.36717120   0.32350101   0.31689581   0.29871551
 [6]   0.25686390   0.25632731  -0.01333862  -0.06789774 -10.12314265

Largest  eigenvalues:
 [1] 64411516 59932779 57280277 55653920 55068576 53505755 52217133 51758458
 [9] 51549442 50961953

Smallest eigenvalues:
 [1]  0.33992151  0.33773102  0.33052832  0.24759088  0.17865735  0.16725219
 [7]  0.13009824  0.12557393  0.06940252 -0.05708416

Largest  eigenvalues:
 [1] 62687074 60046225 57096819 55454949 55099931 53311649 52429309 52254927
 [9] 51307310 51079840

Smallest eigenvalues:
 [1]  0.3734285  0.3578477  0.3031081  0.2387319  0.2306287  0.2039266
 [7]  0.1485060 -0.1171986 -0.3440188 -1.6214314

Largest  eigenvalues:
 [1] 65486043 60113924 57079185 56666044 55185757 53628727 52574929 52359392
 [9] 52009107 51585582

Smallest eigenvalues:
 [1]  0.49486609  0.47791572  0.45526315  0.38861004  0.26367715  0.24308695
 [7]  0.16907081  0.12584112  0.02471961 -0.01684104

Largest  eigenvalues:
 [1] 62945545 60794518 57637850 56261031 54882770 54402627 52808606 52517634
 [9] 51566391 51069462

Smallest eigenvalues:
 [1]  0.40440121  0.33971828  0.32780829  0.26849468  0.18441321  0.14547299
 [7]  0.03445263 -0.35447099 -0.44357899 -4.96304851

Largest  eigenvalues:
 [1] 65527053 60207613 57375006 56259761 55115688 53212988 52481602 52032514
 [9] 51617348 51241593

Smallest eigenvalues:
 [1]  0.2201364  0.1930468  0.1874791 -0.1227888 -0.1273022 -0.2719032
 [7] -0.2880179 -0.3875469 -0.4994241 -1.0144298

Largest  eigenvalues:
 [1] 65057256 61275334 57637187 56391357 56306501 54331565 53877199 52564757
 [9] 52190753 51824437

Smallest eigenvalues:
 [1]  0.4518062  0.3811479  0.3427248  0.3200841  0.2817578  0.2711405
 [7]  0.2704352  0.1788838 -0.2115723 -0.4633926

Largest  eigenvalues:
 [1] 64165066 60755183 58081525 56166649 55246195 53722459 52005370 51939202
 [9] 51843830 50931778

Smallest eigenvalues:
 [1]  0.25074725  0.20080264  0.10458999  0.08528284  0.07400013  0.01865420
 [7] -0.02934871 -0.12047732 -0.15615536 -3.60260821

Largest  eigenvalues:
 [1] 65005210 59847985 57578032 56482285 55144388 53920519 52943505 52327741
 [9] 52276216 51892719

Smallest eigenvalues:
 [1]  0.45241489  0.44066831  0.35509133  0.32710229  0.31067170  0.25264288
 [7]  0.18197227 -0.07615371 -0.23499493 -2.00386152

Largest  eigenvalues:
 [1] 65575740 59738799 56726747 56287922 54373976 52617790 52310861 51390303
 [9] 51134809 50635299

Smallest eigenvalues:
 [1]  0.4649903  0.4474241  0.4294076  0.3502424  0.3471955  0.2751184
 [7]  0.2261942  0.1726147  0.1328097 -0.3506693

Largest  eigenvalues:
 [1] 64730132 59805212 57428042 55376687 55297960 53809419 51715412 51587904
 [9] 51486614 50723969

Smallest eigenvalues:
 [1]  0.53888156  0.45745730  0.39162100  0.36546596  0.32729226  0.24969499
 [7]  0.22215482  0.09068120  0.03596904 -0.16543456

Largest  eigenvalues:
 [1] 64285560 60171025 57302773 55878871 55708304 54134687 52378623 52314474
 [9] 51809959 51710390

Smallest eigenvalues:
 [1]   0.30722470   0.26472251   0.20720361   0.17229991   0.08035100
 [6]   0.06282899  -0.13471021  -0.24564233  -0.84712211 -19.78156914

Largest  eigenvalues:
 [1] 63373225 60139956 57612673 55372237 55048578 53712521 52590324 51754877
 [9] 51208079 50960488

Smallest eigenvalues:
 [1]  0.45094110  0.43401422  0.40202821  0.37104549  0.28886965  0.28196224
 [7]  0.19893324  0.14721583  0.05688805 -0.63896127

Largest  eigenvalues:
 [1] 65752212 59703940 57233182 56738997 54613908 53095906 52639259 52129237
 [9] 51608316 51128829

Smallest eigenvalues:
 [1]  0.538572136  0.515976379  0.469945128  0.430167322  0.366027608
 [6]  0.317178642  0.142653151  0.084944324  0.041586483 -0.008741183

Largest  eigenvalues:
 [1] 64580174 60202693 57517011 55442585 55231930 53796502 52481055 52135800
 [9] 51571013 51344194

Smallest eigenvalues:
 [1]  0.36606927  0.35714062  0.29389149  0.23647287  0.21072451  0.18678329
 [7]  0.09481632 -0.06747963 -0.23553946 -1.14394497

Largest  eigenvalues:
 [1] 64461719 59735997 56821507 56081272 54957468 53379231 52166592 52112757
 [9] 51622284 51044612

Smallest eigenvalues:
 [1]  0.46249793  0.43717746  0.40706058  0.30474117  0.27275971  0.26185734
 [7]  0.22445666  0.19572387  0.03786895 -1.21038559

Largest  eigenvalues:
 [1] 63452371 59579523 57298204 55281584 54737329 53529528 52205879 51839523
 [9] 51449580 51030156

Smallest eigenvalues:
 [1]  0.44583460  0.43792066  0.38713001  0.34232814  0.32319399  0.30532744
 [7]  0.20429410  0.03224634 -0.10057823 -0.38382236

Largest  eigenvalues:
 [1] 62820107 59663631 57056598 55572069 54853961 53197441 51612340 51509818
 [9] 51435912 50413943

Smallest eigenvalues:
 [1]  0.48627473  0.48486213  0.44672818  0.33133222  0.29116410  0.24938516
 [7]  0.17885290  0.15383709  0.03918108 -0.32173457

Largest  eigenvalues:
 [1] 64044075 60455779 57302207 55913636 55661146 53944846 52678631 52321508
 [9] 52078249 51483432

Smallest eigenvalues:
 [1]  0.5002047  0.4877379  0.4363611  0.3618692  0.2871384  0.2837144
 [7]  0.2813088  0.2140507 -0.4797941 -0.9148599

Largest  eigenvalues:
 [1] 63638083 59431396 56612639 55357256 54698638 52886140 52464489 51393630
 [9] 51193909 50785635

Smallest eigenvalues:
 [1]  0.40686541  0.40339525  0.38322734  0.35472292  0.31792274  0.14749524
 [7]  0.10558648  0.01705676 -0.01633554 -1.35660784

Largest  eigenvalues:
 [1] 65858758 59719838 57339255 56055788 54743702 53212222 52241443 51955715
 [9] 51846048 50763179

Smallest eigenvalues:
 [1]  0.43457226  0.39821612  0.39522916  0.33260903  0.30360549  0.27909684
 [7]  0.09056232  0.07132009 -0.03331028 -0.15457582

Largest  eigenvalues:
 [1] 64720423 59776526 57054000 55910283 55196154 53571753 51959316 51679796
 [9] 51182446 50133327

Smallest eigenvalues:
 [1]  0.39260874  0.33435365  0.30692710  0.30182919  0.18902775  0.18174103
 [7]  0.12612453 -0.01734765 -0.23787213 -1.24284197

Largest  eigenvalues:
 [1] 63199803 60239464 57177048 55512057 54614668 53577085 51846545 51628947
 [9] 51002896 50764446

Smallest eigenvalues:
 [1]  0.50145166  0.48650096  0.38400414  0.34200567  0.24375922  0.17251154
 [7]  0.15953227  0.12035749  0.02524313 -0.77626865

Largest  eigenvalues:
 [1] 62208651 59439404 56257202 54771859 54608922 52944998 51956172 51311175
 [9] 50736905 50573517

Smallest eigenvalues:
 [1]  0.56872319  0.55253719  0.52510494  0.38457499  0.37944957  0.32946291
 [7]  0.14578330  0.06764163 -0.02156755 -0.08872731

Largest  eigenvalues:
 [1] 65497041 59685859 56909482 56792229 54671221 52837401 52798023 51602580
 [9] 51214826 50555018

Smallest eigenvalues:
 [1]  0.45195098  0.33012824  0.32135000  0.24388514  0.20623307  0.06529955
 [7]  0.04877222 -0.10096606 -0.42589629 -1.64607516

Largest  eigenvalues:
 [1] 65073717 61262736 57555699 57004377 56014142 54035441 53623577 52585375
 [9] 52541897 52021777

Smallest eigenvalues:
 [1]  0.36025654  0.26378349  0.21604217  0.21202484  0.10607797  0.08405659
 [7] -0.07731024 -0.60904395 -0.67791686 -1.48559029

Largest  eigenvalues:
 [1] 66083921 59610777 56943449 56626455 54251470 52778248 52755492 51933327
 [9] 51177987 51122943

Smallest eigenvalues:
 [1]  0.49283605  0.48350648  0.37031427  0.34334530  0.34313966  0.24508915
 [7]  0.22922330  0.02242962 -0.07046072 -0.09086812

Largest  eigenvalues:
 [1] 64279055 59176574 56610448 55358905 54514337 52907435 51709124 51318291
 [9] 50987734 50327076

Smallest eigenvalues:
 [1]  0.59273904  0.45494010  0.43849772  0.42920931  0.31278377  0.31257013
 [7]  0.26006999  0.15085641 -0.01491967 -0.18238095

Largest  eigenvalues:
 [1] 63841274 59410326 56573212 55552144 54267231 52710932 51581156 51387589
 [9] 50842338 49968115

Smallest eigenvalues:
 [1]  0.32548894  0.28259775  0.26385580  0.25170916  0.18768399  0.17611072
 [7]  0.13279673  0.05586095  0.01349406 -0.62425734

Largest  eigenvalues:
 [1] 65491052 60679702 58281654 56793204 55238631 54039033 52738094 52398507
 [9] 52174768 51299871

Smallest eigenvalues:
 [1]  0.26999467  0.24067227  0.18690195  0.17381151  0.15689405  0.06549953
 [7]  0.02325153 -0.01391736 -0.02708347 -1.39803260

Largest  eigenvalues:
 [1] 65084599 59667335 56795187 55302314 54541184 52989902 51781746 51415711
 [9] 51288702 50928691

Smallest eigenvalues:
 [1]  0.481809313  0.463455723  0.380058870  0.303092990  0.297394438
 [6]  0.296393546  0.260159155  0.245311660  0.001545766 -5.653291840

Largest  eigenvalues:
 [1] 65444898 60920182 58162050 56492742 55877988 54191029 52776147 52371895
 [9] 52288088 51327756

Smallest eigenvalues:
 [1]  0.42724661  0.36254226  0.26973931  0.24610441  0.18356294  0.17923246
 [7]  0.11800548  0.09199347 -0.04562304 -2.16147899

Largest  eigenvalues:
 [1] 64443860 59692638 56612346 55302251 54601411 53081073 51565075 51394645
 [9] 51080771 50329756

Smallest eigenvalues:
 [1]  0.127079620  0.121829523 -0.009105345 -0.098734966 -0.175533379
 [6] -0.252872943 -0.275911775 -0.311978659 -0.407907347 -2.161574917

Largest  eigenvalues:
 [1] 65166770 60394479 57775083 55548521 55184248 53636282 52218048 51709664
 [9] 51565684 51504031

Smallest eigenvalues:
 [1]  0.498621018  0.482464932  0.464719120  0.367635146  0.357574127
 [6]  0.281352521  0.156715382  0.137070219 -0.002578572 -0.026560631

Largest  eigenvalues:
 [1] 63739908 60064686 56938842 55368735 55233402 53695629 52270016 52120536
 [9] 51489855 51181683

Smallest eigenvalues:
 [1]  0.4550115  0.4339077  0.4096776  0.4083677  0.2809894  0.2704890
 [7]  0.2332062  0.1926729  0.1642633 -0.3350256

Largest  eigenvalues:
 [1] 65597075 60361315 57620003 56372938 54974286 53558960 52533581 51877096
 [9] 51684126 51062125

Smallest eigenvalues:
 [1]  0.59293228  0.58439590  0.46079415  0.45680111  0.32576455  0.30668977
 [7]  0.26509910  0.22948079  0.08844987 -0.19775837

Largest  eigenvalues:
 [1] 66080229 60433448 57848196 56491531 55229555 53883980 52610828 52405954
 [9] 51883012 51441355

Smallest eigenvalues:
 [1]  0.37981832  0.36038541  0.35522910  0.32377308  0.27366214  0.22163999
 [7]  0.17251062  0.13792477 -0.08273076 -0.55500850

Largest  eigenvalues:
 [1] 65121254 60782164 58069287 56509829 55274120 53986842 52427337 52286661
 [9] 52056309 51143008

Smallest eigenvalues:
 [1]  0.4922655  0.4512300  0.4361336  0.3612484  0.3577866  0.3213488
 [7]  0.3003183  0.2121997  0.1652579 -0.2157578

Largest  eigenvalues:
 [1] 64907340 59573935 56568121 56394720 54398209 52937925 52218787 51739831
 [9] 51448563 50468316

Smallest eigenvalues:
 [1]  0.5408972  0.5211180  0.5062630  0.4059827  0.3587215  0.3547026
 [7]  0.1936218  0.1909158  0.1808374 -0.1337813

Largest  eigenvalues:
 [1] 63808887 60205071 56991351 55354761 55284676 53747266 52290576 52010319
 [9] 51451656 51267976

Smallest eigenvalues:
 [1]  0.3447919987  0.3307802435  0.2989218221  0.2922549215  0.2223076358
 [6]  0.1546549790  0.1139861743  0.0701401505  0.0005542438 -0.0658164069

Largest  eigenvalues:
 [1] 62031393 60336994 57417077 55937013 55018472 54168102 52646816 52352086
 [9] 51505789 51012184

Smallest eigenvalues:
 [1]  0.6018108  0.5702971  0.5446860  0.4811291  0.4214358  0.4008453
 [7]  0.3032235  0.2026565  0.1251318 -0.6339919

Largest  eigenvalues:
 [1] 64140185 60661946 57032731 55678399 55601213 53980704 52335225 52178298
 [9] 51534697 51069349

Smallest eigenvalues:
 [1]  0.4444439  0.4202566  0.3568545  0.3111323  0.2645969  0.2453223
 [7]  0.1863267  0.1122573  0.1027479 -0.2382730

Largest  eigenvalues:
 [1] 65917226 60080011 57518928 57227433 54856524 53449453 53203666 52068827
 [9] 52001653 51138955

Smallest eigenvalues:
 [1]  0.36775398  0.36635231  0.28628080  0.22434271  0.14659257  0.10947501
 [7]  0.07425764 -0.13103102 -0.46137337 -8.81269989

Largest  eigenvalues:
 [1] 65632878 60315777 57704361 56882175 55055499 53485093 52860971 52488291
 [9] 52332170 51832382

Smallest eigenvalues:
 [1]  0.41436564  0.38280502  0.36637619  0.29972288  0.21380625  0.19608325
 [7]  0.13019916  0.02778648 -0.26604737 -0.36041729

Largest  eigenvalues:
 [1] 63463811 60308786 56959079 55314477 54933507 53235613 52011915 51545353
 [9] 51359442 51117125

Smallest eigenvalues:
 [1]  0.42499966  0.40481843  0.37754132  0.33857223  0.19431705  0.18293681
 [7] -0.08745294 -0.22701228 -0.22901659 -1.85418629

Largest  eigenvalues:
 [1] 64778842 59975199 57334997 56085416 54691803 53210121 52154412 52089627
 [9] 51865965 51359928

Smallest eigenvalues:
 [1]  0.43607020  0.38846239  0.37169210  0.32916283  0.26544295  0.25766863
 [7]  0.23214259  0.19554605 -0.01945274 -0.23953616

Largest  eigenvalues:
 [1] 63577978 59508908 57116957 55813181 54230290 52799328 51803495 51498936
 [9] 51095340 50431225

Smallest eigenvalues:
 [1]  0.382521787  0.303025366  0.233012294  0.222400318  0.217929149
 [6]  0.146430846  0.003283711 -0.071249471 -0.364714792 -2.076921842

Largest  eigenvalues:
 [1] 63389438 60524476 57270817 55576869 54974677 53437762 52024739 51993810
 [9] 51715772 51310069

Smallest eigenvalues:
 [1]  0.35367247  0.34057294  0.30666115  0.23073180  0.22192793  0.18926718
 [7]  0.18611158  0.05033477 -0.67011418 -1.04611634

Largest  eigenvalues:
 [1] 64474348 59593010 57349514 56989253 54446650 52950565 52602283 52560805
 [9] 51821221 51089856

Smallest eigenvalues:
 [1]  0.18523578  0.16596405  0.09903060  0.07801804  0.07507484  0.04546843
 [7]  0.01899126 -0.02363648 -0.57226297 -1.83073925

Largest  eigenvalues:
 [1] 66504444 61601941 58788573 57689326 55697108 54093670 53626734 52955438
 [9] 52543049 52223916

Smallest eigenvalues:
 [1]  0.4544503  0.4184977  0.4027554  0.3353646  0.3245670  0.2896932
 [7]  0.2108479  0.1587453  0.1257685 -0.1317678

Largest  eigenvalues:
 [1] 65259073 60189300 57816812 56136084 54910889 53332152 52055641 52008840
 [9] 51532561 51196078

Smallest eigenvalues:
 [1]  0.45254930  0.44487126  0.39384401  0.38563752  0.34448654  0.29665333
 [7]  0.19905804  0.15241638  0.00551193 -0.03876237

Largest  eigenvalues:
 [1] 65927861 60712931 57938491 56459590 55520595 53970151 52773381 52682583
 [9] 52463471 51814417

Smallest eigenvalues:
 [1]  0.410698714  0.408099959  0.243021489  0.232795109  0.127629407
 [6]  0.083217061  0.003270844 -0.155305548 -0.395444815 -2.934279357

Largest  eigenvalues:
 [1] 65876519 60353230 57619607 56827282 55201571 53869789 52895199 52133512
 [9] 52105097 51236102

Smallest eigenvalues:
 [1]  0.181022704  0.174913007  0.150845916  0.042466630 -0.009345051
 [6] -0.096044263 -0.183298468 -0.187795549 -0.836485269 -3.559519544

Largest  eigenvalues:
 [1] 62707691 59235668 56963571 54769921 54040168 53213604 51564434 51096805
 [9] 50516481 50315509

Smallest eigenvalues:
 [1]  0.165680136  0.146564132  0.112689155  0.046108623 -0.002610232
 [6] -0.023676892 -0.124903852 -0.136475594 -0.232947222 -0.383598663

Largest  eigenvalues:
 [1] 64922418 60290803 57654552 55311559 54784116 53417417 52095025 51496364
 [9] 51305503 51217163

Smallest eigenvalues:
 [1]  0.44105618  0.39454040  0.32722464  0.30564660  0.28974343  0.21912103
 [7]  0.12869477  0.02467714 -0.10971108 -2.06292443

Largest  eigenvalues:
 [1] 65484262 59849210 57211460 56312252 54694300 53293779 52426081 51836154
 [9] 51818290 51009001

Smallest eigenvalues:
 [1]  0.32180552  0.18214718  0.13225753  0.10831086  0.03874408 -0.04069816
 [7] -0.15856280 -0.24018360 -0.87680988 -1.68601624

Largest  eigenvalues:
 [1] 64515020 59466898 56478765 55719171 54747729 52889345 51884086 51712812
 [9] 51281814 50690846

Smallest eigenvalues:
 [1]  0.47174664  0.47005563  0.34241999  0.33970331  0.28957042  0.19171958
 [7]  0.04497320  0.04476324 -0.04559572 -0.31645563

Largest  eigenvalues:
 [1] 64531091 60184811 57181651 56350083 54713090 53098936 52418216 52223430
 [9] 51552641 51090515

Smallest eigenvalues:
 [1]  0.41526513  0.39880820  0.34388130  0.27121541  0.24190545  0.18419011
 [7]  0.07437829 -0.16510526 -0.21212665 -4.52041256

Largest  eigenvalues:
 [1] 62207773 59355186 55921699 54675618 54162259 52702627 51450199 50723030
 [9] 50231418 49925273

Smallest eigenvalues:
 [1]  0.37074429  0.34164873  0.30671791  0.27714647  0.22234495  0.19320356
 [7]  0.16831436  0.07345757  0.04423442 -1.44009343

Largest  eigenvalues:
 [1] 63990438 59830093 57168527 55672086 55412440 53844115 52520037 51969896
 [9] 51625410 51474002

Smallest eigenvalues:
 [1]  0.30022882  0.27236204  0.22714886  0.19124063  0.11819728  0.07276478
 [7] -0.07348596 -0.20636960 -0.21830364 -1.29573249

Largest  eigenvalues:
 [1] 64236562 59801849 56369385 55094268 54736682 52852062 51490881 51162714
 [9] 51105142 50595417

Smallest eigenvalues:
 [1]  0.09820088  0.01650463 -0.07651741 -0.13403839 -0.15289827 -0.22207786
 [7] -0.39813064 -0.48560551 -0.91696221 -3.76682158

Largest  eigenvalues:
 [1] 62954386 59115222 56085525 54841022 54356505 52832332 51992030 51445482
 [9] 50825124 50507288

Smallest eigenvalues:
 [1]  0.420085508  0.393832512  0.376946216  0.357338459  0.277455977
 [6]  0.207533793  0.080876851  0.008207197 -0.168546993 -0.398576622

Largest  eigenvalues:
 [1] 64370745 60413383 57136266 56321755 55023929 53177864 52610524 52328249
 [9] 51732811 51464329

Smallest eigenvalues:
 [1]  0.4724632  0.4370566  0.4265297  0.4231744  0.3627276  0.3252239
 [7]  0.1988408  0.1272765 -0.3075132 -0.9177189

Largest  eigenvalues:
 [1] 63308648 60185682 57366272 55834980 54989849 53201688 51978565 51913818
 [9] 51804414 50900120

Smallest eigenvalues:
 [1]  0.34648664  0.33279024  0.30633631  0.29363954  0.12753658  0.11236166
 [7] -0.01674858 -0.06218904 -0.20278956 -1.65584630

Largest  eigenvalues:
 [1] 62864323 60792602 57091288 55771527 55201640 53898426 52213670 51827805
 [9] 51245487 50946048

Smallest eigenvalues:
 [1]  0.35996701  0.34816292  0.30543824  0.28775183  0.24654443  0.22504584
 [7] -0.07327008 -0.08201719 -0.92335522 -1.33899399

Largest  eigenvalues:
 [1] 63152375 59536511 56998389 55489336 54728026 53018664 51765333 51693990
 [9] 51507978 50776270

Smallest eigenvalues:
 [1]  0.34145843  0.30525460  0.24207377  0.19609694  0.18092572  0.07296567
 [7]  0.04392425 -0.07557654 -0.20843504 -1.00644044

Largest  eigenvalues:
 [1] 64191288 60468457 57349626 55987471 55267367 53752561 52402743 52337988
 [9] 51930716 51342907

Smallest eigenvalues:
 [1]  0.16480505  0.10501115  0.09733584 -0.05264161 -0.11341967 -0.54094444
 [7] -0.62447927 -1.04296375 -1.10775942 -1.28413435

Largest  eigenvalues:
 [1] 65721208 59250519 56443440 55962739 54075474 52612083 52042557 51583471
 [9] 51297542 50731930

Smallest eigenvalues:
 [1]  0.4553532  0.4397757  0.4357501  0.2878770  0.2780496  0.2022769
 [7]  0.1498324  0.1361284  0.1015900 -0.9212881

Largest  eigenvalues:
 [1] 64679249 60718639 57771459 55864558 55720175 54153124 53002686 52082547
 [9] 51922089 51684424

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	3.273444	0.7430787	16.39471	0.035	2.593625	2.965928

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

EDA ~ alt + n + speed + PM1

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- EDA_fd
covariates <- list(altitude = altitude_fd, 
                   noise = noise_fd,
                   speed = speed_fd,
                   pollution = pollution1_fd)
path_plot <- 'figures/model_EDA_alt_noise_speed_PM1_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     noise = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     speed = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     pollution = list(nbetabasis = 80, norder = 4, lambda = 1e3))

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, HR = HR,
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 19.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 496 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Smallest eigenvalues:
 [1]  0.4111067859  0.4060596198  0.3915250907  0.3667542688  0.2747280854
 [6]  0.1836739357  0.0994980542  0.0730505790 -0.0004004443 -0.0564971211

Largest  eigenvalues:
 [1] 64776286 59806579 56995660 56046498 54865431 53214158 52133738 51963655
 [9] 51377558 50380134

Smallest eigenvalues:
 [1]  0.41932427  0.35981599  0.35825030  0.32100910  0.31044862  0.31040949
 [7]  0.21655105  0.11850137  0.09216851 -1.42811397

Largest  eigenvalues:
 [1] 64114397 60417755 57701449 56477539 54715351 53279357 52419901 51941557
 [9] 51841653 50940665

Smallest eigenvalues:
 [1]  0.34746559  0.30655599  0.26388856  0.19530274  0.17362013  0.05345603
 [7] -0.03063299 -0.14074432 -0.86686973 -2.82532815

Largest  eigenvalues:
 [1] 62446331 60010974 57464031 55380578 54991825 53699220 51963773 51925015
 [9] 51193654 50702954

Smallest eigenvalues:
 [1]  0.456027527  0.439197069  0.414925503  0.401800672  0.318674363
 [6]  0.263457887  0.199399706  0.107372129  0.002413811 -0.009647748

Largest  eigenvalues:
 [1] 63269966 59621072 56521866 55407703 54652412 52835529 51487587 51384960
 [9] 51348493 50284578

Smallest eigenvalues:
 [1]  0.34795582  0.30190306  0.29234353  0.27092669  0.23874343  0.20285868
 [7]  0.13030180 -0.05677447 -0.13152799 -0.16863223

Largest  eigenvalues:
 [1] 65182869 59492190 57147297 56272884 54754012 53274887 52349292 51851275
 [9] 51358340 50870318

Smallest eigenvalues:
 [1]  0.42666426  0.39250159  0.34191829  0.34048308  0.27595871  0.25541766
 [7]  0.24606421  0.18622557  0.09519852 -0.25319954

Largest  eigenvalues:
 [1] 64686203 60943774 57505812 56899873 55617922 54073533 52933142 52670288
 [9] 52074406 51595708

Smallest eigenvalues:
 [1]  0.38288370  0.36655658  0.32959381  0.26726602  0.26357324  0.24175543
 [7]  0.05750062  0.04134855 -0.10808766 -0.55646867

Largest  eigenvalues:
 [1] 65106461 60216870 57807132 57067224 54611099 53370733 52891045 52109430
 [9] 52026742 51326348

Smallest eigenvalues:
 [1]  0.4100950  0.3926993  0.3489299  0.2395718  0.2204637  0.1803786
 [7]  0.1548194  0.1356109  0.0586312 -0.8274448

Largest  eigenvalues:
 [1] 65384400 60187214 57143720 56593391 54453800 52841008 52609853 52166583
 [9] 51355190 51335870

Smallest eigenvalues:
 [1]  0.40967101  0.39961533  0.37790619  0.34270204  0.34030965  0.32247737
 [7]  0.26907640  0.02517217 -0.01636911 -0.06923915

Largest  eigenvalues:
 [1] 65261007 59384721 56838961 56379126 54043196 52775407 52173240 51685327
 [9] 51038976 50707233

Smallest eigenvalues:
 [1]  0.5022787  0.4059451  0.3628788  0.3289123  0.2555456  0.2243377
 [7]  0.1938979  0.1416800  0.1286817 -2.1010851

Largest  eigenvalues:
 [1] 64431141 59590009 57218222 56191284 54200245 52453528 52103090 51546390
 [9] 51365994 50771667

Smallest eigenvalues:
 [1]  0.32753087  0.28660565  0.23819976  0.21831565  0.13671448  0.11018802
 [7]  0.09660409  0.09518589  0.06379272 -0.39374274

Largest  eigenvalues:
 [1] 64253153 59994854 57599777 55658141 54809574 53616891 52437973 51884816
 [9] 51823181 51580091

Smallest eigenvalues:
 [1]  0.40346117  0.39854181  0.38753630  0.25290181  0.20491381  0.18177633
 [7]  0.04344643  0.01677451 -0.03913939 -0.17609229

Largest  eigenvalues:
 [1] 64775179 60637979 57621838 56565725 54976012 53429516 52599335 51968080
 [9] 51857839 50621840

Smallest eigenvalues:
 [1]  0.48112129  0.46662833  0.43584216  0.42275464  0.33599547  0.30974390
 [7]  0.05678591  0.03898816 -0.13860770 -2.91531114

Largest  eigenvalues:
 [1] 64691794 60828389 57245667 56589811 55441208 53693200 53431834 52586481
 [9] 51670160 51471212

Smallest eigenvalues:
 [1]  0.36614103  0.34388287  0.26465753  0.25689074  0.25089086  0.14117391
 [7]  0.09406132  0.03769098 -0.23609521 -3.54391180

Largest  eigenvalues:
 [1] 63025192 60080884 57177815 55389350 55252021 53771531 52270610 52225026
 [9] 51341969 51107016

Smallest eigenvalues:
 [1]  0.44061106  0.38370316  0.32256110  0.29240347  0.25207303  0.23990358
 [7]  0.22538252  0.20540340 -0.02396898 -0.05299193

Largest  eigenvalues:
 [1] 65092697 59752620 57118382 56652411 54489553 52929063 52645662 51693008
 [9] 51683653 50864064

Smallest eigenvalues:
 [1]  0.46684848  0.46455623  0.44385813  0.38111165  0.33488923  0.24463498
 [7]  0.06157924  0.04126850 -0.12465960 -0.15389065

Largest  eigenvalues:
 [1] 64854299 59600960 56703000 56264249 54459487 52700279 52238290 52182457
 [9] 51559931 51218870

Smallest eigenvalues:
 [1]  0.25669589  0.22820437  0.21415073  0.09354814 -0.03540017 -0.06424339
 [7] -0.14584829 -0.33104255 -0.42264955 -2.73951310

Largest  eigenvalues:
 [1] 65918448 59534026 56704235 56469173 54446355 52829444 52786999 51674873
 [9] 51206189 50452932

Smallest eigenvalues:
 [1]  0.48311108  0.46754444  0.42026058  0.39779941  0.35393456  0.34280085
 [7]  0.21703309  0.09933597 -0.03776027 -0.85445499

Largest  eigenvalues:
 [1] 62832385 59970809 56542783 55234557 54897699 53438640 52265579 51362351
 [9] 50940999 50442493

Smallest eigenvalues:
 [1]  0.37036520  0.35845806  0.21320802  0.20693907  0.12495424  0.03973884
 [7] -0.04189556 -0.13963061 -0.30328702 -0.53304849

Largest  eigenvalues:
 [1] 65649012 60560699 57382592 56559344 55807553 53892536 52678825 52549933
 [9] 52407890 51384984

Smallest eigenvalues:
 [1]  0.40798411  0.39577985  0.27992797  0.27524419  0.26917476  0.22259952
 [7]  0.21085507  0.01762706 -0.19089999 -0.64791046

Largest  eigenvalues:
 [1] 66148246 59936532 56938692 56737207 54361291 53024794 52703894 52052551
 [9] 51180755 51025623

Smallest eigenvalues:
 [1]  0.41859956  0.38661586  0.38539630  0.31270567  0.28355908  0.18329513
 [7]  0.13084286 -0.07979516 -0.30269587 -1.75181268

Largest  eigenvalues:
 [1] 63312075 59819165 56820222 54857803 54792932 53382808 52040556 51966322
 [9] 51026025 50824184

Smallest eigenvalues:
 [1]  0.45065580  0.44408923  0.39251473  0.28796502  0.24931205  0.21483115
 [7]  0.18864842  0.11894359 -0.06480995 -2.45543060

Largest  eigenvalues:
 [1] 65316430 60383288 57671272 56991201 54726515 53389863 52828170 52095731
 [9] 51723794 51125035

Smallest eigenvalues:
 [1]  0.4683560  0.3985859  0.3958591  0.3198591  0.3148761  0.2789644
 [7]  0.2765103  0.1530935 -0.6180494 -1.1234251

Largest  eigenvalues:
 [1] 64901428 59732531 56683090 56446438 54166473 52547745 52419617 51279064
 [9] 51116933 50252196

Smallest eigenvalues:
 [1]  0.40889761  0.40548754  0.38093545  0.32265653  0.31419768  0.29392001
 [7]  0.28559350  0.22841887  0.04085756 -0.03215193

Largest  eigenvalues:
 [1] 63714213 59722760 56863218 55605542 54407699 52706481 51678167 51332580
 [9] 51269465 50370549

Smallest eigenvalues:
 [1]  0.430266651  0.407953318  0.407932440  0.365711687  0.361813138
 [6]  0.312648265  0.265442346  0.218579524 -0.006299881 -0.159976375

Largest  eigenvalues:
 [1] 63342268 59943320 57077323 55388994 54915008 53239025 51780660 51701445
 [9] 51469768 50864582

Smallest eigenvalues:
 [1]  0.5087335  0.4917932  0.4690036  0.4529612  0.4189303  0.3891217
 [7]  0.3818905  0.1945198  0.1553195 -0.2295465

Largest  eigenvalues:
 [1] 64786430 60109120 56822273 56003811 54638389 52698395 52101328 51775439
 [9] 51393498 50974535

Smallest eigenvalues:
 [1]  0.28533345  0.23417890  0.22138217  0.20451751  0.14382624  0.10672599
 [7] -0.03808189 -0.54828249 -0.72582920 -1.46781903

Largest  eigenvalues:
 [1] 65740527 60518065 57842226 56957398 55095913 53048971 53043423 52949699
 [9] 51849419 51749296

Smallest eigenvalues:
 [1]  0.3645848496  0.3614161559  0.3261276958  0.2835010152  0.2314311827
 [6]  0.2242678111  0.1778167700  0.0959320039  0.0008347958 -0.1527933507

Largest  eigenvalues:
 [1] 63239619 60502852 57679271 55495275 55389795 54022119 52579505 52134410
 [9] 51511486 51035661

Smallest eigenvalues:
 [1]  0.337408164  0.330771843  0.244612008  0.238668427  0.219901188
 [6]  0.182588058  0.180819122  0.068154489  0.029216102 -0.001743209

Largest  eigenvalues:
 [1] 64893718 59187935 56707445 56138859 54313201 52755766 52136583 51761702
 [9] 51019511 50706542

Smallest eigenvalues:
 [1]  0.417875053  0.386816177  0.330835252  0.307963965  0.200738602
 [6]  0.151420132  0.116478234  0.109863568  0.005544936 -0.020929634

Largest  eigenvalues:
 [1] 63371402 59345571 56994568 55449610 54622016 52943287 51638224 51549504
 [9] 51474957 50632506

Smallest eigenvalues:
 [1]  0.33566072  0.27121461  0.24859670  0.22550764  0.18029414  0.11280523
 [7]  0.10655890  0.06922503  0.04628951 -0.37365294

Largest  eigenvalues:
 [1] 61588691 59009095 56166019 54601949 54102143 52230984 50956356 50813038
 [9] 50559184 49634210

Smallest eigenvalues:
 [1]  0.2935846  0.2455671  0.2241380  0.1885087  0.1504163  0.1423864
 [7]  0.1340019 -0.4380236 -0.4785979 -5.0220223

Largest  eigenvalues:
 [1] 63855459 60582627 57544086 56534516 55535467 54802364 52893934 51948811
 [9] 51657106 51170757

Smallest eigenvalues:
 [1]  0.37900212  0.34292936  0.25403431  0.23092215  0.21864850  0.20914778
 [7]  0.15253268  0.07504411  0.04965593 -0.01201788

Largest  eigenvalues:
 [1] 63424796 60683036 57534926 55960092 54988766 53556368 51983129 51920619
 [9] 51903241 50633303

Smallest eigenvalues:
 [1]  0.36845861  0.36218236  0.34715168  0.29601468  0.27956358  0.25117287
 [7]  0.22010688  0.21475405 -0.02979225 -0.51878155

Largest  eigenvalues:
 [1] 63720488 60094697 57397907 56148258 54997583 53337317 52563635 52172712
 [9] 51524321 51026322

Smallest eigenvalues:
 [1]  0.40641253  0.37725052  0.36152601  0.34473107  0.31464252  0.29481929
 [7]  0.14523208  0.07203331  0.02375869 -0.38660684

Largest  eigenvalues:
 [1] 62686817 59129639 56076682 55559913 54234740 52377899 51453696 51177205
 [9] 51036717 49891869

Smallest eigenvalues:
 [1]  0.47386376  0.44647779  0.41744761  0.30609730  0.25286853  0.22763894
 [7]  0.10418029  0.05621746 -0.05317571 -0.17907467

Largest  eigenvalues:
 [1] 64617178 60278766 57683557 56755755 54833653 53126542 52650332 52110486
 [9] 51791825 50977613

Smallest eigenvalues:
 [1]  0.38697427  0.37851103  0.34798907  0.29813017  0.24645090  0.20580741
 [7] -0.09538171 -0.34392516 -0.35418749 -2.51850878

Largest  eigenvalues:
 [1] 65195565 59431694 56620593 56394111 54210596 52517191 52259828 51903675
 [9] 51134386 50770169

Smallest eigenvalues:
 [1]  0.30460289  0.24902795  0.24378799  0.24056480  0.21196222  0.08181235
 [7]  0.06595614  0.01182288 -0.10864379 -0.50939880

Largest  eigenvalues:
 [1] 63897877 58969414 56345817 55609982 54132315 52283775 51549099 51408710
 [9] 51056792 50116509

Smallest eigenvalues:
 [1]  0.46472842  0.39754446  0.38327359  0.33155064  0.30238399  0.20216482
 [7]  0.14200928  0.04891835 -0.07681344 -0.21892836

Largest  eigenvalues:
 [1] 65738328 61193814 57482269 56913549 55845190 54089362 53009626 52892388
 [9] 52171353 51921838

Smallest eigenvalues:
 [1]  0.47253552  0.42018637  0.39705278  0.33586691  0.31965066  0.25882492
 [7]  0.19703330  0.15759150  0.04297667 -3.93959590

Largest  eigenvalues:
 [1] 64697851 61135291 57808662 56035212 56010846 54151177 52771924 52316137
 [9] 52235069 51660277

Smallest eigenvalues:
 [1]  0.47403206  0.46325011  0.39645051  0.35196463  0.34587219  0.26327375
 [7]  0.22499491  0.19503739  0.09328555 -0.07000572

Largest  eigenvalues:
 [1] 63590085 59935078 56910186 55355015 55053166 53296053 52119637 51472066
 [9] 51453457 50936874

Smallest eigenvalues:
 [1]  0.5042682  0.4957445  0.4711529  0.4002012  0.3733133  0.2939521
 [7]  0.2819625  0.2229576  0.1654210 -0.1289347

Largest  eigenvalues:
 [1] 65137782 59851491 56995899 55903658 55038764 53257397 52140155 51609227
 [9] 51549448 50369119

Smallest eigenvalues:
 [1]  0.38142517  0.37274411  0.35776423  0.17734417  0.17006631  0.10158363
 [7] -0.01243380 -0.06234247 -0.24472521 -0.54180621

Largest  eigenvalues:
 [1] 65193181 59765852 56988311 56971148 54439948 52988641 52843269 51891463
 [9] 51769392 50924555

Smallest eigenvalues:
 [1]  0.52890241  0.50520436  0.43107167  0.36139184  0.35691020  0.34803100
 [7]  0.30239200  0.22797505  0.01712836 -1.72110422

Largest  eigenvalues:
 [1] 63312265 60028109 56795456 55474236 55066779 53629254 52138711 51475981
 [9] 51198505 50604615

Smallest eigenvalues:
 [1]  0.57259226  0.52724697  0.41433012  0.38918462  0.34405067  0.29060570
 [7]  0.25968765  0.21073526  0.16407224 -0.06270084

Largest  eigenvalues:
 [1] 63061481 60093141 56929986 55620924 54844072 53210847 51798200 51659437
 [9] 51561301 50744667

Smallest eigenvalues:
 [1]  0.4629470  0.3735626  0.3428416  0.3177159  0.3076850  0.2051303
 [7]  0.1756806  0.1749230  0.1584508 -0.6929274

Largest  eigenvalues:
 [1] 63622784 59299134 56581855 55124306 54872565 53218955 51656725 51211841
 [9] 50892179 50080756

Smallest eigenvalues:
 [1]  0.43787493  0.42586114  0.34936057  0.30228151  0.26226710  0.25898663
 [7]  0.24720131  0.12523122  0.06132591 -0.03893736

Largest  eigenvalues:
 [1] 63210731 58994405 56485940 55125110 54112918 52606117 51397917 51161450
 [9] 51120059 50186689

Smallest eigenvalues:
 [1]  0.423535025  0.399340685  0.350846534  0.348249226  0.279995345
 [6]  0.144745777  0.136606622  0.007269806 -0.003594220 -0.140345556

Largest  eigenvalues:
 [1] 61914811 59257636 56322632 55120593 53973184 53275122 51750323 51367791
 [9] 50324151 50084642

Smallest eigenvalues:
 [1]  4.163020e-01  3.837330e-01  3.542165e-01  2.693236e-01  2.347104e-01
 [6]  2.012945e-01  1.823881e-01  1.405314e-01  8.516289e-02 -2.344407e-05

Largest  eigenvalues:
 [1] 63208380 60061732 56880170 55607659 54978209 53328298 52656110 52041426
 [9] 51680873 51482270

Smallest eigenvalues:
 [1]  0.33215143  0.27876901  0.27561970  0.25239191  0.24495329  0.23861548
 [7]  0.19227594  0.16427481 -0.09162574 -0.09464162

Largest  eigenvalues:
 [1] 63229112 58816289 56374734 54726694 54676849 52898033 51416744 50916668
 [9] 50855595 50133268

Smallest eigenvalues:
 [1]  0.4147003164  0.4039546899  0.3911389589  0.3379692885  0.2910189415
 [6]  0.2685145538  0.1562274291  0.1184301786 -0.0001589854 -0.6446075474

Largest  eigenvalues:
 [1] 65578304 60348906 57553373 56778727 54783787 53229979 52896141 51937282
 [9] 51467342 50908595

Smallest eigenvalues:
 [1]  0.4157501  0.4153980  0.4004454  0.3988825  0.3227513  0.2862461
 [7]  0.2703148  0.2072963 -0.1682199 -0.7203737

Largest  eigenvalues:
 [1] 64269381 60742275 57354458 56683065 55191957 53510756 52607619 52499626
 [9] 52049502 51364003

Smallest eigenvalues:
 [1]  0.513935574  0.449616132  0.414397072  0.412105909  0.397535673
 [6]  0.348660922  0.234639311  0.200582564  0.006845092 -0.184814437

Largest  eigenvalues:
 [1] 64396621 59730961 57313462 55661346 54707706 53632760 52029463 51760870
 [9] 51477575 50856704

Smallest eigenvalues:
 [1]  0.42395456  0.35746282  0.34650781  0.25418387  0.16691537  0.13977310
 [7]  0.10221085 -0.03885257 -0.05896622 -0.07901664

Largest  eigenvalues:
 [1] 62299054 60506216 57084514 55562827 55136925 53786765 52523373 52490245
 [9] 51307302 51129061

Smallest eigenvalues:
 [1]  0.42714140  0.40437521  0.35513403  0.32138062  0.30815829  0.29377149
 [7]  0.21810485  0.14733562  0.06677596 -1.57385290

Largest  eigenvalues:
 [1] 64915524 60290007 57258047 56045798 55454941 53903655 52230443 52059623
 [9] 52011283 51308714

Smallest eigenvalues:
 [1]  0.4375071  0.4163303  0.3892812  0.3629351  0.3431135  0.2732576
 [7]  0.2542686  0.2375373  0.1760501 -0.3738515

Largest  eigenvalues:
 [1] 65797041 60336589 57253003 57110398 54300392 53106568 52568494 51855116
 [9] 51331634 51059262

Smallest eigenvalues:
 [1]  0.309308394  0.280202595  0.224181619  0.153702976  0.104855876
 [6]  0.094462373  0.048514453  0.001636483 -0.146414654 -0.308949610

Largest  eigenvalues:
 [1] 63937953 60589349 57127462 56005491 55178997 53542959 53027880 52091574
 [9] 51795621 51716421

Smallest eigenvalues:
 [1]  0.47821198  0.44648237  0.43950381  0.42388484  0.41408850  0.37335460
 [7]  0.21289649  0.03040335 -0.02260064 -0.14560059

Largest  eigenvalues:
 [1] 64905274 59984785 57022605 56299374 54535734 52642684 52442960 51463678
 [9] 51007285 50250031

Smallest eigenvalues:
 [1]  0.4770757  0.4389563  0.3958883  0.2874747  0.2529428  0.2488271
 [7]  0.1948643  0.1788865  0.1313565 -0.1380460

Largest  eigenvalues:
 [1] 64666835 60249432 57849938 56393640 54840400 53482917 52588832 52420611
 [9] 51935029 51683320

Smallest eigenvalues:
 [1]  0.4559853  0.4135622  0.3302414  0.3089361  0.2851032  0.2386932
 [7]  0.2236101  0.1522095 -0.8410498 -5.4109808

Largest  eigenvalues:
 [1] 66596712 59870452 57315632 56722126 54228914 53291565 52493670 51731060
 [9] 51214712 50689076

Smallest eigenvalues:
 [1]  0.37463844  0.35407140  0.33249877  0.29121754  0.28514685  0.26966769
 [7]  0.20700293  0.13063432  0.06274704 -0.59291370

Largest  eigenvalues:
 [1] 64028069 59466943 56448107 56276999 54472723 52736518 52062873 51776550
 [9] 51710027 50841575

Smallest eigenvalues:
 [1]  0.45370720  0.41746077  0.38474299  0.30601530  0.30575321  0.24755227
 [7]  0.23548911  0.12005640 -0.07512968 -1.33675093

Largest  eigenvalues:
 [1] 65626744 60850485 57794433 56981762 55660667 53989801 53198138 53055165
 [9] 52150807 51730168

Smallest eigenvalues:
 [1]  0.38659604  0.34104758  0.33047231  0.29781052  0.21338135  0.18997626
 [7]  0.05679216 -0.11263587 -1.10506400 -1.52074106

Largest  eigenvalues:
 [1] 63054991 60153707 56968472 55855674 55266404 53533718 52268163 52001163
 [9] 51600067 50997361

Smallest eigenvalues:
 [1]  0.50060689  0.45660494  0.41715382  0.41137887  0.38002651  0.34964750
 [7]  0.20837024  0.18424049  0.02820403 -1.85161083

Largest  eigenvalues:
 [1] 63295154 59861234 56645150 54947579 54661893 52952763 51513694 51107188
 [9] 51038847 50332309

Smallest eigenvalues:
 [1]  0.4770865  0.4483542  0.4173920  0.3905126  0.3798266  0.3792588
 [7]  0.2378632  0.1712681 -0.4537652 -1.0035315

Largest  eigenvalues:
 [1] 65079455 59802719 57286363 56359055 54542118 52903017 52319485 51994926
 [9] 51904962 51150141

Smallest eigenvalues:
 [1]  0.4749295  0.4102342  0.3931711  0.3399493  0.3040926  0.2530724
 [7]  0.1707636  0.1688260 -0.0674789 -5.3894161

Largest  eigenvalues:
 [1] 65686553 60376660 57941207 57060740 55241484 53788840 52990489 52644283
 [9] 52373160 51623773

Smallest eigenvalues:
 [1]  0.05784091  0.02952196  0.01261396 -0.03971815 -0.10855747 -0.21352522
 [7] -0.30843741 -0.62711038 -0.77494692 -1.95812448

Largest  eigenvalues:
 [1] 66206502 59817238 57267568 57081256 54279468 53056365 53024913 51934690
 [9] 51886921 51183354

Smallest eigenvalues:
 [1]  0.4387407  0.4062699  0.3853362  0.3184361  0.2886097  0.2858855
 [7]  0.2385515  0.2375246  0.1293310 -4.7552705

Largest  eigenvalues:
 [1] 65948819 59714655 57183056 57030250 54700796 53084953 52969253 52158724
 [9] 51814698 51246049

Smallest eigenvalues:
 [1]  0.45539080  0.34197461  0.33845521  0.31480683  0.27999123  0.20581157
 [7]  0.18201863  0.16258885  0.02738596 -0.01186590

Largest  eigenvalues:
 [1] 63342308 60708724 57505649 55570253 55506964 53929813 52263287 51794836
 [9] 51606952 51014797

Smallest eigenvalues:
 [1]  0.394497530  0.381129220  0.266990056  0.233745799  0.206133045
 [6]  0.155111969  0.084627541  0.023333878 -0.007756513 -0.032460323

Largest  eigenvalues:
 [1] 64623753 60925903 57964271 56969706 54617420 53308408 52809280 51893762
 [9] 51655611 50917559

Smallest eigenvalues:
 [1]  0.42118161  0.34597774  0.32546703  0.20560167  0.20216586  0.19148582
 [7]  0.17773152  0.08563578 -0.46133472 -0.51239087

Largest  eigenvalues:
 [1] 63795689 59739643 56690781 55656712 54932216 53460686 52452321 51937507
 [9] 51631518 51349230

Smallest eigenvalues:
 [1]  0.40511651  0.40389447  0.37068046  0.34024774  0.32062752  0.21066618
 [7]  0.15957844  0.05668655 -0.01959660 -0.06373214

Largest  eigenvalues:
 [1] 62521052 59354904 56748330 55179535 54739505 52799342 51675347 51599739
 [9] 51125288 50577512

Smallest eigenvalues:
 [1]  0.54264528  0.50092400  0.47570980  0.43237444  0.39971448  0.34315201
 [7]  0.32916607  0.23155452  0.18255630 -0.08849715

Largest  eigenvalues:
 [1] 62958704 60642463 57290614 55439755 55368675 53617192 52378322 52098263
 [9] 51465661 50922475

Smallest eigenvalues:
 [1]  0.48493551  0.47455061  0.40050141  0.29050258  0.25940824  0.23842616
 [7]  0.23531196  0.22731032 -0.04005743 -0.18128685

Largest  eigenvalues:
 [1] 65224287 60974191 58090111 57048375 55320195 53780563 53064111 52663689
 [9] 52273230 51491540

Smallest eigenvalues:
 [1]  0.55489215  0.53206278  0.52033071  0.47228161  0.42434380  0.39763010
 [7]  0.37059699  0.31041877  0.15222602 -0.04864723

Largest  eigenvalues:
 [1] 65768202 60154193 57263187 56555667 54450551 52723593 52646440 52110896
 [9] 51202982 51129351

Smallest eigenvalues:
 [1]  0.3300423  0.3296091  0.3001157  0.2585520  0.2250404  0.2173399
 [7]  0.1344559 -0.1556361 -0.2503543 -3.9281720

Largest  eigenvalues:
 [1] 62939742 59527136 56926141 55654634 55192152 53445833 51889388 51685488
 [9] 51556724 50513184

Smallest eigenvalues:
 [1]  0.30033249  0.25172429  0.19605676  0.17847207  0.09115679  0.05481704
 [7]  0.04101656  0.01562529 -0.82241850 -4.47677978

Largest  eigenvalues:
 [1] 64874073 59461977 56574650 56187258 54608269 52978057 52163514 51352543
 [9] 51282230 50458182

Smallest eigenvalues:
 [1]  0.38865787  0.34726590  0.30768725  0.28431863  0.26403695  0.23211328
 [7]  0.18397852  0.16484702  0.04968852 -0.26449748

Largest  eigenvalues:
 [1] 61386416 59578826 56754557 55184652 54145391 53244921 51886943 51061337
 [9] 50320485 50262684

Smallest eigenvalues:
 [1]  0.34104983  0.32610285  0.29095574  0.27022214  0.26569540  0.20892956
 [7]  0.19145478  0.07754775  0.06867515 -1.20845806

Largest  eigenvalues:
 [1] 64413442 59454864 56957389 55325678 55201264 53412482 51741070 51627566
 [9] 50790370 50258723

Smallest eigenvalues:
 [1]  0.46315197  0.40150090  0.39414803  0.35436059  0.34697991  0.23998470
 [7]  0.21091155  0.19262153  0.09640275 -0.01958691

Largest  eigenvalues:
 [1] 63024552 59431094 56797882 54923387 54688887 53168965 51653565 51591610
 [9] 51034663 50757027

Smallest eigenvalues:
 [1]  0.3881591  0.3840806  0.3614975  0.3052538  0.2894149  0.1820190
 [7]  0.1152468 -0.1138531 -0.1644902 -0.1752864

Largest  eigenvalues:
 [1] 64990633 60785142 58388146 55848438 55316000 53721633 52547209 52414458
 [9] 52057515 51834471

Smallest eigenvalues:
 [1]  0.36033977  0.33333958  0.30786123  0.22595951  0.20053913  0.03342066
 [7]  0.01975513 -0.25250002 -0.25489441 -0.80448272

Largest  eigenvalues:
 [1] 63687493 59376285 57282945 56063134 54275990 52727241 52018724 51564004
 [9] 51455906 50547549

Smallest eigenvalues:
 [1]  0.5727016  0.5492716  0.5140339  0.5054864  0.4769919  0.4218387
 [7]  0.3548869  0.3207122  0.2406381 -2.3514650

Largest  eigenvalues:
 [1] 64423801 60060008 57177027 56197578 54621647 52745500 52184481 51614125
 [9] 51445337 50622501

Smallest eigenvalues:
 [1]  0.4515304  0.4245778  0.4050474  0.3938016  0.3802573  0.3169860
 [7]  0.3143473  0.2583652  0.1878882 -0.1361578

Largest  eigenvalues:
 [1] 62814752 59900893 56743619 55340590 54486987 52802739 51544732 51311213
 [9] 51200714 50375242

Smallest eigenvalues:
 [1]  0.44356768  0.42046722  0.39950031  0.32870009  0.27196653  0.12560192
 [7]  0.09464374  0.06988762 -0.00171136 -0.05019119

Largest  eigenvalues:
 [1] 64132448 59781318 57110843 56383614 54761570 53001506 52282623 52098521
 [9] 51712448 50714730

Smallest eigenvalues:
 [1]  0.49438405  0.38946797  0.34314212  0.34017865  0.32713573  0.32277015
 [7]  0.18083315  0.02447813  0.02023877 -0.15580430

Largest  eigenvalues:
 [1] 63568568 59220209 56877904 54653450 54109074 52544329 51248206 51018887
 [9] 50925513 50444026

Smallest eigenvalues:
 [1]  0.441213482  0.402187823  0.360054823  0.343298783  0.278579172
 [6]  0.238515338  0.123659971  0.006826894 -0.020851861 -0.141814677

Largest  eigenvalues:
 [1] 61651023 59652665 56786901 54878602 54452827 53338772 51918450 51387919
 [9] 50480596 50331876

Smallest eigenvalues:
 [1]  0.3877520  0.3760961  0.3414564  0.2800164  0.2292212  0.2151944
 [7]  0.1657069  0.1569507  0.1014188 -1.6737793

Largest  eigenvalues:
 [1] 62767736 58823411 56322571 54968439 53912538 52535779 51207713 50984160
 [9] 50920675 50143326

Smallest eigenvalues:
 [1]  0.40413041  0.37107023  0.34796408  0.30040353  0.29680009  0.18375282
 [7]  0.12303743 -0.08728291 -0.37144939 -5.39282504

Largest  eigenvalues:
 [1] 62556374 59968023 57365673 55205314 54800629 53256619 51601316 51377913
 [9] 51367763 50564854

Smallest eigenvalues:
 [1]  0.27247301  0.24561616  0.22882619  0.16914650  0.07215156  0.04366907
 [7]  0.01613879  0.01025008 -0.03466485 -0.67967206

Largest  eigenvalues:
 [1] 64452351 60932428 57664256 55994006 55930112 54006657 53073763 52262155
 [9] 52088678 51815908

Smallest eigenvalues:
 [1]  0.3426507  0.3272725  0.3152655  0.2504503  0.2025221  0.1619278
 [7]  0.1159838  0.1037998 -0.1736154 -0.5895960

Largest  eigenvalues:
 [1] 67211058 60168152 57837245 57313590 54546741 53800700 52795025 52218388
 [9] 51265936 51109886

Smallest eigenvalues:
 [1]  0.5213977  0.4707618  0.4384802  0.4284494  0.4211158  0.3637000
 [7]  0.3120819  0.3117351  0.2867010 -0.3436925

Largest  eigenvalues:
 [1] 65104927 60196287 57651473 56533494 54727265 53278819 52557329 51834401
 [9] 51662417 50788674

Smallest eigenvalues:
 [1]  0.419861415  0.378044758  0.375408021  0.373814674  0.348674096
 [6]  0.315929850  0.203400380  0.070829478 -0.006275546 -3.475224676

Largest  eigenvalues:
 [1] 63873301 60584258 57021513 55899508 55695041 53760897 52429273 52300099
 [9] 51920751 51409538

Smallest eigenvalues:
 [1]  0.282628072  0.279136691  0.269935974  0.230440702  0.181195615
 [6]  0.075532723 -0.008834248 -0.266524326 -0.302874711 -3.178384059

Largest  eigenvalues:
 [1] 61257017 59772518 56841432 54579859 54165949 53125736 51372423 51212731
 [9] 50365860 50137497

Smallest eigenvalues:
 [1]  0.5770307  0.5518265  0.4480035  0.3917223  0.3914581  0.3000425
 [7]  0.2956454  0.2344597  0.2169452 -1.2452503

Largest  eigenvalues:
 [1] 66800240 60316173 57954366 57523528 54946296 53655724 52829071 52581605
 [9] 51583791 51472788

Smallest eigenvalues:
 [1]  0.49971376  0.41094068  0.41070446  0.39090868  0.38785315  0.31521481
 [7]  0.24441046  0.08525905 -0.03795092 -0.26106001

Largest  eigenvalues:
 [1] 65880126 60399752 57582090 57368490 54628447 53423525 52714113 52092630
 [9] 51583037 50978100

Smallest eigenvalues:
 [1]  0.4741982  0.4243970  0.4105458  0.4047667  0.2823013  0.2792638
 [7]  0.1988400  0.1740771 -0.1861228 -2.4816150

Largest  eigenvalues:
 [1] 65308973 61228708 57381934 56254641 55678196 53732927 53299441 52485245
 [9] 52103898 51787031

Smallest eigenvalues:
 [1]  0.47454213  0.45891185  0.42725572  0.34099575  0.22886042  0.22066373
 [7]  0.21248619  0.15628414  0.06437691 -5.19893093

Largest  eigenvalues:
 [1] 64217030 59344675 56778044 55720375 54378806 52640763 51843352 51336131
 [9] 50828638 50041225

Smallest eigenvalues:
 [1]  0.29297725  0.28043615  0.28037020  0.27389825  0.26965176  0.16793444
 [7]  0.08639555  0.01533882 -0.05557310 -0.17052829

Largest  eigenvalues:
 [1] 63259686 60847492 57501259 55965853 55351122 53859808 52272128 51901143
 [9] 51804168 50700061

Smallest eigenvalues:
 [1]  0.23676217  0.20308198  0.15102903  0.14670640  0.01808751 -0.02944477
 [7] -0.03503629 -0.18284821 -0.48185254 -3.46820603

Largest  eigenvalues:
 [1] 62258108 58723590 56235991 55143845 53705898 52044222 51125190 51024809
 [9] 50885708 50086042

Smallest eigenvalues:
 [1]  0.50613441  0.49117951  0.44386310  0.41918374  0.29258286  0.29014648
 [7]  0.28964740  0.27785474  0.01645168 -0.08981621

Largest  eigenvalues:
 [1] 63961524 59855917 56487649 55730013 54750051 53121008 51724709 51687729
 [9] 51380431 50430069

Smallest eigenvalues:
 [1]  0.248427886  0.243321433  0.196383449  0.192962959  0.173939308
 [6]  0.133182304  0.044087191  0.028209020  0.004579953 -0.004315265

Largest  eigenvalues:
 [1] 64849236 59130549 56498432 56324704 53958165 52586604 52272278 51170907
 [9] 50651078 50039970

Smallest eigenvalues:
 [1]  0.5358907  0.4709333  0.4434988  0.4271307  0.3459811  0.3011736
 [7]  0.2720542  0.2438596  0.2149343 -0.1345852

Largest  eigenvalues:
 [1] 65061266 60799338 57630644 56641802 55476500 53561575 52928370 52677211
 [9] 52102212 51663789

Smallest eigenvalues:
 [1]  0.4669376  0.4262264  0.4222228  0.4110763  0.4098774  0.3357056
 [7]  0.3162517  0.2903874  0.1181259 -0.2042448

Largest  eigenvalues:
 [1] 62702205 59717564 56833266 54949744 54740071 53367135 51829026 51271738
 [9] 51075252 50382148

Smallest eigenvalues:
 [1]  0.3564605  0.3379122  0.2666972  0.2577763  0.1975894  0.1799183
 [7]  0.1646375  0.1571492  0.0495473 -0.1143141

Largest  eigenvalues:
 [1] 62415326 60130318 56962788 55511463 54694636 53438410 52249442 51903216
 [9] 51220832 50930486

Smallest eigenvalues:
 [1]  0.34817203  0.34478925  0.25536370  0.23282984  0.03256536  0.02003475
 [7] -0.08669589 -0.15071883 -0.33437422 -2.73316779

Largest  eigenvalues:
 [1] 64184380 60399753 57474712 56031828 55255020 53614193 52447999 52191569
 [9] 51848394 51482291

Smallest eigenvalues:
 [1]  0.4002912  0.3920378  0.3803596  0.3319668  0.2603523  0.2557682
 [7]  0.1833026  0.1692031  0.1038402 -0.2996123

Largest  eigenvalues:
 [1] 65166026 61031786 57493028 57440839 55173659 53428531 53201509 52433327
 [9] 52221193 51189900

Smallest eigenvalues:
 [1]  0.4773357  0.4322349  0.4277388  0.4074611  0.3379200  0.3224901
 [7]  0.2508553  0.1897822  0.1633150 -0.2071923

Largest  eigenvalues:
 [1] 64811912 60389184 57360359 56115393 55169470 53518990 52231843 52114082
 [9] 52062995 51019275

Smallest eigenvalues:
 [1]  0.50790366  0.49553333  0.46245753  0.41270948  0.37911392  0.32490067
 [7]  0.23257606  0.23211016  0.08148267 -0.04511486

Largest  eigenvalues:
 [1] 64444705 60608707 57239046 56044315 54796436 53161129 52143397 52087485
 [9] 51566364 51115935

Smallest eigenvalues:
 [1]  0.5612749  0.5359034  0.5253435  0.4658084  0.4478112  0.3726987
 [7]  0.3456432  0.3369135  0.2894344 -1.4250324

Largest  eigenvalues:
 [1] 63692022 60501164 57480760 55641568 55586480 53940256 52347555 52291657
 [9] 51739695 51293942

Smallest eigenvalues:
 [1]  0.34655462  0.34385016  0.32608559  0.29230773  0.15530102  0.14938306
 [7]  0.12599973 -0.09265381 -1.48306356 -5.13933612

Largest  eigenvalues:
 [1] 63210911 60523521 56831054 55786968 55023987 53218020 52059341 51741703
 [9] 51513400 50678949

Smallest eigenvalues:
 [1]  0.55210557  0.53274515  0.39634421  0.37393257  0.33599339  0.33547757
 [7]  0.30088601  0.20839500  0.15654078 -0.04782717

Largest  eigenvalues:
 [1] 63670765 59841913 57095141 55264414 54971001 53383251 51733768 51704545
 [9] 51483539 50802676

Smallest eigenvalues:
 [1]  0.41081868  0.35789094  0.32431733  0.25331339  0.24594816  0.20196975
 [7]  0.06648996 -0.25247954 -0.29926274 -2.10070285

Largest  eigenvalues:
 [1] 64479788 59503616 56505641 54903711 54515314 52820223 51846282 51736510
 [9] 51121159 50973167

Smallest eigenvalues:
 [1]  0.5588531  0.5565010  0.5478989  0.5245142  0.4885647  0.3853234
 [7]  0.3453767  0.3385378  0.3300172 -0.9846933

Largest  eigenvalues:
 [1] 64571054 60221812 56952203 56406567 55106991 53019567 52509069 52414262
 [9] 51271921 51153828

Smallest eigenvalues:
 [1]  0.45326344  0.44126318  0.43210967  0.38033081  0.35906289  0.35556418
 [7]  0.33805985  0.26565419  0.04989744 -0.28649507

Largest  eigenvalues:
 [1] 63905414 60473745 57157903 55718577 55653370 53896673 51912006 51873557
 [9] 51787004 50914756

Smallest eigenvalues:
 [1]  0.375933796  0.357535298  0.317645466  0.290888206  0.287197275
 [6]  0.216235857  0.179441355  0.139911031  0.009581873 -0.010343354

Largest  eigenvalues:
 [1] 62987539 59705183 56949430 55695002 54302762 53126617 51754630 51684240
 [9] 51540785 50937803

Smallest eigenvalues:
 [1]  0.4989466  0.4439029  0.4260818  0.4111692  0.3944669  0.3718408
 [7]  0.3592386  0.3329371  0.2462802 -2.5850923

Largest  eigenvalues:
 [1] 63471358 59125182 56354942 54955889 54384338 52444011 51157702 51052770
 [9] 50996951 50136678

Smallest eigenvalues:
 [1]  0.350482800  0.334216462  0.306708386  0.237499496  0.204614811
 [6]  0.164931184  0.000620337 -0.056680235 -0.225653384 -0.748413086

Largest  eigenvalues:
 [1] 64340358 60229812 57403027 55533234 54710753 53271723 51853251 51842995
 [9] 51602765 50963871

Smallest eigenvalues:
 [1]  0.38106906  0.36502182  0.29874376  0.24322162  0.23465017  0.22239371
 [7]  0.18785561  0.12854075  0.11143335 -0.02587055

Largest  eigenvalues:
 [1] 62923039 59824114 57215507 55705231 55048949 53373988 52009795 51792748
 [9] 51610529 50688017

Smallest eigenvalues:
 [1]  0.25594940  0.25352542  0.20925942  0.18340075  0.16309732  0.09991428
 [7]  0.07994251 -0.09777252 -0.15790057 -0.30520783

Largest  eigenvalues:
 [1] 62953180 59296101 56425221 54775886 54228180 53132707 51901829 51086362
 [9] 50610786 50451629

Smallest eigenvalues:
 [1]  0.45265675  0.37653387  0.36834970  0.35151217  0.26993865  0.19171175
 [7]  0.17288609  0.11440164  0.09632834 -0.07923113

Largest  eigenvalues:
 [1] 64437847 60127334 56916808 56643667 55098444 53158446 52527415 52453714
 [9] 52174719 51357155

Smallest eigenvalues:
 [1]  0.4160336  0.3826172  0.3617871  0.3091674  0.2775094  0.2728752
 [7]  0.2174199  0.1582686  0.1249701 -1.0470558

Largest  eigenvalues:
 [1] 65223701 60419950 57117786 56831839 55325708 53515005 52771579 52255756
 [9] 52215799 51339682

Smallest eigenvalues:
 [1]  0.5657418  0.4635853  0.4614540  0.4474245  0.3572797  0.3342631
 [7]  0.3295908  0.2744666 -0.1018610 -0.1026448

Largest  eigenvalues:
 [1] 63971440 59693029 56394983 55291144 54636746 52738955 51484399 51433412
 [9] 51312340 50484840

Smallest eigenvalues:
 [1]  0.41424884  0.40433995  0.37400008  0.25853790  0.20621991  0.20032496
 [7]  0.08329316  0.06992070  0.04101541 -0.15343428

Largest  eigenvalues:
 [1] 62635686 60016299 56686036 55483228 54534221 53617484 52304692 51748725
 [9] 50862412 50719428

Smallest eigenvalues:
 [1]  0.5334944  0.5115820  0.5049301  0.4543785  0.4254876  0.3626894
 [7]  0.3127751  0.3032202  0.2164003 -2.7029730

Largest  eigenvalues:
 [1] 64380181 60486534 56944037 56306504 55270629 53268230 52250087 52160096
 [9] 51569097 50776476

Smallest eigenvalues:
 [1]  0.29072874  0.23287835  0.19129834  0.17457923  0.16019336  0.13673828
 [7]  0.12871361 -0.02144208 -0.31162891 -0.62560096

Largest  eigenvalues:
 [1] 64870252 60114606 56719741 56292118 55076071 53409337 52507852 52361203
 [9] 51779929 51059506

Smallest eigenvalues:
 [1]  0.41188949  0.35505182  0.30752965  0.30326280  0.26482320  0.22502483
 [7]  0.19528615  0.11011382 -0.04549129 -0.44046956

Largest  eigenvalues:
 [1] 65867372 59586229 57621231 56070963 54556516 53056541 52303459 51915895
 [9] 51817845 51363636

Smallest eigenvalues:
 [1]  0.4659042  0.3374656  0.3291542  0.3060817  0.2766187  0.2653688
 [7]  0.2411973  0.1925782 -0.1095380 -0.3198741

Largest  eigenvalues:
 [1] 64551544 60284695 57858394 55990424 55424467 54107168 52204372 52111868
 [9] 51788471 50899960

Smallest eigenvalues:
 [1]  0.27562717  0.26891897  0.25174171  0.19222617  0.13113442  0.11615997
 [7]  0.06624774 -0.03770178 -0.16346759 -0.24808153

Largest  eigenvalues:
 [1] 63418185 59998394 57062633 55871883 54834082 53281010 52310525 51856968
 [9] 51804878 51287640

Smallest eigenvalues:
 [1]  0.42738336  0.42591558  0.35928664  0.34219982  0.26651808  0.18232250
 [7]  0.17615264  0.14551789  0.11658508 -0.09916294

Largest  eigenvalues:
 [1] 65950767 59945301 57396804 56632060 54674904 53176559 52706504 51697866
 [9] 51534714 50680063

Smallest eigenvalues:
 [1]  0.29942865  0.28905598  0.26138978  0.24718670  0.20226184  0.12294696
 [7]  0.07168579  0.04922947 -0.18015582 -0.81582743

Largest  eigenvalues:
 [1] 65332109 59668015 56910747 56872076 54326135 52911123 52669904 52150774
 [9] 51292458 51106581

Smallest eigenvalues:
 [1]  0.52447316  0.47972043  0.46426207  0.46380191  0.43599805  0.39567602
 [7]  0.21026910  0.16457606 -0.06039464 -0.06327350

Largest  eigenvalues:
 [1] 65617452 60269158 57088453 56144673 54759249 52878128 52348133 51649140
 [9] 51532915 50661340

Smallest eigenvalues:
 [1]  0.23942874  0.17651654  0.14249827  0.13202542  0.11534802  0.06752890
 [7]  0.06106508  0.04564529 -0.22124934 -0.48210028

Largest  eigenvalues:
 [1] 64581802 60867241 57528691 56454189 55350422 53722351 52425744 52291580
 [9] 52126968 51500843

Smallest eigenvalues:
 [1]  0.409211467  0.402491613  0.373694249  0.319309942  0.263419237
 [6]  0.223992995  0.014341119  0.003170013 -0.258042811 -0.545635353

Largest  eigenvalues:
 [1] 64255836 58611573 56023519 55130481 53605190 51788496 51213976 50725944
 [9] 50529430 50040484

Smallest eigenvalues:
 [1]  0.50454111  0.46195100  0.44234163  0.40015859  0.36645976  0.18381692
 [7]  0.12772568  0.08965871 -0.06893770 -0.30760598

Largest  eigenvalues:
 [1] 65251042 59596176 56614368 56580237 54249189 52385200 52322695 51348742
 [9] 51293314 50471448

Smallest eigenvalues:
 [1]  0.31097468  0.27989480  0.23952482  0.21417065  0.21076989  0.18889046
 [7]  0.16752048  0.09886603 -0.48717312 -1.16803782

Largest  eigenvalues:
 [1] 65918057 60955064 57531931 57493382 55723497 53545038 53487643 53031926
 [9] 52438267 51909198

Smallest eigenvalues:
 [1]  0.5347585  0.4962192  0.4255062  0.4047164  0.3692113  0.3375820
 [7]  0.1765398  0.1406169  0.1035736 -0.1270950

Largest  eigenvalues:
 [1] 63940892 59953786 56838897 55605485 54927820 53288604 51981493 51692192
 [9] 51656494 50943779

Smallest eigenvalues:
 [1]  0.48618303  0.47693342  0.37951685  0.35497047  0.31433391  0.24618331
 [7]  0.19677847  0.12570931 -0.04603824 -2.70202496

Largest  eigenvalues:
 [1] 64417458 59837771 57264574 55969609 54538839 52879705 52133972 51686824
 [9] 51297385 50451719

Smallest eigenvalues:
 [1]  0.5427545  0.5323213  0.5031192  0.4519202  0.4153887  0.4069469
 [7]  0.3799532  0.3327700  0.1820873 -0.1219847

Largest  eigenvalues:
 [1] 63735594 60097533 57089637 55743636 54875691 53417459 51798248 51660182
 [9] 51351787 50335888

Smallest eigenvalues:
 [1]  0.42717029  0.38094080  0.32333697  0.30030779  0.29063465  0.27173922
 [7]  0.15401350  0.02718579 -0.09521869 -1.21557704

Largest  eigenvalues:
 [1] 65557926 60126774 57418143 55929693 55312638 53846228 52168909 52116231
 [9] 51828579 51154824

Smallest eigenvalues:
 [1]  0.52954933  0.50364698  0.45379738  0.44857760  0.42567845  0.38853342
 [7]  0.37767700  0.24280915  0.09184402 -0.26225527

Largest  eigenvalues:
 [1] 65057042 60817518 57341751 57339614 54977045 53099162 53088693 52416216
 [9] 51891920 51152261

Smallest eigenvalues:
 [1]  0.47676592  0.40378951  0.35269869  0.34613978  0.33166163  0.29253198
 [7]  0.25704289  0.16549965  0.05799535 -0.01630693

Largest  eigenvalues:
 [1] 64683309 59312175 56287695 55929348 54314478 52722339 51994006 51350820
 [9] 51325661 50553036

Smallest eigenvalues:
 [1]  0.5073037  0.4522031  0.3818365  0.3621858  0.3617883  0.3377283
 [7]  0.2809963  0.2096979 -0.1787391 -1.2845520

Largest  eigenvalues:
 [1] 64802861 60475512 57086631 56363785 55170281 53430022 52290035 51869812
 [9] 51746509 50802714

Smallest eigenvalues:
 [1]  0.30121826  0.27099400  0.25932784  0.18160536  0.14910535  0.11057145
 [7]  0.07840236 -0.17346582 -0.41175763 -0.66080469

Largest  eigenvalues:
 [1] 66198288 60254655 57749206 57107450 54680851 53298514 53172401 51854172
 [9] 51794194 50868717

Smallest eigenvalues:
 [1]  0.332561804  0.310327261  0.234901611  0.187475054  0.180170886
 [6]  0.110566983  0.094393847  0.002502927 -0.006820422 -1.199379987

Largest  eigenvalues:
 [1] 63849965 59470350 56687821 55715458 54801608 52739169 51763127 51715845
 [9] 51708859 50967127

Smallest eigenvalues:
 [1]  0.50999921  0.48427337  0.38216766  0.31021745  0.29265576  0.27097036
 [7]  0.27060036  0.01992409 -0.01046537 -0.02088294

Largest  eigenvalues:
 [1] 64375007 60012951 57179871 56609076 54748825 52939657 52504509 52081094
 [9] 51484969 50802789

Smallest eigenvalues:
 [1]  0.3315742  0.3101312  0.2919505  0.2493203  0.2309198  0.1793975
 [7]  0.1331548 -0.0929467 -0.3174801 -0.9253021

Largest  eigenvalues:
 [1] 64540686 61134227 58002340 56442246 55891066 54055955 53156787 52821624
 [9] 52425341 52095934

Smallest eigenvalues:
 [1]  0.42769089  0.41339694  0.40684762  0.37344477  0.34179767  0.23001413
 [7]  0.09815963  0.07755874  0.04446335 -0.08367472

Largest  eigenvalues:
 [1] 64052760 59496140 56652988 55528109 54111435 52387599 51544405 51203085
 [9] 51087690 50317411

Smallest eigenvalues:
 [1]  0.46702998  0.38863824  0.34560776  0.34271825  0.30671153  0.26041598
 [7]  0.23690849  0.23114173  0.01155683 -1.37711687

Largest  eigenvalues:
 [1] 63058859 60057280 57348262 55837121 54849419 54209392 52661456 51431591
 [9] 51083422 50904534

Smallest eigenvalues:
 [1]  0.40329994  0.38167413  0.33441614  0.32431277  0.29996045  0.27877185
 [7]  0.27107046  0.15097807  0.03485868 -0.49860524

Largest  eigenvalues:
 [1] 65645306 60630493 57742387 56901914 55243188 53691589 52950037 52441033
 [9] 52268909 51424201

Smallest eigenvalues:
 [1]  0.43270039  0.41508788  0.40370674  0.39151875  0.34197521  0.26516462
 [7]  0.25379765  0.24191011  0.14626610 -0.07802057

Largest  eigenvalues:
 [1] 62186020 59778345 56776566 54809062 54235535 52722520 51133921 51047573
 [9] 50880643 50122481

Smallest eigenvalues:
 [1]  0.40581734  0.36008267  0.32632249  0.31615059  0.27311864  0.23838390
 [7]  0.21197199  0.10693850  0.03298843 -0.48786478

Largest  eigenvalues:
 [1] 66461087 61132142 57758045 57537067 55392971 53533293 53475558 53298905
 [9] 52168236 51750259

Smallest eigenvalues:
 [1]  0.33798862  0.33350160  0.32367642  0.24976225  0.21313896  0.18427831
 [7]  0.11491321  0.09639502  0.06794379 -0.08795605

Largest  eigenvalues:
 [1] 64996760 60185786 57316037 56721282 55037070 53517572 52629413 52093354
 [9] 51954334 51270225

Smallest eigenvalues:
 [1]  0.47990346  0.45709159  0.43070159  0.41197428  0.37093862  0.27102989
 [7]  0.26656596  0.24417665  0.02223501 -0.17136428

Largest  eigenvalues:
 [1] 64492383 60363583 57304388 56035519 55238382 53345425 52119218 52085773
 [9] 51897495 50918669

Smallest eigenvalues:
 [1]  0.41877829  0.41447196  0.37515555  0.35777618  0.35464348  0.32437595
 [7]  0.23704118  0.03877728 -0.03406485 -0.07046079

Largest  eigenvalues:
 [1] 64504919 60302811 57710668 55825027 55066531 53678887 52220212 51945812
 [9] 51909234 51022094

Smallest eigenvalues:
 [1]  0.44646009  0.41056660  0.40114501  0.35833293  0.29206463  0.29040661
 [7]  0.27573772  0.26316542  0.22643311 -0.04504442

Largest  eigenvalues:
 [1] 62802961 59942073 56741447 55079609 55032415 53280863 51551208 51524280
 [9] 51149306 50470997

Smallest eigenvalues:
 [1]  0.50796688  0.45523848  0.44627339  0.41772109  0.32986013  0.30240848
 [7]  0.25318194  0.18577283  0.09487684 -0.37937425

Largest  eigenvalues:
 [1] 65701761 60680424 57484925 57023649 55353348 53660301 53152121 53052277
 [9] 51673014 51252648

Smallest eigenvalues:
 [1]  0.39219512  0.33266557  0.30997414  0.29020731  0.27230677  0.24935759
 [7]  0.24171324  0.12746831  0.04870696 -0.34468129

Largest  eigenvalues:
 [1] 63777464 60361450 57255632 55932966 55239462 53637076 52013071 51943481
 [9] 51910557 50755544

Smallest eigenvalues:
 [1]  0.48165712  0.47417802  0.31211785  0.30923073  0.30631704  0.27206626
 [7]  0.26430906  0.22188948  0.17087950 -0.01100268

Largest  eigenvalues:
 [1] 64185511 59677400 57154415 55824226 54243626 52889444 51910089 51412890
 [9] 51088831 50625849

Smallest eigenvalues:
 [1]  0.4491140  0.4464624  0.3494821  0.2592410  0.2309093  0.2167945
 [7]  0.1560999 -0.1374232 -0.8270159 -5.0634316

Largest  eigenvalues:
 [1] 65597031 60651933 58016032 56740935 54895621 53195047 52774862 52159326
 [9] 52113517 51586302

Smallest eigenvalues:
 [1]  0.29622484  0.23915821  0.23509350  0.23487333  0.16764420  0.15183665
 [7]  0.14332240  0.12477499 -0.01985016 -0.03498369

Largest  eigenvalues:
 [1] 63178213 60105040 57181904 56281338 54932369 54210849 52447885 51670601
 [9] 50899631 50678038

Smallest eigenvalues:
 [1]  0.588385518  0.529411822  0.475822506  0.456254117  0.445050444
 [6]  0.438608587  0.379695366  0.208796035  0.089453067 -0.002246488

Largest  eigenvalues:
 [1] 66044248 60037349 57501698 56998809 54800453 53092749 52765833 52097725
 [9] 51627944 51168662

Smallest eigenvalues:
 [1]  0.32927765  0.29881761  0.29527221  0.24803150  0.19902564 -0.02338507
 [7] -0.06301828 -0.17670915 -0.55219787 -3.51883974

Largest  eigenvalues:
 [1] 65513023 60265189 57276996 56321771 55491066 53808001 52523534 52161743
 [9] 51906913 51066207

Smallest eigenvalues:
 [1]  0.5120147  0.4902305  0.4279274  0.3249458  0.3186632  0.2736615
 [7]  0.2342692  0.1737507  0.1399606 -1.7090498

Largest  eigenvalues:
 [1] 63528716 59484670 57129229 55601654 54543136 53150110 51758713 51603425
 [9] 51365691 50577859

Smallest eigenvalues:
 [1]  0.5060602  0.4541361  0.3075310  0.3032671  0.2913096  0.2756836
 [7]  0.2318237  0.2295834  0.2243743 -0.5578332

Largest  eigenvalues:
 [1] 64970375 60145520 57462197 56262273 54930904 53570362 52234123 51884440
 [9] 51468482 50674500

Smallest eigenvalues:
 [1]  0.30786794  0.29715886  0.28676674  0.24580613  0.23071977  0.14116524
 [7]  0.11489875  0.10592681  0.01524733 -0.13985453

Largest  eigenvalues:
 [1] 65226360 60289127 57669349 56336281 55162949 53374729 53130307 52598554
 [9] 51744520 51582214

Smallest eigenvalues:
 [1]  0.44877412  0.42320217  0.41062041  0.29966239  0.27905187  0.08478913
 [7]  0.06798686  0.03887282 -0.28346315 -0.33274652

Largest  eigenvalues:
 [1] 64168026 59904256 56665032 55331946 54540515 53092721 51649508 51597945
 [9] 51404244 50888228

Smallest eigenvalues:
 [1]  0.29852339  0.28700359  0.26902276  0.24486402  0.21711633  0.10498651
 [7]  0.06584258 -0.04016976 -0.10621229 -0.63810147

Largest  eigenvalues:
 [1] 64306733 59727134 57010731 55780813 54841150 53488188 51981938 51825529
 [9] 51780404 51163424

Smallest eigenvalues:
 [1]  0.58756124  0.55031381  0.40203394  0.39449552  0.33908763  0.30757219
 [7]  0.29281944  0.24704331  0.05327901 -0.12842555

Largest  eigenvalues:
 [1] 64314663 60502582 57157259 55976922 55115413 53280331 52175693 52069018
 [9] 51707675 50820973

Smallest eigenvalues:
 [1]  0.40169634  0.36238506  0.35380109  0.32671150  0.31461695  0.23331964
 [7]  0.18580917  0.17222265  0.01182588 -0.33033398

Largest  eigenvalues:
 [1] 65134397 60433704 58005429 56388136 55575484 54324000 52848194 52582932
 [9] 52378177 51824302

Smallest eigenvalues:
 [1]  0.43948897  0.39629211  0.36047301  0.26414728  0.25710602  0.25483879
 [7]  0.22808060  0.03166845 -0.18000824 -0.48135630

Largest  eigenvalues:
 [1] 63773738 60273211 56488171 55576385 54764199 53014431 51612270 51452388
 [9] 50920382 50173800

Smallest eigenvalues:
 [1]  0.4574529  0.4294386  0.3964928  0.3700166  0.3663983  0.2016658
 [7]  0.1530145  0.1489632 -1.6178774 -2.2031930

Largest  eigenvalues:
 [1] 65243289 59572539 56883002 56800788 54419113 52680525 52527658 52416351
 [9] 51557262 51325714

Smallest eigenvalues:
 [1]  0.41786046  0.40295364  0.38707463  0.32375821  0.27768959  0.21925706
 [7]  0.21455049  0.07039857 -0.03699965 -0.27624821

Largest  eigenvalues:
 [1] 62196768 59658703 56314073 55309677 54479038 52683108 51967333 51512327
 [9] 51222784 50730770

Smallest eigenvalues:
 [1]  0.3035823  0.2212409  0.2154011  0.2062859  0.1990763  0.1938541
 [7]  0.1596840  0.0548550  0.0320958 -0.1692106

Largest  eigenvalues:
 [1] 66142160 60332402 57794061 56567923 55050964 53472329 53008055 51920514
 [9] 51701106 50833244

Smallest eigenvalues:
 [1]  0.45932737  0.39271114  0.38297706  0.34107954  0.29288405  0.27909868
 [7]  0.25270731  0.16194959  0.15263188 -0.04051266

Largest  eigenvalues:
 [1] 62832764 59342784 56727162 54970955 54508602 53012522 51722862 51357914
 [9] 50962398 50382907

Smallest eigenvalues:
 [1]  0.47577080  0.47074609  0.44853104  0.44104044  0.42526933  0.41566454
 [7]  0.29011880  0.21557019  0.00950453 -0.11174865

Largest  eigenvalues:
 [1] 63632665 60300709 57342019 55695599 54911652 53369035 52058654 51862302
 [9] 51608868 50778887

Smallest eigenvalues:
 [1]  0.47404903  0.45525679  0.42329400  0.36164076  0.35454958  0.26831721
 [7]  0.19221343  0.04257136 -0.10671445 -6.96697582

Largest  eigenvalues:
 [1] 63642147 59474460 56524493 55650766 54264493 52780178 51516685 51354372
 [9] 51330918 50301659

Smallest eigenvalues:
 [1]  0.34612221  0.33736227  0.33315305  0.23277696  0.13115882  0.11311170
 [7]  0.07567395 -0.35443778 -0.58975453 -3.44584909

Largest  eigenvalues:
 [1] 63824244 60348349 57421645 55753516 55650829 53616359 52539408 51957746
 [9] 51804787 51075666

Smallest eigenvalues:
 [1]  0.215741956  0.193440114  0.192256962  0.144103487  0.109000049
 [6] -0.006112014 -0.217082728 -0.269809294 -0.428519875 -0.473183415

Largest  eigenvalues:
 [1] 63399611 59326360 56294557 55566521 54667926 53074863 51880150 51571208
 [9] 50821388 50195623

Smallest eigenvalues:
 [1]  0.39917552  0.39525696  0.33925254  0.29942161  0.29097067  0.27999483
 [7]  0.19164328  0.17227190 -0.05526377 -1.26181739

Largest  eigenvalues:
 [1] 64704102 60461461 57633976 56122917 54639881 53058217 52474655 52270723
 [9] 51615739 51471803

Smallest eigenvalues:
 [1]  0.38868897  0.36877991  0.31140916  0.29722876  0.29043014  0.19141210
 [7]  0.10573200  0.09423908 -0.11340411 -0.26125671

Largest  eigenvalues:
 [1] 63890772 60417013 57135184 56600135 55584797 53640976 52608453 52356314
 [9] 52308943 51198826

Smallest eigenvalues:
 [1]  0.5283175  0.4956874  0.4851959  0.4838516  0.4014163  0.3769120
 [7]  0.3639069  0.3003085  0.1638212 -0.1029271

Largest  eigenvalues:
 [1] 64838039 59949207 56973242 56953182 54194953 52719309 52438542 51342320
 [9] 51157056 50101972

Smallest eigenvalues:
 [1]  0.37397298  0.35897612  0.35072556  0.32049585  0.31000401  0.27111053
 [7]  0.21637655  0.12339520 -0.01119300 -0.03449607

Largest  eigenvalues:
 [1] 64835509 60796951 57459527 57159236 55224446 53653997 52988938 52714353
 [9] 52053021 51572485

Smallest eigenvalues:
 [1]  0.4237647  0.3942397  0.3548675  0.3528174  0.3031715  0.2709671
 [7]  0.2147404  0.1376591 -0.3181742 -1.5986810

Largest  eigenvalues:
 [1] 63529531 60489765 57367720 56159536 54893598 53217256 52247038 52230391
 [9] 52078855 51147332

Smallest eigenvalues:
 [1]  0.44358032  0.38589475  0.37619039  0.28206063  0.26945306  0.20097575
 [7]  0.18631274  0.08630402  0.08288487 -0.00694323

Largest  eigenvalues:
 [1] 62165192 59133159 56218087 54379090 53997843 52482821 51146133 51078889
 [9] 50565301 50362020

Smallest eigenvalues:
 [1]  0.46363012  0.35697754  0.30067607  0.29201585  0.29080292  0.26675858
 [7]  0.21059676  0.03016882 -0.03019872 -0.09614621

Largest  eigenvalues:
 [1] 64935858 60810406 57700579 56809224 55185833 53858493 52736293 52500808
 [9] 52308451 51422649

Smallest eigenvalues:
 [1]  0.473970844  0.421234355  0.395283399  0.386577443  0.306521414
 [6]  0.221815956  0.130092306  0.109075044  0.008464154 -0.074206859

Largest  eigenvalues:
 [1] 63681412 60355025 57320650 55601879 55417537 53871513 52506467 52165013
 [9] 51639563 51051069

Smallest eigenvalues:
 [1]  0.5000428  0.4191230  0.3895635  0.3802932  0.3013627  0.2857498
 [7]  0.2754820  0.2668090  0.1170964 -0.1498062

Largest  eigenvalues:
 [1] 61997183 59564069 56431249 54933208 54542058 53230276 51865863 51363860
 [9] 50605070 50311315

Smallest eigenvalues:
 [1]  0.45335624  0.43025851  0.36416624  0.27939724  0.24438702  0.23138496
 [7]  0.19645169 -0.03686460 -0.07908756 -0.12252773

Largest  eigenvalues:
 [1] 65144966 60362593 57735024 56175889 55040973 53497948 52333859 51819611
 [9] 51770744 50774426

Smallest eigenvalues:
 [1]  0.45074843  0.44143114  0.42290250  0.38807240  0.32599663  0.26255333
 [7]  0.11050881  0.09203367  0.01680314 -0.16696491

Largest  eigenvalues:
 [1] 63935309 59876959 57182240 55869605 54731559 53062138 51867907 51833400
 [9] 51648071 50575471

Smallest eigenvalues:
 [1]  0.36401192  0.31918027  0.24459720  0.21421691  0.21335935  0.13611351
 [7]  0.01837308 -0.14135963 -0.16466506 -1.15254031

Largest  eigenvalues:
 [1] 63244794 59229842 56767267 55724536 54298440 52649063 52138534 51605013
 [9] 51286795 50373537

Smallest eigenvalues:
 [1]  0.4458314  0.4119143  0.3856932  0.3483522  0.2662103  0.2541812
 [7]  0.2349929  0.1373263 -0.3723466 -0.6398042

Largest  eigenvalues:
 [1] 65727685 60366597 57809837 57326222 54590417 53548817 52492496 52204945
 [9] 51347274 50923999

Smallest eigenvalues:
 [1]  0.48875719  0.44663210  0.38840025  0.36729165  0.31143062  0.30435465
 [7]  0.18617017  0.16640290 -0.02860812 -0.04143211

Largest  eigenvalues:
 [1] 63148506 60437476 57437841 56051470 54810058 54209097 52476003 52310780
 [9] 51328712 51033940

Smallest eigenvalues:
 [1]  0.5351956  0.4427493  0.4338828  0.4209067  0.3734884  0.2995147
 [7]  0.2585971  0.2077876 -0.1092852 -0.5931205

Largest  eigenvalues:
 [1] 65111816 60474293 57298758 56486830 55216463 52993319 52567364 51987613
 [9] 51730072 50999712

Smallest eigenvalues:
 [1]  0.46909584  0.40489763  0.36685301  0.34977575  0.33654319  0.24879438
 [7]  0.23174085  0.19775960  0.16721987 -0.05690472

Largest  eigenvalues:
 [1] 64908571 60900981 57236829 56486094 55807187 53833691 53615792 52527918
 [9] 51872704 51592904

Smallest eigenvalues:
 [1]  0.3619604645  0.3147112281  0.2966078104  0.1212452143  0.0242330430
 [6]  0.0119903666 -0.0006817226 -0.3637461561 -1.0601011343 -2.1250127537

Largest  eigenvalues:
 [1] 63470445 60892853 57922165 55759763 55676635 54243466 52723418 52278691
 [9] 51857004 51299359

Smallest eigenvalues:
 [1]  0.3229187  0.3141152  0.3130450  0.2973672  0.2477959  0.2316078
 [7]  0.1887063  0.1586283  0.1404220 -0.1526431

Largest  eigenvalues:
 [1] 65102605 59719498 57013797 56088033 54073234 52723526 52085322 51861673
 [9] 51216363 51171907

Smallest eigenvalues:
 [1]  0.37139749  0.37015411  0.35523001  0.33940621  0.32625948  0.28524301
 [7]  0.08116374 -0.16498333 -0.16634324 -0.44501849

Largest  eigenvalues:
 [1] 64235361 59192184 57110478 55431953 54639039 53286536 51675227 51670450
 [9] 50839331 50170692

Smallest eigenvalues:
 [1]  0.280525393  0.249422463  0.228567787  0.176906862  0.036208156
 [6]  0.008537243 -0.009228669 -0.158428537 -0.500985944 -2.100663651

Largest  eigenvalues:
 [1] 64627961 61042930 57961111 56809558 55350547 53855669 53369133 52684511
 [9] 52553042 52266782

Smallest eigenvalues:
 [1]  0.4361604  0.3956956  0.3692113  0.3033934  0.2623944  0.2238133
 [7]  0.1847326  0.1436362  0.0382388 -0.1312401

Largest  eigenvalues:
 [1] 63879060 60424812 57200625 55410573 55329883 53749746 52121627 51830840
 [9] 51432448 50965917

Smallest eigenvalues:
 [1]  0.46163234  0.43157492  0.40011987  0.33992454  0.31500426  0.28797693
 [7]  0.16589392  0.05438029 -0.11109404 -2.32486400

Largest  eigenvalues:
 [1] 64490502 59886391 57242559 56650062 54465874 52563263 52412007 51858934
 [9] 51439252 50772787

Smallest eigenvalues:
 [1]  0.4447652  0.4376073  0.3383682  0.3038996  0.2345920  0.1971537
 [7]  0.1710760  0.1480594  0.1072307 -7.7668647

Largest  eigenvalues:
 [1] 63469948 59651569 57414414 55441716 54778946 53244337 52087971 51441766
 [9] 51316261 50630420

Smallest eigenvalues:
 [1]  0.36754535  0.32107313  0.27980799  0.25447509  0.23266415  0.07767757
 [7]  0.02722315 -0.10423419 -0.33327080 -2.83987847

Largest  eigenvalues:
 [1] 63584550 60082602 57352709 56343256 54766013 53377536 52162298 51696595
 [9] 51611748 50484382

Smallest eigenvalues:
 [1]  0.376242743  0.335009546  0.282948960  0.205561046  0.130162646
 [6]  0.094770415  0.078240822  0.042109668  0.006704996 -0.892918355

Largest  eigenvalues:
 [1] 65095754 59819902 56976254 56685741 54744924 53071648 52629834 52139859
 [9] 52026980 51176498

Smallest eigenvalues:
 [1]  0.42938478  0.41198881  0.40497164  0.38030466  0.36372245  0.30553506
 [7]  0.23309877  0.06698100  0.05435017 -0.53364051

Largest  eigenvalues:
 [1] 63688782 59709442 57042996 55929155 54386294 52956519 51787536 51727538
 [9] 51263209 50666235

Smallest eigenvalues:
 [1]  0.534394160  0.516405416  0.380551189  0.338181827  0.318908256
 [6]  0.308456714  0.207898544 -0.009723578 -0.079089033 -1.295718728

Largest  eigenvalues:
 [1] 64718979 59980378 57306269 55227918 54865041 53327516 52410385 51557769
 [9] 51512587 51392588

Smallest eigenvalues:
 [1]  0.41474771  0.38422039  0.37773948  0.32338191  0.30560072  0.21064246
 [7]  0.16969864  0.16770283  0.09400382 -0.34636825

Largest  eigenvalues:
 [1] 64166244 60252959 56793012 56111754 54642611 52883319 52124968 52002316
 [9] 51523922 51034564

Smallest eigenvalues:
 [1]  0.39896429  0.33249402  0.31035185  0.25004980  0.20849593  0.09166945
 [7]  0.07698422 -0.16171684 -0.18755093 -0.38099873

Largest  eigenvalues:
 [1] 63205095 60179044 57342956 55083383 55030675 53395412 52126634 52055328
 [9] 51390228 51136442

Smallest eigenvalues:
 [1]  0.199524667  0.198956359  0.107469790  0.035149325 -0.008544322
 [6] -0.248373492 -0.342425641 -0.434322374 -0.477978919 -5.574439878

Largest  eigenvalues:
 [1] 62831870 59415961 56810063 55152822 54895667 53120709 51363481 51282138
 [9] 51207718 50341227

Smallest eigenvalues:
 [1]  0.492768178  0.489489532  0.342775765  0.337879982  0.237183970
 [6]  0.156307548  0.126677538  0.057773629  0.055365682 -0.002867192

Largest  eigenvalues:
 [1] 64119002 60346902 57078446 55758313 55231461 53501354 52445300 51930354
 [9] 51888121 51442768

Smallest eigenvalues:
 [1]  0.37031347  0.35822274  0.32945791  0.29700730  0.24262529  0.19415295
 [7]  0.11728352  0.06967865 -0.09578262 -0.35947702

Largest  eigenvalues:
 [1] 63429221 59438151 56438282 55132397 54868233 52773621 52126172 51420110
 [9] 51320070 50764285

Smallest eigenvalues:
 [1]  0.40892337  0.38620366  0.36398714  0.21508130  0.10915918  0.01543246
 [7] -0.06695919 -0.06935118 -0.17342179 -0.56954462

Largest  eigenvalues:
 [1] 65908594 59837633 57322594 56285004 54346088 52598391 52375925 51721267
 [9] 51352141 50880765

Smallest eigenvalues:
 [1]  0.37312103  0.36926382  0.35059090  0.29775826  0.28878935  0.23913253
 [7]  0.21841198  0.16399680  0.06506278 -0.12079797

Largest  eigenvalues:
 [1] 64651512 59904345 56986965 55953025 54817845 53350910 51957141 51486585
 [9] 51206939 49976101

Smallest eigenvalues:
 [1]  0.4845686  0.4628490  0.4247119  0.3903149  0.3576087  0.3417928
 [7]  0.3283418  0.3024886  0.2993924 -1.6324833

Largest  eigenvalues:
 [1] 63081148 59974171 56969033 55197042 54928467 53375996 51559258 51530143
 [9] 51124067 50623377

Smallest eigenvalues:
 [1]  0.40314414  0.39994863  0.38166553  0.32279453  0.25520310  0.18422688
 [7]  0.11820144  0.08111155  0.01046393 -0.05450520

Largest  eigenvalues:
 [1] 62240468 59675357 56646137 55395774 54488987 53466295 51925381 51490426
 [9] 50662493 50481243

Smallest eigenvalues:
 [1]  0.5136513  0.4779015  0.4628519  0.4294315  0.2141643  0.2003939
 [7]  0.1446269  0.1199344  0.1074424 -0.4250706

Largest  eigenvalues:
 [1] 61995704 59819447 56422681 55071260 54882567 53175748 52217901 51613534
 [9] 50861880 50738777

Smallest eigenvalues:
 [1]  0.42776228  0.40484304  0.39926866  0.28902663  0.23347426  0.21957151
 [7]  0.18620175  0.04740884 -0.01363339 -3.25296052

Largest  eigenvalues:
 [1] 65164658 59269651 56364924 56145355 54433225 52631690 52258202 51274561
 [9] 51068785 50319909

Smallest eigenvalues:
 [1]  0.49070551  0.46827063  0.42385440  0.41981484  0.40253580  0.40003505
 [7]  0.31313067  0.22382779  0.06227231 -0.13859479

Largest  eigenvalues:
 [1] 65464808 59535191 57072455 56639084 54366558 52656421 52641336 51668349
 [9] 51536385 50836801

Smallest eigenvalues:
 [1]  0.3699698  0.3557506  0.3232749  0.2523010  0.1577299  0.1465086
 [7] -0.2610783 -0.6345601 -1.1700548 -1.4296391

Largest  eigenvalues:
 [1] 65128269 60497678 57119561 56951426 55325458 53518821 53103623 52752657
 [9] 52140477 51575346

Smallest eigenvalues:
 [1]  0.34232953  0.33262702  0.30512283  0.24292146  0.21515361  0.16818948
 [7]  0.15009903  0.09289172 -0.03311363 -0.69528299

Largest  eigenvalues:
 [1] 65241872 59904600 56674642 56253206 54916682 53207414 52358692 52159373
 [9] 51848139 51196547

Smallest eigenvalues:
 [1]  0.3823116  0.3755541  0.3217533  0.3019909  0.3016130  0.1485883
 [7]  0.1124787  0.0714449 -0.2078827 -0.3906785

Largest  eigenvalues:
 [1] 63939503 59125152 56275464 55306338 54007616 52478829 51435756 51323875
 [9] 51186785 50361919

Smallest eigenvalues:
 [1]  0.50882689  0.50075317  0.48144842  0.44519441  0.42594167  0.33753583
 [7]  0.27869258  0.25456696 -0.06069958 -0.06535618

Largest  eigenvalues:
 [1] 63854675 59703959 56572040 55585389 54537211 52669914 51658262 51433524
 [9] 50815700 50015836

Smallest eigenvalues:
 [1]  0.45649287  0.41412221  0.37667398  0.35182485  0.32954510  0.32636299
 [7]  0.29448418  0.27915808  0.19058528 -0.02391875

Largest  eigenvalues:
 [1] 63808570 59670117 56915312 56116770 54461710 52804472 52178820 51686886
 [9] 51106699 50588447

Smallest eigenvalues:
 [1]  0.220724914  0.181054654  0.121851653  0.075105997  0.014370919
 [6]  0.003954583 -0.068102525 -0.117293554 -0.270865423 -0.598483811

Largest  eigenvalues:
 [1] 65179290 60040329 57626844 56214835 55025747 53791653 52418467 52321234
 [9] 51646798 50898794

Smallest eigenvalues:
 [1]  0.3477265  0.3382494  0.2864824  0.2788496  0.2288106  0.2053901
 [7]  0.1158699  0.1123578 -0.1736892 -2.2765180

Largest  eigenvalues:
 [1] 62516799 60576083 57220393 55263765 55214019 53796931 52263598 52047624
 [9] 51273721 51056053

Smallest eigenvalues:
 [1]  0.304863670  0.280426175  0.269769894  0.261061491  0.259985276
 [6]  0.190197306  0.008451877 -0.017938571 -0.515318793 -2.022076797

Largest  eigenvalues:
 [1] 64614596 59906279 56820091 55943537 54836449 53144701 51973884 51807784
 [9] 51606833 50637371

Smallest eigenvalues:
 [1]  0.37998711  0.28192784  0.27723401  0.26139988  0.23183547  0.18427750
 [7]  0.16469401  0.14824012  0.06731416 -5.12656472

Largest  eigenvalues:
 [1] 65314815 60387067 57638136 56210152 55045487 53474856 52451586 51889012
 [9] 51739090 50963747

Smallest eigenvalues:
 [1]  0.38020275  0.34922766  0.28844905  0.25673680  0.22629373  0.21778674
 [7]  0.18830183  0.14889710  0.03192554 -0.03693272

Largest  eigenvalues:
 [1] 63693108 59171143 56713225 55495852 54662422 52979472 52127056 51536485
 [9] 51386932 50847659

Smallest eigenvalues:
 [1]  0.56942348  0.47956819  0.47432258  0.46612022  0.45594268  0.41610416
 [7]  0.26361871  0.08286752 -0.04269034 -0.17091968

Largest  eigenvalues:
 [1] 64096855 60086363 56675723 55765869 54851525 53141721 51804636 51789820
 [9] 51301106 50391147

Smallest eigenvalues:
 [1]  0.4340350  0.4024907  0.3888212  0.3581736  0.3032138  0.2707824
 [7]  0.2470293  0.1834053 -0.3641796 -2.7561827

Largest  eigenvalues:
 [1] 64464764 60129902 57460781 56067361 55387508 53883150 52046812 52004648
 [9] 51905391 50825009

Smallest eigenvalues:
 [1]  0.43369943  0.41951322  0.37719865  0.31316405  0.29335078  0.20834640
 [7]  0.20475525  0.09493602 -0.18010660 -0.66490814

Largest  eigenvalues:
 [1] 63806335 59907766 56864545 55966184 54665014 52981852 52198139 52017662
 [9] 51102728 50711855

Smallest eigenvalues:
 [1]  0.50064484  0.42639591  0.38077752  0.35239346  0.30284503  0.29561547
 [7]  0.28893717  0.13885856  0.02390817 -0.05246068

Largest  eigenvalues:
 [1] 63973422 60374186 57137324 55824788 55228202 53516670 52507648 51944496
 [9] 51830404 51185042

Smallest eigenvalues:
 [1]  0.49950708  0.49100664  0.45904088  0.44496387  0.37752922  0.31594269
 [7]  0.20897183  0.18017701  0.16348505 -0.07820728

Largest  eigenvalues:
 [1] 64705591 60594599 57230747 56233877 55330313 53719943 52314337 52205351
 [9] 51984186 51227376

Smallest eigenvalues:
 [1]  0.4613428  0.3986235  0.3563802  0.3221114  0.3209026  0.2802571
 [7]  0.2450980  0.2176601 -0.3305451 -1.5069816

Largest  eigenvalues:
 [1] 65246208 60759944 57569629 56405666 55600683 53894562 52570849 52499804
 [9] 52431337 51417580

Smallest eigenvalues:
 [1]  0.48950277  0.42835856  0.40392864  0.28254733  0.26561703  0.23598338
 [7]  0.23279718  0.19785960 -0.05522623 -0.05696261

Largest  eigenvalues:
 [1] 64852783 60617888 57702054 56371880 55571485 53894456 52618612 52477220
 [9] 52161761 51462191

Smallest eigenvalues:
 [1]  0.38212052  0.35174725  0.29528500  0.27939766  0.20196418  0.07794977
 [7] -0.03871463 -0.05635074 -0.19285943 -0.51522753

Largest  eigenvalues:
 [1] 64691927 60554210 57526722 55881709 55194237 53746334 52406788 52078161
 [9] 51725391 50890734

Smallest eigenvalues:
 [1]  0.42094983  0.40035735  0.39629503  0.33488797  0.32065761  0.31621719
 [7]  0.06825558 -0.11076073 -0.65539756 -0.87563403

Largest  eigenvalues:
 [1] 64429779 60451116 56747914 56670787 54867924 52937451 52377013 52093379
 [9] 51557568 50609782

Smallest eigenvalues:
 [1]  0.5317492  0.5202339  0.4558578  0.4418403  0.4375726  0.4259148
 [7]  0.3322293  0.2072673  0.1764485 -0.0496080

Largest  eigenvalues:
 [1] 64050908 60634957 57265849 56115769 55102682 53152151 52505481 52166370
 [9] 51563940 51078031

Smallest eigenvalues:
 [1]  0.294209991  0.292330954  0.276242530  0.252170137  0.235196059
 [6]  0.112033404  0.059416381  0.016941972 -0.007679314 -0.599304713

Largest  eigenvalues:
 [1] 62244391 60110364 57361500 55319892 55135051 53752747 52393298 51878541
 [9] 51256527 51097344

Smallest eigenvalues:
 [1]  0.5529925  0.5007083  0.4856654  0.4268885  0.3535266  0.3483023
 [7]  0.2474378  0.1294687 -0.0660236 -0.3445050

Largest  eigenvalues:
 [1] 63851328 60630562 56920193 55900352 55440496 53696604 52397252 52121257
 [9] 51760574 50977081

Smallest eigenvalues:
 [1]  0.4631743  0.4062614  0.3764578  0.3439337  0.2456474  0.2172864
 [7]  0.1375874  0.1151171  0.1064158 -0.4026055

Largest  eigenvalues:
 [1] 66046082 60051299 57370045 57070409 54527651 53067612 52985447 51801438
 [9] 51522632 51077707

Smallest eigenvalues:
 [1]  0.40851832  0.31176804  0.30685172  0.29311884  0.28822228  0.24267490
 [7]  0.22840652  0.18635389  0.15495509 -0.03761303

Largest  eigenvalues:
 [1] 65794694 60112379 57648243 57407047 54379094 53225263 52782900 52335047
 [9] 51588838 51501845

Smallest eigenvalues:
 [1]  0.50038327  0.49819707  0.49508231  0.45654407  0.37995865  0.37448820
 [7]  0.26296750  0.25297191  0.18827253 -0.04836541

Largest  eigenvalues:
 [1] 63598554 60285943 57021770 55901587 55066847 53351813 52069165 51833540
 [9] 51442387 50808918

Smallest eigenvalues:
 [1]  0.47729340  0.46810693  0.45222123  0.44119277  0.38592354  0.27908271
 [7]  0.18593310  0.05595294 -0.20137736 -0.24072081

Largest  eigenvalues:
 [1] 64564122 60510889 57519256 56626031 55086099 53122789 52518509 52201380
 [9] 52066684 51220293

Smallest eigenvalues:
 [1]  0.31260264  0.30041979  0.25099713  0.21121671  0.20899542  0.17953973
 [7]  0.17330198 -0.06270073 -0.07479795 -0.48259157

Largest  eigenvalues:
 [1] 63314190 59237743 56816773 55734408 54420744 52891623 51687334 51464597
 [9] 50977761 50220009

Smallest eigenvalues:
 [1]  0.4957815  0.4795986  0.4753241  0.3948453  0.3395536  0.3115004
 [7]  0.2884822  0.2474319  0.1079045 -0.0887370

Largest  eigenvalues:
 [1] 63438133 59564410 56664560 55324030 54333513 52850595 51456978 51386354
 [9] 51375945 50537189

Smallest eigenvalues:
 [1]  0.4633509  0.4445126  0.4412881  0.4122093  0.3917410  0.3652278
 [7]  0.3366746  0.2389127  0.1048716 -0.2694398

Largest  eigenvalues:
 [1] 64033161 59678940 56629527 55948074 54366138 52877022 51943062 51552260
 [9] 51236344 50390062

Smallest eigenvalues:
 [1]  0.35394668  0.28631417  0.25581224  0.24583801  0.23292979  0.20598352
 [7]  0.13047551  0.09912355 -1.00590826 -1.38320515

Largest  eigenvalues:
 [1] 64374489 59693340 57297582 56977487 54467650 52851328 52691341 52420035
 [9] 51778876 51040013

Smallest eigenvalues:
 [1]  0.44106608  0.40134040  0.33587903  0.27944389  0.27379946  0.24821555
 [7]  0.14185147  0.11705653  0.08756123 -0.04054477

Largest  eigenvalues:
 [1] 64863547 60618870 57752143 56599667 54748520 53394360 52694306 52124310
 [9] 51863780 51276195

Smallest eigenvalues:
 [1]  0.36408603  0.32962644  0.31988793  0.27237173  0.25490129  0.20409077
 [7]  0.17844088  0.12175815 -0.09523532 -0.36860257

Largest  eigenvalues:
 [1] 64622641 58959299 56694585 55359260 54151218 52917551 51434798 51418116
 [9] 51307143 50736781

Smallest eigenvalues:
 [1]  0.51595807  0.48387446  0.44453058  0.39112117  0.31122284  0.27453355
 [7]  0.23527914  0.17078696  0.07306644 -0.11596416

Largest  eigenvalues:
 [1] 65959074 60750900 57844802 56604327 55054734 53369771 52846290 52777213
 [9] 51980374 51839210

Smallest eigenvalues:
 [1]  0.4717270  0.4619197  0.4492732  0.3876351  0.2778257  0.2219278
 [7]  0.1663721  0.1292486  0.1001942 -0.5059503

Largest  eigenvalues:
 [1] 65543615 60676412 57495507 56957477 55051492 53347799 53035588 52191254
 [9] 51804116 50863386

Smallest eigenvalues:
 [1]  0.322364538  0.319415501  0.284282692  0.234698264  0.221925329
 [6]  0.206847339  0.134694006  0.121866050 -0.007448306 -0.047132048

Largest  eigenvalues:
 [1] 62402494 59599538 56973013 54864892 54452469 53198741 51637902 51377556
 [9] 50689237 50533438

Smallest eigenvalues:
 [1]  0.42972070  0.35759064  0.31985157  0.30513731  0.30014486  0.18214671
 [7]  0.17132069 -0.06005723 -0.50149860 -0.66058149

Largest  eigenvalues:
 [1] 63535603 60575743 57195175 55878468 55413652 54228227 52416290 52320219
 [9] 51471640 51382763

Smallest eigenvalues:
 [1]  0.4730594  0.4723298  0.3875682  0.3636253  0.3084050  0.2921532
 [7]  0.2883358  0.2839556  0.2566918 -1.5453906

Largest  eigenvalues:
 [1] 64487831 60219380 57025283 56051735 55135554 53280492 52232604 51883890
 [9] 51866596 50857787

Smallest eigenvalues:
 [1]  0.4923777  0.4276504  0.4261334  0.3695037  0.3281602  0.2684967
 [7]  0.2340769 -0.0222209 -0.3504534 -0.3717939

Largest  eigenvalues:
 [1] 61947844 59529735 55951716 54729097 54579152 52785993 51529579 50852895
 [9] 50414549 49885903

Smallest eigenvalues:
 [1]  0.45371213  0.38330189  0.37402194  0.35301727  0.31285717  0.15689945
 [7]  0.08411424 -0.12633500 -0.13436219 -1.97514557

Largest  eigenvalues:
 [1] 63748909 60776223 57492472 56407362 55224990 53296355 52725199 52223794
 [9] 52023805 51341911

Smallest eigenvalues:
 [1]  0.5568921  0.5059484  0.4857746  0.4213832  0.3725788  0.3629504
 [7]  0.3123681  0.2489832 -0.1864722 -0.7249718

Largest  eigenvalues:
 [1] 63523906 60026876 56453536 55408456 55292547 53557662 51862772 51709792
 [9] 51363418 50484367

Smallest eigenvalues:
 [1]  0.25872611  0.22385998  0.18992172  0.08852940  0.05421065 -0.26298729
 [7] -0.29247447 -0.33589173 -1.08957848 -2.30670822

Largest  eigenvalues:
 [1] 62651502 59184391 56037805 55193004 54219086 52743950 51956099 51178018
 [9] 50959584 50410758

Smallest eigenvalues:
 [1]  0.39581122  0.38604809  0.35553013  0.35164822  0.35058575  0.31245521
 [7]  0.24660694  0.22503179  0.11628918 -0.03972061

Largest  eigenvalues:
 [1] 63614140 59747250 57063923 55395705 54699561 52939569 51701444 51617349
 [9] 51402437 50762495

Smallest eigenvalues:
 [1]  0.40082217  0.38534420  0.32855951  0.27519062  0.25700268  0.17681739
 [7]  0.14350263  0.08445469  0.01886748 -0.11080579

Largest  eigenvalues:
 [1] 64801888 59882907 57416602 56865422 54268813 53046832 52599210 52203628
 [9] 51539387 51373566

Smallest eigenvalues:
 [1]  0.4451139  0.3707244  0.3628837  0.3242300  0.3212832  0.2605088
 [7]  0.2602818  0.2534940  0.0933153 -0.4194682

Largest  eigenvalues:
 [1] 64586921 60232214 57325084 56804853 54651113 52870518 52693745 51701106
 [9] 51682407 50609113

Smallest eigenvalues:
 [1]  0.2773769457  0.2466841660  0.1524207671  0.1100507705  0.0002145748
 [6] -0.0064816387 -0.0115964540 -0.2729710510 -2.3236728171 -2.4096397131

Largest  eigenvalues:
 [1] 64932344 59967095 56477193 56423892 54875608 53071056 52373851 52138874
 [9] 51895539 50948653

Smallest eigenvalues:
 [1]  0.43891113  0.43832794  0.33146422  0.27594118  0.26724295  0.24046931
 [7]  0.17155929  0.06486833  0.06062705 -0.50427221

Largest  eigenvalues:
 [1] 64244579 60375632 57450183 55822722 55800982 54246862 52868183 52344301
 [9] 51852977 51499258

Smallest eigenvalues:
 [1]  0.44490175  0.42732571  0.37549910  0.37041748  0.29964370  0.17053014
 [7]  0.15161033  0.09095674 -0.02519998 -0.25556530

Largest  eigenvalues:
 [1] 61480744 59480948 56700459 54966493 54148092 53134158 52088275 51270395
 [9] 50802329 50291877

Smallest eigenvalues:
 [1]  0.32603648  0.23016485  0.20202962  0.17249560  0.14478631  0.12305024
 [7]  0.09516992 -0.04390640 -0.09717173 -0.11822092

Largest  eigenvalues:
 [1] 66520084 60342715 58119381 57627007 54349701 53799534 52840737 52087247
 [9] 51333497 51140675

Smallest eigenvalues:
 [1]  0.26433176  0.25963595  0.22714342  0.18307801  0.11048732  0.09315866
 [7] -0.01542112 -0.19597882 -0.55328859 -1.55760018

Largest  eigenvalues:
 [1] 64442765 60279945 57518453 56335313 55351739 53916937 52372324 52286943
 [9] 51972740 51052697

Smallest eigenvalues:
 [1]  0.3935927  0.3632513  0.3155366  0.3056787  0.2989560  0.2075036
 [7]  0.1792987  0.1058581  0.1011199 -0.2692723

Largest  eigenvalues:
 [1] 63609665 60345560 57057754 55715710 55117751 53231003 51992807 51773928
 [9] 51601203 50889416

Smallest eigenvalues:
 [1]  0.41314827  0.40292175  0.36772344  0.27771785  0.18290842  0.15014140
 [7]  0.12939764  0.05872944  0.05575680 -0.16431440

Largest  eigenvalues:
 [1] 63395269 60620655 57672706 56215761 54938609 54557485 52964852 52421742
 [9] 51611522 51161601

Smallest eigenvalues:
 [1]  0.48951589  0.47653992  0.47204199  0.43040406  0.39677860  0.39196331
 [7]  0.37851048  0.26780086  0.20230774 -0.01708545

Largest  eigenvalues:
 [1] 64370650 59392463 57038013 55922031 54400195 52705268 51984636 51629093
 [9] 51157895 50555465

Smallest eigenvalues:
 [1]  0.5576762  0.4256872  0.3558410  0.3376075  0.3219118  0.3133606
 [7]  0.2933233  0.2650482  0.1978047 -4.3005222

Largest  eigenvalues:
 [1] 65056478 60080402 57738824 55843326 54906169 53203319 52082865 52019591
 [9] 51940266 51331020

Smallest eigenvalues:
 [1]  0.4235342  0.3891179  0.3317569  0.3236358  0.3018352  0.2954184
 [7]  0.2920747  0.1576114  0.0838847 -0.1329351

Largest  eigenvalues:
 [1] 63203963 59980444 56583331 55423797 54943226 53047239 52006140 51452873
 [9] 51303284 50541442

Smallest eigenvalues:
 [1]  0.4050876  0.3624469  0.2798633  0.2679924  0.2435277  0.2413218
 [7]  0.2215689  0.2203864  0.1954278 -0.4585967

Largest  eigenvalues:
 [1] 64198624 59813463 57115264 55863741 54816674 52540609 52305276 51966151
 [9] 51198161 51171881

Smallest eigenvalues:
 [1]  0.5409602  0.4896571  0.4542637  0.4467150  0.3401741  0.3149995
 [7]  0.2900210  0.2478140  0.2408017 -0.4522807

Largest  eigenvalues:
 [1] 64723394 60080808 56836151 56575522 54238570 52518110 52418623 51542299
 [9] 51345115 50753420

Smallest eigenvalues:
 [1]  0.41541482  0.39159716  0.31991593  0.25163735  0.22166079  0.17612604
 [7]  0.14000807  0.13832142 -0.04133121 -0.08987305

Largest  eigenvalues:
 [1] 63330289 60423889 57440436 55437813 55374415 53843860 52506838 52108934
 [9] 51515899 51175301

Smallest eigenvalues:
 [1]  0.5522211  0.5143494  0.5006699  0.4490609  0.4264392  0.3741724
 [7]  0.3491604  0.2839451  0.1711908 -0.8154333

Largest  eigenvalues:
 [1] 64537279 60544596 57149150 56243049 55397666 53416625 52873906 52281691
 [9] 51737125 51523865

Smallest eigenvalues:
 [1]  0.4365364  0.4240506  0.3880275  0.3797212  0.3523477  0.3335104
 [7]  0.3298973  0.2569515  0.1833409 -0.2126094

Largest  eigenvalues:
 [1] 64539378 59931672 57202722 55624605 54209567 52792670 51942334 51728573
 [9] 51180882 51096091

Smallest eigenvalues:
 [1]  0.53734204  0.53421694  0.47891289  0.46447700  0.44463593  0.39498166
 [7]  0.36024749  0.08392692 -0.36473080 -0.45188977

Largest  eigenvalues:
 [1] 63497211 59741086 56457751 55472272 54588654 52714377 51471080 51419748
 [9] 51266083 50343097

Smallest eigenvalues:
 [1]  0.455879155  0.431250995  0.403890545  0.291130857  0.264666562
 [6]  0.256026095  0.243279912  0.196337352  0.002324291 -4.291024385

Largest  eigenvalues:
 [1] 64727395 59730632 56680760 56045738 54515943 52673836 52126816 51684678
 [9] 51586234 50956544

Smallest eigenvalues:
 [1]  0.45172103  0.44937817  0.42916564  0.40353396  0.33316969  0.30067627
 [7]  0.21539090  0.00869245 -0.11960191 -0.27441437

Largest  eigenvalues:
 [1] 63129611 60080379 56531005 55738000 54654023 52949026 51914329 51556125
 [9] 51315527 50526067

Smallest eigenvalues:
 [1]  0.40793568  0.35362448  0.29991313  0.28271367  0.24527347  0.22715089
 [7]  0.11398558  0.05128599 -0.21137692 -0.57406391

Largest  eigenvalues:
 [1] 64364083 59629359 56856694 56626747 54222221 52888910 52481750 51529016
 [9] 51408446 50634832

Smallest eigenvalues:
 [1]  0.4831740  0.4266035  0.4149914  0.4080387  0.3812790  0.3322192
 [7]  0.2152770  0.1731276 -0.1424544 -0.7218193

Largest  eigenvalues:
 [1] 64226474 60361275 57226824 55961587 54960020 53417411 52247232 52067095
 [9] 51989561 51233428

Smallest eigenvalues:
 [1]  0.37490704  0.33041294  0.31739777  0.27703350  0.24685853  0.22841607
 [7]  0.16970585  0.15677786 -0.06554758 -0.18122120

Largest  eigenvalues:
 [1] 63903510 60647159 58199739 55963358 55485044 54508171 52797062 52672777
 [9] 51858170 51597173

Smallest eigenvalues:
 [1]  0.4279425  0.4228308  0.4195979  0.3874378  0.3423814  0.3200809
 [7]  0.2627291  0.2485164  0.2138260 -0.1986564

Largest  eigenvalues:
 [1] 65469788 60465411 57512828 56619930 54518265 52715243 52660222 51946620
 [9] 51261617 51192516

Smallest eigenvalues:
 [1]  0.5796327  0.5122445  0.4957780  0.4823543  0.4115190  0.3703398
 [7]  0.2632388  0.2431749  0.2416874 -0.0313019

Largest  eigenvalues:
 [1] 63408431 60008307 56592589 55356582 55035046 53159374 51717234 51621763
 [9] 51468049 50567924

Smallest eigenvalues:
 [1]  0.4842995  0.4790832  0.4593683  0.4590637  0.4055636  0.3859144
 [7]  0.2801304  0.1912505  0.1405093 -0.5958165

Largest  eigenvalues:
 [1] 64380246 60764756 57290992 55911807 55623290 54129129 52377148 51945671
 [9] 51900558 50992775

Smallest eigenvalues:
 [1]  0.4916623  0.4790996  0.4693066  0.4012584  0.4006772  0.3954213
 [7]  0.3906656  0.3725708  0.3486859 -1.9300247

Largest  eigenvalues:
 [1] 64702295 59820296 57335457 56191358 55004838 53241282 52323635 52172893
 [9] 51566821 51092873

Smallest eigenvalues:
 [1]  0.47990139  0.45238224  0.40259296  0.38256312  0.30227513  0.26535360
 [7]  0.24292439  0.13868423 -0.06141004 -0.21891877

Largest  eigenvalues:
 [1] 63946157 60140374 56663768 55704405 54885120 52933251 51809082 51759477
 [9] 51647852 50698286

Smallest eigenvalues:
 [1]  0.51157235  0.49522121  0.46731462  0.33745805  0.30334810  0.30140608
 [7]  0.22643429  0.13796497  0.08756840 -0.06544513

Largest  eigenvalues:
 [1] 64710870 59857441 56751433 56019946 54751169 53122990 52010800 51971413
 [9] 51423895 50903149

Smallest eigenvalues:
 [1]  0.39949087  0.37235502  0.30856421  0.22903655  0.21925367  0.15862647
 [7]  0.14623276 -0.02565325 -0.04445784 -0.27550225

Largest  eigenvalues:
 [1] 63415089 60009727 56889798 55295528 54840613 53276551 52285753 51551078
 [9] 51491608 51372653

Smallest eigenvalues:
 [1]  0.359829483  0.331258276  0.303209906  0.299162247  0.256095785
 [6]  0.252738631  0.188437860  0.157476675  0.001085834 -0.579429972

Largest  eigenvalues:
 [1] 65001954 60241882 57449551 56570135 55203748 53494362 52521684 52271228
 [9] 51994277 51241550

Smallest eigenvalues:
 [1]  0.37676805  0.36729280  0.34050572  0.30216720  0.28579262  0.26278719
 [7]  0.11360760  0.07049062 -0.05468144 -0.18554301

Largest  eigenvalues:
 [1] 63544284 59593588 56683525 55480151 54766561 53089252 51922600 51494918
 [9] 51215943 50400754

Smallest eigenvalues:
 [1]  0.39184921  0.30040396  0.29393589  0.28115497  0.27231923  0.24368198
 [7]  0.16124018  0.09885927 -0.06887028 -1.69150468

Largest  eigenvalues:
 [1] 63088719 59321166 56728169 55434641 54537993 52702113 51473535 51351258
 [9] 51119368 50069754

Smallest eigenvalues:
 [1]  0.4553332  0.3971022  0.2933993  0.2720232  0.2656623  0.2252195
 [7]  0.1037370 -0.2840356 -0.4677035 -1.5076144

Largest  eigenvalues:
 [1] 65795423 60244141 57655530 56558759 54526442 52821614 52631452 51932744
 [9] 51692279 51259193

Smallest eigenvalues:
 [1]  0.53513915  0.51730906  0.41651519  0.41455471  0.39496722  0.39406956
 [7]  0.32016504  0.26737337  0.22457298 -0.05265831

Largest  eigenvalues:
 [1] 65488487 60272135 57388174 56976371 54927802 53415494 53030421 51860383
 [9] 51832425 50784738

Smallest eigenvalues:
 [1]  0.35224357  0.34422440  0.31197112  0.30782255  0.29258321  0.17575419
 [7]  0.16322178 -0.01798261 -0.26720890 -0.72588366

Largest  eigenvalues:
 [1] 65272261 60743599 57368458 57266427 54841104 53282623 53004851 52068704
 [9] 51706089 50602336

Smallest eigenvalues:
 [1]  0.35759596  0.31716139  0.29613703  0.26070347  0.21753092  0.20600154
 [7]  0.13654233  0.09757256 -0.22408220 -0.34184706

Largest  eigenvalues:
 [1] 63308571 58903990 56657513 55239267 54244798 52713841 51286837 51235296
 [9] 50998925 50031864

Smallest eigenvalues:
 [1]  0.4075897  0.3894776  0.3545177  0.3155203  0.3123807  0.2864491
 [7]  0.2572327  0.1990279 -0.1027109 -0.2176474

Largest  eigenvalues:
 [1] 65475929 60299338 57604392 56918074 54445914 53268217 52532546 51918874
 [9] 51472021 50887152

Smallest eigenvalues:
 [1]  0.417262373  0.370415172  0.318272783  0.298750854  0.260924276
 [6]  0.235796585  0.212527031  0.109641262  0.018504889 -0.009456925

Largest  eigenvalues:
 [1] 64232646 59833300 57141033 55547940 54994029 53595169 52421594 51695527
 [9] 51569081 51000073

Smallest eigenvalues:
 [1]  0.46129383  0.45564494  0.45311222  0.42202348  0.40970332  0.33243629
 [7]  0.31537362  0.20116386  0.11811596 -0.01583709

Largest  eigenvalues:
 [1] 65264468 60252003 57210923 56639838 54519328 53085982 52557245 52098320
 [9] 51766660 51391227

Smallest eigenvalues:
 [1]  0.5596549  0.5408345  0.5291771  0.4029025  0.3659956  0.3277107
 [7]  0.3147081  0.2236991  0.2153930 -0.4273122

Largest  eigenvalues:
 [1] 63493791 60264180 56534822 55601952 55186272 53402944 52323426 51577385
 [9] 51520428 51024610

Smallest eigenvalues:
 [1]  0.53273152  0.52131649  0.50268057  0.47818130  0.47777905  0.38559107
 [7]  0.38175112  0.32922218  0.07503022 -0.02680991

Largest  eigenvalues:
 [1] 63530336 59917992 57334925 55060569 54752303 53452412 51722245 51375344
 [9] 51316142 50572724

Smallest eigenvalues:
 [1]  0.3916677  0.3309254  0.2970611  0.2724763  0.2476844  0.2261488
 [7]  0.1857745  0.1826592  0.1298817 -0.3144904

Largest  eigenvalues:
 [1] 64584752 59583116 57189172 56006554 54817252 53497694 52134606 51771477
 [9] 51449029 50532788

Smallest eigenvalues:
 [1]  0.29512525  0.23333020  0.22457436  0.21964919  0.17558932  0.16705179
 [7]  0.15335058  0.09649002 -0.11227937 -0.38290823

Largest  eigenvalues:
 [1] 64859590 60396723 57411961 57316175 55201171 53461962 53026159 52991053
 [9] 51875831 51737098

Smallest eigenvalues:
 [1]  0.40319651  0.38871163  0.36230782  0.32975262  0.31450860  0.23242065
 [7]  0.16751442  0.01600815 -0.19571888 -1.54780793

Largest  eigenvalues:
 [1] 64310420 60724044 56858840 56566576 55525964 53634657 52464549 52350785
 [9] 51382783 50757362

Smallest eigenvalues:
 [1]  0.42645423  0.39457535  0.39052401  0.37274862  0.35373979  0.32300083
 [7]  0.28534645  0.07733687  0.02175007 -0.10766890

Largest  eigenvalues:
 [1] 64250624 59357636 56502570 55500244 54328037 52605530 51597715 51185999
 [9] 51170640 50375457

Smallest eigenvalues:
 [1]  0.4940081  0.4512550  0.4480651  0.3450871  0.3081547  0.2801896
 [7]  0.2209954  0.1930185  0.1417486 -2.4633483

Largest  eigenvalues:
 [1] 64473988 60201569 57484231 56087414 55009464 53502326 52109001 52105646
 [9] 51991123 51036796

Smallest eigenvalues:
 [1]  0.34094894  0.30247352  0.29784051  0.22030799  0.20937260  0.18245877
 [7]  0.13034914  0.11024254  0.05144119 -0.10024005

Largest  eigenvalues:
 [1] 63604271 59757937 56929159 56077979 54338481 53058201 51882309 51307312
 [9] 51096078 50179560

Smallest eigenvalues:
 [1]  0.4365313  0.3545631  0.3024808  0.2439440  0.2417295  0.2346421
 [7]  0.2000289  0.1833187  0.1436633 -0.1930913

Largest  eigenvalues:
 [1] 66323308 59696128 57210281 56948276 54319203 53108030 52997645 51673164
 [9] 51583620 50908623

Smallest eigenvalues:
 [1]  0.36944669  0.30323915  0.29815414  0.28669323  0.28087647  0.20646380
 [7]  0.19130047  0.09419390 -0.02681965 -0.27967117

Largest  eigenvalues:
 [1] 64070969 59333893 56834971 55775071 54723354 53337260 51844360 51793372
 [9] 51525385 50499832

Smallest eigenvalues:
 [1]  0.35656785  0.34963449  0.34894534  0.32420575  0.30647333  0.28473943
 [7]  0.18946273 -0.02356753 -0.04769855 -0.58674645

Largest  eigenvalues:
 [1] 62203021 59169540 56333433 54764608 54477282 53108377 51681541 51310681
 [9] 50450407 50099064

Smallest eigenvalues:
 [1]  0.5325449  0.4831067  0.4282271  0.4122233  0.3171908  0.2517061
 [7]  0.2103692  0.1131749 -0.1703525 -0.2257619

Largest  eigenvalues:
 [1] 62279427 59686807 56649691 54982989 54802630 53386692 52092308 51349748
 [9] 50773898 50365945

Smallest eigenvalues:
 [1]  0.44211832  0.40863511  0.34859993  0.24051583  0.23440299  0.13783851
 [7]  0.10078551 -0.02014391 -0.25833555 -1.63120835

Largest  eigenvalues:
 [1] 63798169 59627777 57067799 55704278 54884957 52773462 52585041 51661808
 [9] 51546183 51142853

Smallest eigenvalues:
 [1]  0.39176050  0.36830837  0.35747625  0.27621652  0.23309476  0.20905463
 [7]  0.15521606  0.14552030  0.11963724 -0.04574377

Largest  eigenvalues:
 [1] 64162241 60200539 57470088 55426386 55416852 53962289 52139995 52055183
 [9] 51650950 50854422

Smallest eigenvalues:
 [1]  0.5133241  0.4682534  0.4410342  0.3521795  0.3230714  0.2765439
 [7]  0.2744915  0.2442786 -0.1708914 -4.2609585

Largest  eigenvalues:
 [1] 65302313 60850035 57578047 57223528 55392549 53387620 53287285 52844640
 [9] 51668311 51217112

Smallest eigenvalues:
 [1]  0.4532789  0.4330580  0.4226647  0.3164623  0.2903435  0.2696899
 [7]  0.2389523  0.2116961  0.1760464 -0.3022617

Largest  eigenvalues:
 [1] 65397717 59995175 57439600 56629345 54959946 52939278 52824757 52408738
 [9] 51442629 51115656

Smallest eigenvalues:
 [1]  0.31748105  0.26053256  0.25016996  0.20884109  0.19721868  0.17607537
 [7]  0.10524407  0.00560777 -0.02931751 -0.64303134

Largest  eigenvalues:
 [1] 65497215 59730601 57105664 56801009 54388392 52983851 52892659 51533260
 [9] 51141710 50486499

Smallest eigenvalues:
 [1]  0.41720201  0.39661915  0.35727929  0.35456673  0.28845945  0.27680765
 [7]  0.18218221  0.05004232 -0.01128930 -0.12347167

Largest  eigenvalues:
 [1] 65356931 60522465 57507781 56627338 55620113 54105904 52672460 52629708
 [9] 52218538 51318308

Smallest eigenvalues:
 [1]  0.36205589  0.34871849  0.28273238  0.22418022  0.20875546  0.17437463
 [7]  0.16567923 -0.04916439 -0.26702663 -3.18829811

Largest  eigenvalues:
 [1] 62209697 59452920 56069235 55084966 54606492 53297058 51617332 51198385
 [9] 50566128 50256301

Smallest eigenvalues:
 [1]  0.40457757  0.37105234  0.34206980  0.33927739  0.15868956 -0.02547031
 [7] -0.07879285 -0.43813273 -1.14065626 -1.17479422

Largest  eigenvalues:
 [1] 65432187 60870258 58019615 55968546 55479928 53833269 52701600 52351659
 [9] 52130279 51692544

Smallest eigenvalues:
 [1]  0.34341878  0.30212456  0.29010952  0.28025838  0.27375064  0.27019492
 [7]  0.16770015  0.09688249  0.07176449 -0.24946901

Largest  eigenvalues:
 [1] 62711165 59656769 57379756 55073601 54723046 53294179 51954264 51603531
 [9] 51115351 50906062

Smallest eigenvalues:
 [1]  0.54474061  0.50659142  0.46336812  0.42630154  0.33749079  0.33244587
 [7]  0.28352365  0.14666376  0.07919596 -0.06035519

Largest  eigenvalues:
 [1] 63805937 59164911 56530360 55624688 54218193 52554919 51560218 51339992
 [9] 51314967 50360362

Smallest eigenvalues:
 [1]  0.30101602  0.28826169  0.27843258  0.25444936  0.22981135  0.22476269
 [7]  0.15038949  0.05483666 -0.16478223 -0.19878346

Largest  eigenvalues:
 [1] 64047387 60445556 58050191 55737252 55293267 53975380 52530610 52200607
 [9] 51928691 51519915

Smallest eigenvalues:
 [1]  0.20294527  0.20005520  0.16803595  0.03827905 -0.16311319 -0.33929826
 [7] -0.38956689 -1.07044696 -1.37095910 -1.38460793

Largest  eigenvalues:
 [1] 63932747 60135675 56932395 56290436 55127858 53340011 52155455 51666176
 [9] 51444684 50595903

Smallest eigenvalues:
 [1]  0.492724720  0.481167581  0.426896712  0.405638200  0.393113643
 [6]  0.357733413  0.265071693  0.235734511 -0.008893704 -2.288256463

Largest  eigenvalues:
 [1] 64697231 60364936 56868480 56120573 55122591 53428250 52140123 52108474
 [9] 51889065 51187687

Smallest eigenvalues:
 [1]  0.52633209  0.51642719  0.49476744  0.38630909  0.32661979  0.26909337
 [7]  0.23463650  0.18014555  0.08618074 -0.10813541

Largest  eigenvalues:
 [1] 64330205 60470271 57279212 56333215 55347612 53512567 52402168 52346187
 [9] 52109575 51169935

Smallest eigenvalues:
 [1]  0.4930265  0.4871813  0.4809229  0.4053347  0.3108328  0.3063834
 [7]  0.2436045  0.1817364  0.1237841 -0.2755930

Largest  eigenvalues:
 [1] 65716885 59705953 56986734 56550361 53870348 52945000 52268727 51484461
 [9] 50731342 50412256

Smallest eigenvalues:
 [1]  0.44994614  0.42942450  0.35324007  0.33329498  0.30203708  0.29279263
 [7]  0.23324230  0.15109102 -0.09354433 -0.35239474

Largest  eigenvalues:
 [1] 65744021 60041569 57747700 57038537 54784736 53050326 53018727 52797879
 [9] 51919454 51816021

Smallest eigenvalues:
 [1]  0.4915165  0.4872079  0.4370600  0.3214289  0.2785962  0.2576738
 [7]  0.2525378  0.1907475  0.1704417 -0.1586498

Largest  eigenvalues:
 [1] 65727945 60759489 57711568 57705463 54880238 53525622 52450331 52388966
 [9] 51291747 51035598

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	0.9909572	0.5825788	15.19244	0.215	2.768191	1.895482

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

EDA ~ alt + n + steps + PM1

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- EDA_fd
covariates <- list(altitude = altitude_fd, 
                   noise = noise_fd,
                   steps = steps_fd,
                   pollution = pollution1_fd)
path_plot <- 'figures/model_EDA_alt_noise_steps_PM1_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 80, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     noise = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     steps = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     pollution = list(nbetabasis = 80, norder = 4, lambda = 1e3))

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, HR = HR, 
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 18.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Warning message in `^.fd`((outcome - yhatfd), 2):
"The maximum error exceeds the tolerance level."
Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 494 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Smallest eigenvalues:
 [1]   0.11759975   0.11519453   0.05519783   0.02168391  -0.04459219
 [6]  -0.09989738  -1.05867264  -1.47554572 -11.60490337 -13.53925404

Largest  eigenvalues:
 [1] 59245918 56629705 53475221 52475840 51757610 50512526 49485579 48628830
 [9] 48218405 47962559

Smallest eigenvalues:
 [1]  0.2968488  0.2902908  0.2559251  0.1743317  0.1023142 -0.2114283
 [7] -0.8582463 -1.0708047 -1.1728633 -5.7160740

Largest  eigenvalues:
 [1] 57335614 55646417 53634531 51594638 50710648 50208133 48894550 48682473
 [9] 47749715 47297030

Smallest eigenvalues:
 [1]  0.46646169  0.43266819  0.40268675  0.34542728  0.33899549  0.27604763
 [7]  0.21518843 -0.04439961 -0.08697455 -0.10675487

Largest  eigenvalues:
 [1] 61891445 56833394 54174126 53124009 52035557 50227685 49511141 49117547
 [9] 48753677 48086907

Smallest eigenvalues:
 [1]   0.29240381   0.25898917   0.16912645   0.09819217   0.08802493
 [6]  -0.19444433  -1.01707435 -11.44428156 -13.99880807 -42.19122326

Largest  eigenvalues:
 [1] 61693579 57109248 54324750 52873440 52594541 51243848 49695208 49374592
 [9] 49181295 48454970

Smallest eigenvalues:
 [1]  0.3290388  0.3046865  0.1934457  0.1716797  0.1638666  0.1561956
 [7]  0.1255125 -0.2168174 -0.2202073 -1.6885551

Largest  eigenvalues:
 [1] 60775416 55947781 53303029 52021440 51501452 49876116 48674032 48384849
 [9] 48329665 47793670

Smallest eigenvalues:
 [1]  0.35693130  0.35556831  0.29404053  0.26534479  0.23321912  0.23250682
 [7]  0.20574500 -0.03224006 -0.90437380 -5.19732786

Largest  eigenvalues:
 [1] 62864191 57828059 55246663 54568444 52453687 50897463 50631186 50154481
 [9] 49299434 48973227

Smallest eigenvalues:
 [1]  0.55228671  0.52477481  0.50700061  0.46892508  0.42574676  0.35019430
 [7]  0.34164607  0.28353283  0.23420201 -0.09955738

Largest  eigenvalues:
 [1] 59749237 56959547 53668197 52594403 52017224 50788609 49017217 48761961
 [9] 48391576 47687237

Smallest eigenvalues:
 [1]   0.34691679   0.30183280   0.21546352   0.18962791   0.11094857
 [6]   0.05107483   0.01350571  -4.33859106  -6.87438138 -10.93928184

Largest  eigenvalues:
 [1] 61814410 56408173 54134546 53708707 51795569 50161435 49810957 49726725
 [9] 48944852 48843286

Smallest eigenvalues:
 [1]  0.4479376  0.4420109  0.4150566  0.3618554  0.3291921  0.2802027
 [7]  0.2724389  0.2164615  0.2148165 -0.8769721

Largest  eigenvalues:
 [1] 61112611 57309352 54400590 53302545 52513984 51012538 49860963 49634059
 [9] 49308484 48695084

Smallest eigenvalues:
 [1]  0.36765701  0.27709309  0.24644595  0.21760698  0.20000906  0.07727509
 [7]  0.05621599 -0.46268686 -0.67529846 -3.04380053

Largest  eigenvalues:
 [1] 58499610 56591831 54457543 52769628 51170826 51070651 49436369 48831489
 [9] 48013527 47987099

Smallest eigenvalues:
 [1]  0.54331783  0.46039474  0.35717020  0.34185921  0.34055743  0.30891443
 [7]  0.25758706  0.10036070  0.07583772 -0.02015530

Largest  eigenvalues:
 [1] 61056489 57482029 54531451 53524846 52419883 50654515 49816701 49771907
 [9] 49247928 48748222

Smallest eigenvalues:
 [1]   0.42712189   0.36935038   0.33173277   0.26881560   0.15675431
 [6]   0.08015566   0.00677776  -0.11457602  -0.68594026 -15.44410703

Largest  eigenvalues:
 [1] 60197362 56625966 54049204 52607662 52127553 51045418 49729883 49373652
 [9] 48550413 48444360

Smallest eigenvalues:
 [1]  0.37240511  0.34305442  0.31520964  0.29327685  0.22128216  0.09462863
 [7] -0.08661080 -0.50111993 -0.98650489 -5.63090737

Largest  eigenvalues:
 [1] 62254350 56400819 53909758 53682415 51618808 50157738 49962612 48554508
 [9] 48444314 47701039

Smallest eigenvalues:
 [1]  0.3863344  0.3813188  0.3012086  0.2897377  0.2519886  0.2326829
 [7]  0.2099434 -0.1670564 -0.2601984 -0.8751103

Largest  eigenvalues:
 [1] 60100246 56911689 54086487 52407588 52367403 50788343 50090434 48853006
 [9] 48781638 48566371

Smallest eigenvalues:
 [1]  -0.2731970  -0.4286934  -0.8271097  -1.1930917  -2.0237089  -2.0915327
 [7]  -2.3495205 -11.5548913 -12.0930681 -69.8219340

Largest  eigenvalues:
 [1] 59375038 57712448 54297011 53246840 52938850 51605419 49806368 49748626
 [9] 49014867 48612300

Smallest eigenvalues:
 [1]  0.4611782  0.4279020  0.4050982  0.2933056  0.2739197  0.2696547
 [7]  0.1832078  0.1753487 -0.1893700 -0.6278470

Largest  eigenvalues:
 [1] 60425330 56734544 54477260 52943308 52069613 50950880 49347148 49153974
 [9] 49074688 48461820

Smallest eigenvalues:
 [1]  0.33737855  0.31209078  0.27228518  0.24297865  0.17020246  0.04907851
 [7] -0.29359870 -0.37106095 -0.97303966 -2.48997571

Largest  eigenvalues:
 [1] 62930916 56840134 53972054 53782999 51666865 50145720 49733692 49476632
 [9] 48758477 48707332

Smallest eigenvalues:
 [1]  0.44592438  0.42762621  0.41546562  0.35814751  0.33036455  0.28248199
 [7]  0.03454255 -0.14562384 -0.35093582 -1.59169841

Largest  eigenvalues:
 [1] 61579943 56653299 54001202 53404481 51883928 49999807 49648605 49288175
 [9] 48856094 48358405

Smallest eigenvalues:
 [1]  0.45363288  0.35412169  0.34089316  0.32415592  0.30423113  0.26846921
 [7]  0.23922576  0.03197619 -0.08439322 -0.46382878

Largest  eigenvalues:
 [1] 60728630 56320359 53806531 52960559 51507639 50066450 49458109 49182146
 [9] 48893742 48284364

Smallest eigenvalues:
 [1]   0.23418695   0.21495560   0.18868886   0.18093427   0.11169582
 [6]   0.03139363  -0.17483405  -1.82412015 -10.74849169 -22.07613889

Largest  eigenvalues:
 [1] 60720412 56915818 54803061 53104835 51901310 50713366 50020050 49293391
 [9] 49194108 49044345

Smallest eigenvalues:
 [1]  0.4791541  0.3776639  0.3062627  0.3002259  0.2444965  0.2004157
 [7] -0.3939639 -0.6318045 -1.4427837 -3.3612877

Largest  eigenvalues:
 [1] 61161939 56879840 54232730 53100902 52329578 50507937 49799715 49424589
 [9] 49252267 48757219

Smallest eigenvalues:
 [1]  0.3236475  0.2880414  0.2326896  0.2230478  0.1632813  0.1424908
 [7]  0.1251832  0.1068714 -1.9343528 -9.7313114

Largest  eigenvalues:
 [1] 62155928 57747025 54689623 54266140 52733209 50887048 50538968 50010091
 [9] 49671569 48917473

Smallest eigenvalues:
 [1]  0.4872420  0.4487984  0.4271718  0.4192335  0.4017726  0.3225788
 [7]  0.1729355  0.1591491 -0.2141052 -0.8487638

Largest  eigenvalues:
 [1] 60504797 57239842 54175451 52539333 52444032 50726191 50443102 48908511
 [9] 48728045 48683492

Smallest eigenvalues:
 [1]  0.53461271  0.48547053  0.47406165  0.39456752  0.32932617  0.32184410
 [7]  0.29093931  0.28071698  0.18775976 -0.07469584

Largest  eigenvalues:
 [1] 60073449 57040056 54248758 52667126 52603923 51047712 49768308 49426886
 [9] 48931052 48570327

Smallest eigenvalues:
 [1]  0.44119098  0.41827476  0.39213393  0.34028222  0.25456716  0.16724314
 [7]  0.10696716  0.04529755 -0.06778547 -0.36721073

Largest  eigenvalues:
 [1] 61457079 56621538 54340759 52857037 51636916 50182194 49232907 48666262
 [9] 48594763 48136801

Smallest eigenvalues:
 [1]   0.2594248   0.2516792   0.2480985   0.1578670   0.1519393   0.1081103
 [7]  -0.1278886  -0.5668698  -1.6745653 -10.0845201

Largest  eigenvalues:
 [1] 61314579 56684920 53893412 53561468 51942446 50368371 49859886 49695803
 [9] 49383547 48777180

Smallest eigenvalues:
 [1]   0.22798913   0.21909386   0.16941158   0.05328828  -0.09062188
 [6]  -0.86903849  -1.26128342  -3.07959504 -10.95140912 -29.20921916

Largest  eigenvalues:
 [1] 62962353 56386879 53853135 53815449 51603355 50163768 50035777 48931640
 [9] 48787791 48168370

Smallest eigenvalues:
 [1]   0.4188670   0.3932071   0.1894995   0.1368815   0.1012176  -0.1680160
 [7]  -0.2088754  -1.0543885  -8.4287623 -11.4399237

Largest  eigenvalues:
 [1] 60679256 56937760 54121591 52664065 51967571 50636571 49281409 48997111
 [9] 48837546 48252386

Smallest eigenvalues:
 [1]  0.5221675  0.3894817  0.3861179  0.3683855  0.2644577  0.1943920
 [7]  0.1692925  0.1275275 -0.0937813 -0.5795524

Largest  eigenvalues:
 [1] 63008211 57009017 54208604 54070344 51666105 50386115 50114857 49485544
 [9] 48574724 48542878

Smallest eigenvalues:
 [1]  0.4145045  0.4004049  0.3528923  0.3325280  0.3027909  0.2276010
 [7]  0.1843536 -0.1353789 -0.3149606 -7.9084575

Largest  eigenvalues:
 [1] 60235442 56507991 53940088 51935999 51925229 50535442 49266401 49192223
 [9] 48546096 48220159

Smallest eigenvalues:
 [1]  0.54718904  0.45704070  0.44215172  0.37311816  0.31923690  0.28381915
 [7]  0.23811836  0.22528975  0.20187192 -0.02876468

Largest  eigenvalues:
 [1] 62013844 57437373 55188980 53925129 52026848 50680396 50280096 49839331
 [9] 49197142 48960719

Smallest eigenvalues:
 [1]  0.4764141  0.4610814  0.4021038  0.3001321  0.2733321  0.2050224
 [7]  0.1822829  0.1470086 -0.2307073 -0.5491573

Largest  eigenvalues:
 [1] 61318845 57163105 54560978 53143360 52114501 50817331 49467576 49458077
 [9] 49076698 48213066

Smallest eigenvalues:
 [1]   0.3391626   0.3055882   0.2921771   0.2559696   0.2400783   0.1816054
 [7]   0.1794299   0.1246618  -0.8123703 -15.5866890

Largest  eigenvalues:
 [1] 62064495 56931142 53938643 53925033 51708935 50153576 49985154 49254215
 [9] 48975858 48145325

Smallest eigenvalues:
 [1]  0.4146259  0.4100722  0.3598118  0.3239598  0.2661714  0.1991941
 [7] -0.1440754 -0.1987744 -0.3481176 -4.1354358

Largest  eigenvalues:
 [1] 60056153 56326656 54107198 52343688 51643112 50229536 48925766 48711834
 [9] 48644806 48013559

Smallest eigenvalues:
 [1]   0.5114456   0.5110935   0.4277844   0.3714690   0.3198004   0.3138220
 [7]   0.2850153   0.2095667   0.1482962 -29.0201435

Largest  eigenvalues:
 [1] 60851866 56728473 54098955 52715965 52136091 50514027 49100554 48993319
 [9] 48970296 48290553

Smallest eigenvalues:
 [1]  0.3944503  0.3516754  0.3143969  0.3047692  0.2429552  0.2102555
 [7]  0.1502172 -0.3353203 -1.2060121 -3.1789042

Largest  eigenvalues:
 [1] 61070546 57394393 54315127 53480998 52162167 50340978 49867109 49708462
 [9] 49244724 48857077

Smallest eigenvalues:
 [1]   0.113088231   0.094316288   0.075390459   0.036136766   0.002208176
 [6]  -0.006923469  -2.984921289  -9.321882566 -12.690959167 -15.554148219

Largest  eigenvalues:
 [1] 63490961 57049906 54923155 53913797 51910793 50243260 50146537 50070822
 [9] 49223306 48676352

Smallest eigenvalues:
 [1]  0.4183586  0.3950555  0.3725973  0.3288589  0.3176722  0.3142408
 [7]  0.3025289  0.2595539  0.1312363 -0.1145698

Largest  eigenvalues:
 [1] 59744426 57442701 54790866 52463562 52447190 50858899 49539838 49442668
 [9] 48882692 48442816

Smallest eigenvalues:
 [1]  0.48956398  0.42135454  0.37455086  0.29762072  0.24342317  0.19116131
 [7]  0.03167908 -0.08248460 -0.96648072 -2.47144597

Largest  eigenvalues:
 [1] 61759559 56761289 54534142 52995044 52191875 50653175 49461866 49392142
 [9] 49285025 48580510

Smallest eigenvalues:
 [1]   0.4238634   0.3818149   0.3597098   0.2911985   0.2626952   0.1885168
 [7]   0.1605276  -0.4311474  -0.5174386 -10.2106185

Largest  eigenvalues:
 [1] 61179995 56396167 54087079 53098194 51861298 50522799 49441731 49251275
 [9] 49070439 48609179

Smallest eigenvalues:
 [1]  0.4147044  0.4015553  0.3394930  0.3121006  0.2667017  0.2616047
 [7]  0.2528266  0.1812171  0.1657170 -1.7011160

Largest  eigenvalues:
 [1] 61157518 56521960 54365071 53442703 51823245 50411063 49669646 49153948
 [9] 48835764 48329098

Smallest eigenvalues:
 [1]   0.18942804   0.14448785   0.13239920   0.05528852  -0.27432728
 [6]  -0.30785054  -0.31640422  -0.36618001  -6.34829127 -22.13692338

Largest  eigenvalues:
 [1] 58635530 55438487 53012841 51771735 50907036 49148899 48882610 48075347
 [9] 47881398 47110458

Smallest eigenvalues:
 [1]   0.249695769   0.211028418   0.202322279   0.169881178   0.122353370
 [6]   0.008093507  -0.161168349  -0.932892518  -6.524469994 -10.180626411

Largest  eigenvalues:
 [1] 61962853 57838443 54984396 53987142 53495190 52378410 50263005 50144084
 [9] 49734618 49407434

Smallest eigenvalues:
 [1]  0.361174024  0.330285475  0.258207747  0.195258201  0.183085791
 [6]  0.001193101 -0.705694625 -3.681444560 -5.112545924 -9.283382626

Largest  eigenvalues:
 [1] 60413866 57641720 54872685 52966248 52286935 50973801 49471675 49355282
 [9] 49256283 48274166

Smallest eigenvalues:
 [1]  0.6166202  0.4695622  0.3833293  0.3734358  0.3288334  0.2833482
 [7]  0.2628883  0.1881330 -0.1394222 -1.4746451

Largest  eigenvalues:
 [1] 59726850 56940808 54267439 52532132 52407333 50778447 49584830 49035800
 [9] 48775019 48276421

Smallest eigenvalues:
 [1]  0.43779533  0.36497834  0.36094199  0.29900326  0.28646825  0.24572136
 [7]  0.23743605  0.17479466 -0.06053218 -0.08321880

Largest  eigenvalues:
 [1] 59942459 57176870 54388728 52768363 51714161 50301213 49189077 49001275
 [9] 48613944 47952766

Smallest eigenvalues:
 [1]  0.50769080  0.50138379  0.48418870  0.46307965  0.43256934  0.33604290
 [7]  0.32475068  0.05034399  0.03016553 -3.52485595

Largest  eigenvalues:
 [1] 61472170 57305477 54491434 53249254 52491182 50721421 49635856 49456923
 [9] 49088985 48414204

Smallest eigenvalues:
 [1]  0.4131480  0.3989692  0.3425488  0.3156007  0.2979224  0.2150130
 [7]  0.1968052  0.1802540 -1.3699372 -2.1946783

Largest  eigenvalues:
 [1] 60309041 56449268 53882962 53386097 52003840 50401483 49431240 49393710
 [9] 49339898 48046268

Smallest eigenvalues:
 [1]  0.454983217  0.447439925  0.415389735  0.336387445  0.271972727
 [6]  0.221753311  0.186994865  0.007259486 -0.153224177 -0.520963187

Largest  eigenvalues:
 [1] 60111228 56733244 54218667 52489072 52083331 50524250 49455240 49239889
 [9] 48811009 48504413

Smallest eigenvalues:
 [1]   0.35546959   0.24179450   0.21292127   0.20954633  -0.03963395
 [6]  -0.26582023  -1.14257157  -2.42615706 -11.40986207 -15.78527904

Largest  eigenvalues:
 [1] 62298669 56637372 54096249 53545406 51799385 50061752 49712836 49471073
 [9] 48898662 48566474

Smallest eigenvalues:
 [1]   0.2836360   0.2369638   0.2292395   0.2147618   0.2067926   0.1418923
 [7]   0.1319408  -0.1273847  -2.2732207 -13.4753350

Largest  eigenvalues:
 [1] 62440982 56411608 54562908 53736822 51432623 50099069 49890788 48694702
 [9] 48652586 48123596

Smallest eigenvalues:
 [1]  0.51912687  0.50254954  0.45571812  0.44412072  0.35295712  0.30750587
 [7]  0.26695784  0.11186332  0.09387339 -0.61540948

Largest  eigenvalues:
 [1] 60591727 56626455 54070547 52735474 51572975 50134909 49031375 49013942
 [9] 48920168 48202195

Smallest eigenvalues:
 [1]  0.5307333  0.4908078  0.4671842  0.4239771  0.3775175  0.3350041
 [7]  0.3130766  0.2655266  0.1010292 -0.2088797

Largest  eigenvalues:
 [1] 60300559 57573436 54105856 53031227 52870246 51056802 50095453 49275359
 [9] 49201315 48887680

Smallest eigenvalues:
 [1]  0.3973149  0.3556538  0.3340458  0.3114995  0.2456433  0.1992295
 [7]  0.1964905  0.1137582 -0.3499786 -2.4821498

Largest  eigenvalues:
 [1] 61325200 57390753 54660974 53222116 52402501 50961781 49797175 49540658
 [9] 49505228 48866784

Smallest eigenvalues:
 [1]  0.35802820  0.34471978  0.32447953  0.28311807  0.12905468  0.09609255
 [7] -0.17173486 -0.81161470 -1.49030615 -8.01710727

Largest  eigenvalues:
 [1] 61105056 57600613 54252543 52846901 52746143 51178089 49955702 49401403
 [9] 49054536 48925471

Smallest eigenvalues:
 [1]   0.43390788   0.37073338   0.36964699   0.35097726   0.29428743
 [6]   0.28881210   0.26866382   0.23325600   0.04592056 -11.75393737

Largest  eigenvalues:
 [1] 61016677 56412659 53930387 52725276 52052943 50438193 49097018 49000895
 [9] 48883758 48055595

Smallest eigenvalues:
 [1]   0.4111781   0.3725650   0.3368662   0.2958664   0.2206949   0.2140575
 [7]   0.1535194  -0.2664744  -1.3362325 -11.0143638

Largest  eigenvalues:
 [1] 59599315 57114738 53600852 52393269 52067428 50648499 49057992 48984109
 [9] 48384993 48122583

Smallest eigenvalues:
 [1]  0.3581320  0.2834164  0.2573484  0.2416377  0.1712044  0.1697558
 [7]  0.1219815 -0.4340061 -0.5299346 -0.6310965

Largest  eigenvalues:
 [1] 60694692 56190538 53771517 53017580 51315582 50191127 49258926 49008045
 [9] 48771213 48227428

Smallest eigenvalues:
 [1]   -0.06957346   -0.69990562   -0.91569788   -3.87719687   -7.24516399
 [6]   -9.99605959  -12.17572032  -32.59852715  -77.44131140 -142.68799897

Largest  eigenvalues:
 [1] 60926567 56669758 54270644 52934279 51757160 50086238 49290057 49030890
 [9] 48539484 47856430

Smallest eigenvalues:
 [1]  0.44679968  0.41970681  0.38915842  0.38427637  0.37684401  0.28202215
 [7]  0.23731764  0.08698706 -0.10962923 -0.18634335

Largest  eigenvalues:
 [1] 61183873 57811999 54796575 53229648 52923125 51169044 50545780 49613827
 [9] 49608897 49159634

Smallest eigenvalues:
 [1]  0.4973586  0.4885806  0.4161627  0.4074907  0.3329852  0.2052987
 [7]  0.1725354  0.1279403 -0.2014513 -4.0684164

Largest  eigenvalues:
 [1] 60557047 56582110 53711961 52599003 52142463 50456394 49254656 48991196
 [9] 48761541 48038835

Smallest eigenvalues:
 [1]  0.4206073  0.4119398  0.3644903  0.3559738  0.3550427  0.1870505
 [7]  0.1499121  0.1292920 -0.4167845 -4.4295726

Largest  eigenvalues:
 [1] 61477673 56866303 54329184 53066082 52453835 50883401 49741483 49568486
 [9] 49310784 48834912

Smallest eigenvalues:
 [1]  0.4456224  0.4168914  0.4087419  0.3977425  0.3261181  0.2809803
 [7]  0.2306873  0.2027823  0.1898369 -1.0165076

Largest  eigenvalues:
 [1] 61172848 57042612 54016712 53647687 52008150 50555613 49786323 49371571
 [9] 49229520 48526436

Smallest eigenvalues:
 [1]  0.3731567  0.3267541  0.3154992  0.2682366  0.2471300  0.2036301
 [7]  0.1528135 -1.2046827 -1.4145005 -5.3339228

Largest  eigenvalues:
 [1] 59857068 56182176 53494297 52266129 52252567 50493172 49088951 48560899
 [9] 48401003 47804132

Smallest eigenvalues:
 [1]  0.42126079  0.37101802  0.25585390  0.24573844  0.22444463  0.09371462
 [7] -0.39882779 -0.43058873 -1.56692294 -3.56178020

Largest  eigenvalues:
 [1] 61081531 56030956 53920676 52651019 51311079 50000893 48925123 48606546
 [9] 48496508 47713954

Smallest eigenvalues:
 [1]   0.49432625   0.44908377   0.41304375   0.39721556   0.27296106
 [6]   0.21336588   0.08215902   0.06022717   0.04705052 -13.97191738

Largest  eigenvalues:
 [1] 59269030 56279917 53747922 52145189 51331423 50578244 48986019 48848520
 [9] 47981560 47698970

Smallest eigenvalues:
 [1]  0.4295923  0.4140698  0.4068561  0.3687875  0.3117716  0.2848645
 [7]  0.2307433  0.1739668 -0.2250700 -0.5682320

Largest  eigenvalues:
 [1] 58437369 56598188 53572341 52148164 51591648 50412770 49331875 49180125
 [9] 48251262 47891608

Smallest eigenvalues:
 [1]  0.3989619  0.3247437  0.2543453  0.2067893  0.0680325 -0.1619079
 [7] -0.1753853 -0.5725849 -1.7198096 -3.9826874

Largest  eigenvalues:
 [1] 60555950 55718039 53242434 52062238 51672767 49991698 48591294 48459830
 [9] 48372495 47610866

Smallest eigenvalues:
 [1]  0.4416527  0.4242140  0.3336121  0.2590310  0.2322976  0.1830904
 [7]  0.1564058  0.1431793  0.0863002 -0.1187603

Largest  eigenvalues:
 [1] 60342299 57835459 54374215 53187720 52552721 50994644 49725055 49646410
 [9] 49458075 48710997

Smallest eigenvalues:
 [1]  0.5261730  0.5088191  0.4159429  0.3292228  0.2934735  0.2896869
 [7]  0.2499551 -0.1812845 -0.4459341 -0.5181454

Largest  eigenvalues:
 [1] 61262176 56608542 54414812 52811980 51951915 50777890 49236254 49189165
 [9] 49122921 48461773

Smallest eigenvalues:
 [1]   0.306810571   0.236969787   0.185972633   0.153230686   0.004056011
 [6]  -0.066945430  -0.997909603  -1.801615016  -6.788588521 -10.613827741

Largest  eigenvalues:
 [1] 63697119 57601193 55451158 54906184 52344810 51167320 50836596 50222501
 [9] 49753105 49596851

Smallest eigenvalues:
 [1]  0.43087060  0.42819020  0.37351278  0.34727754  0.25345057  0.21872589
 [7]  0.20082096  0.08937241 -0.06069351 -1.09444289

Largest  eigenvalues:
 [1] 61338026 56809605 54086211 53246091 52102294 50360118 49419697 48989028
 [9] 48961458 47936963

Smallest eigenvalues:
 [1]  0.4785558  0.4545345  0.4355433  0.3834228  0.3795366  0.2817536
 [7]  0.2795443  0.2356011  0.1524734 -0.4032405

Largest  eigenvalues:
 [1] 59641447 57278318 54118455 52686964 52301256 50937531 49413421 48827461
 [9] 48616556 47989657

Smallest eigenvalues:
 [1]  0.3547494  0.3340287  0.3149641  0.3004229  0.2511517  0.2173563
 [7]  0.1908252 -0.1218631 -0.2195041 -6.8143711

Largest  eigenvalues:
 [1] 62522106 57373142 54621037 54071964 51838623 50428058 50188222 49520846
 [9] 49027912 48795444

Smallest eigenvalues:
 [1]  0.25413821  0.22440340  0.19354317  0.18093980  0.16034082  0.06936268
 [7]  0.05456476 -0.15390239 -0.78322330 -3.96930435

Largest  eigenvalues:
 [1] 62267157 57384473 54311082 53286428 52311041 50776157 49695586 49495533
 [9] 49270716 48825298

Smallest eigenvalues:
 [1]  0.403415460  0.372922764  0.339053058  0.308029621  0.296865242
 [6]  0.257756560  0.211835773  0.006137938 -0.039944218 -0.091656262

Largest  eigenvalues:
 [1] 62005980 57669417 54862619 53372524 52728561 51079601 50723890 49881147
 [9] 49521612 49286148

Smallest eigenvalues:
 [1]  0.48421445  0.42266337  0.41061960  0.37540273  0.35247323  0.31382722
 [7]  0.10349166  0.06073065  0.04195059 -4.97035155

Largest  eigenvalues:
 [1] 61108550 57018537 54354470 53153835 51677289 50253458 49456921 49062800
 [9] 48984406 48415007

Smallest eigenvalues:
 [1]  0.4597145  0.3911165  0.3713723  0.3047817  0.2637179  0.2540702
 [7]  0.2459730  0.2313930 -0.4791964 -6.3026274

Largest  eigenvalues:
 [1] 61306977 57334890 54582804 53793788 52392278 50984607 50100755 49872235
 [9] 49510908 49029129

Smallest eigenvalues:
 [1]  0.4897942  0.4739730  0.4319149  0.3257935  0.2791753  0.2598534
 [7]  0.2526025  0.2086651  0.1217125 -0.3170514

Largest  eigenvalues:
 [1] 60485843 56521823 53884756 52759899 52065255 50292977 49146549 49073745
 [9] 48698429 48135526

Smallest eigenvalues:
 [1]  0.48148525  0.47626800  0.46879729  0.39841969  0.39055755  0.37036864
 [7]  0.30480696  0.29716127  0.09492443 -0.04393594

Largest  eigenvalues:
 [1] 61086914 56652700 54365087 53124494 51840947 50383637 49431866 49089863
 [9] 48646044 48145694

Smallest eigenvalues:
 [1]  0.26611074  0.25478846  0.23320243  0.22843295  0.21715994  0.17639351
 [7] -0.01506566 -0.41094364 -2.71405257 -3.49042894

Largest  eigenvalues:
 [1] 61215433 57051291 54076384 53546532 51973888 50601201 49845991 49775417
 [9] 49103010 48800738

Smallest eigenvalues:
 [1]  0.447222948  0.396876004  0.311891116  0.275035248  0.240900106
 [6]  0.150489201  0.086193432  0.006348429 -1.201057540 -5.934954429

Largest  eigenvalues:
 [1] 61794747 56796461 53656606 53090329 52016389 50216736 49412447 49216863
 [9] 48949739 48057932

Smallest eigenvalues:
 [1]  0.4169468  0.4169186  0.3431241  0.3123001  0.2875054  0.2140677
 [7]  0.1974103  0.1139702  0.0975766 -0.1464623

Largest  eigenvalues:
 [1] 60524750 56542780 54161682 52268750 51900306 50212497 48939315 48666610
 [9] 48394236 47714533

Smallest eigenvalues:
 [1]  0.33377520  0.29669175  0.25779849  0.19924455  0.15468778  0.14136234
 [7]  0.06924209  0.01030865 -0.83360067 -8.31590613

Largest  eigenvalues:
 [1] 62050605 56879991 54525441 53493738 52258673 50492890 49906021 49615972
 [9] 48977404 48828274

Smallest eigenvalues:
 [1]   0.50058824   0.39455557   0.35382297   0.34451543   0.22634708
 [6]   0.18915167   0.03251033  -6.37260431 -13.26185894 -17.67832275

Largest  eigenvalues:
 [1] 60572361 58024267 54600930 53503349 52983186 51861155 50027642 49522153
 [9] 49314065 48637627

Smallest eigenvalues:
 [1]   0.41945312   0.38515364   0.34761576   0.27592034   0.27075476
 [6]   0.17238199  -0.08076965  -5.78931843 -19.62834862 -20.10019192

Largest  eigenvalues:
 [1] 60196312 56652116 53977135 52185610 52182334 50751620 49244330 48723249
 [9] 48487178 48186290

Smallest eigenvalues:
 [1]  0.408462003  0.380986416  0.378335412  0.322107615  0.311387884
 [6]  0.307542467  0.265929143 -0.005566618 -0.265109312 -0.409352524

Largest  eigenvalues:
 [1] 59587111 57182708 53826952 52441984 52037795 50569805 49189556 48761287
 [9] 48347380 48043992

Smallest eigenvalues:
 [1]   0.3932513   0.3331562   0.3227514   0.2262686   0.1743011  -0.1437699
 [7]  -1.7674359 -12.6282563 -18.2846170 -20.2854838

Largest  eigenvalues:
 [1] 60391028 56085431 53849415 52415926 51822335 50401537 49470672 49012327
 [9] 48598764 48182975

Smallest eigenvalues:
 [1]  0.4585123  0.4461084  0.4249138  0.2899170  0.2285372  0.2049880
 [7]  0.1622307  0.1256476 -0.3369741 -0.3867203

Largest  eigenvalues:
 [1] 61269712 57390183 54975354 53205469 52783058 51392109 50252786 49922589
 [9] 49549337 49242031

Smallest eigenvalues:
 [1]  0.45219267  0.43940677  0.42820670  0.37751718  0.37465681  0.17953060
 [7]  0.14428141  0.09077744  0.01352761 -0.80323463

Largest  eigenvalues:
 [1] 59999976 56566075 53701652 52051650 51729929 50021719 48928094 48672877
 [9] 48406386 48098398

Smallest eigenvalues:
 [1]  0.49965674  0.48492225  0.46107986  0.38251331  0.28348803  0.25407320
 [7]  0.19090658  0.13405570  0.01850294 -2.61042749

Largest  eigenvalues:
 [1] 60238845 56672888 53875686 52380399 52059900 50433273 49015866 48863855
 [9] 48728360 47946459

Smallest eigenvalues:
 [1]  0.61565611  0.52233607  0.47578075  0.39249330  0.37199130  0.33022113
 [7]  0.32125124  0.27509777 -0.02030376 -0.05628125

Largest  eigenvalues:
 [1] 60286176 56856941 53860023 52812890 51856791 50005682 49230675 49133814
 [9] 48444190 47939792

Smallest eigenvalues:
 [1]  0.28164146  0.23851359  0.18457693  0.12258670  0.11383483  0.09470023
 [7]  0.06534050 -1.44717167 -1.60317122 -9.28455724

Largest  eigenvalues:
 [1] 62150861 57151954 54729817 53831207 51976395 50889562 49958038 49759145
 [9] 49481168 48884867

Smallest eigenvalues:
 [1]  0.2993253  0.2821829  0.2598497  0.2368275  0.2041751  0.1596735
 [7]  0.1095080 -1.4313192 -3.1491655 -5.5037315

Largest  eigenvalues:
 [1] 61018699 56340256 53368652 53132473 52030079 50437178 49757096 49239209
 [9] 49124996 48372487

Smallest eigenvalues:
 [1]  0.4516830  0.4360128  0.4112397  0.3552742  0.3454499  0.2918701
 [7]  0.2885161  0.2324237  0.2250454 -0.1474921

Largest  eigenvalues:
 [1] 61690822 56916206 54439533 53782931 52181547 50798969 49883515 49111756
 [9] 48944308 48114081

Smallest eigenvalues:
 [1]  0.28538274  0.28202882  0.23848967  0.18042887  0.12495418  0.03194275
 [7] -0.22312054 -0.32481396 -0.39048135 -4.58400882

Largest  eigenvalues:
 [1] 61825049 57079564 54225154 53042584 51508847 50012325 49356596 48860871
 [9] 48558914 48387418

Smallest eigenvalues:
 [1]  0.28357656  0.21813584  0.17968909  0.17494122  0.15614628  0.14061061
 [7]  0.03631024 -0.03953230 -0.25040715 -1.52006269

Largest  eigenvalues:
 [1] 59164882 57838843 54478613 52617481 52459788 51151450 49980419 49455649
 [9] 48742913 48522301

Smallest eigenvalues:
 [1]  0.3624519  0.3207424  0.3172560  0.3113898  0.2914644  0.2641308
 [7]  0.1717547 -0.5380479 -1.0863691 -2.0025998

Largest  eigenvalues:
 [1] 61755019 56590527 54282711 53327268 51638264 50442226 49622802 49100932
 [9] 49039210 48419945

Smallest eigenvalues:
 [1]  0.43946763  0.33247870  0.31606122  0.31490379  0.23805887  0.21511067
 [7]  0.14832635  0.09288727  0.08143682 -1.30062209

Largest  eigenvalues:
 [1] 60620452 57134791 53938702 52770365 52266613 50738889 49553374 49292226
 [9] 49083803 48648888

Smallest eigenvalues:
 [1]  0.39322027  0.33423365  0.31371202  0.30882274  0.24341675  0.08990376
 [7] -0.05676246 -0.09629991 -1.03522009 -4.82005734

Largest  eigenvalues:
 [1] 62185374 57275931 55023556 53532910 52403124 51019629 49962576 49826114
 [9] 49232766 48577439

Smallest eigenvalues:
 [1]  0.36732900  0.36029602  0.30194448  0.25616272  0.23158903  0.22158520
 [7]  0.09939661  0.05015184 -0.63015971 -5.26621088

Largest  eigenvalues:
 [1] 59002037 55741746 53269409 52261739 51529384 49810198 48992140 48978161
 [9] 48311860 47777005

Smallest eigenvalues:
 [1]  0.4918751  0.4818147  0.4359612  0.4082334  0.3729911  0.2993039
 [7]  0.2710861  0.2103083  0.1652060 -0.2060750

Largest  eigenvalues:
 [1] 60465603 57068268 54279561 52978452 52123235 50329800 49669936 49280694
 [9] 48998277 48486508

Smallest eigenvalues:
 [1]  0.3742797  0.3518233  0.2982323  0.2850500  0.2735075  0.2697046
 [7]  0.1588766 -0.5200624 -0.5337557 -2.1151559

Largest  eigenvalues:
 [1] 61419550 57598873 55079997 53557571 52766210 51559348 50521184 50042266
 [9] 49805927 49491838

Smallest eigenvalues:
 [1]  0.41925081  0.39552453  0.35476501  0.29666376  0.24516182  0.22831872
 [7]  0.17512874  0.04962938 -1.48088563 -1.50109603

Largest  eigenvalues:
 [1] 61966505 56921398 54077921 53457072 51486025 49946881 49743238 49029868
 [9] 48348249 48275735

Smallest eigenvalues:
 [1]   0.34750070   0.34392474   0.31983349   0.24479434   0.19355093
 [6]   0.16902388   0.06062803  -0.43001296  -4.57618396 -67.61167732

Largest  eigenvalues:
 [1] 59890647 56753342 53980393 52767092 52662107 50992010 49436140 49169291
 [9] 48930821 48158614

Smallest eigenvalues:
 [1]  0.42976168  0.42867276  0.41702242  0.39540675  0.34286921  0.33325330
 [7]  0.27704931  0.24961441  0.10811142 -0.06421055

Largest  eigenvalues:
 [1] 60208890 56174969 53748667 52598145 52008989 50302445 48805470 48544888
 [9] 48416265 47448496

Smallest eigenvalues:
 [1]  0.49609546  0.41397837  0.40428179  0.39174439  0.29675067  0.21328185
 [7]  0.14918387  0.12184916  0.08974958 -0.30092874

Largest  eigenvalues:
 [1] 58828755 56369016 53138310 51975999 51881947 50106312 49172607 48445260
 [9] 48018967 47533019

Smallest eigenvalues:
 [1]   0.27677352   0.20726174   0.17413171   0.14882560   0.13487215
 [6]  -0.08843992  -2.05902642  -3.75043712 -21.58718655 -22.43561207

Largest  eigenvalues:
 [1] 61832370 56588091 54263195 53103169 52436414 50918757 49407490 49218035
 [9] 48510981 47801855

Smallest eigenvalues:
 [1]  0.38981231  0.32775102  0.32558476  0.29948230  0.17919565  0.16901748
 [7] -0.01251332 -0.07140321 -1.25485213 -4.63885013

Largest  eigenvalues:
 [1] 59869351 56398776 53834176 52282723 52045708 50600043 49360865 49217364
 [9] 48563768 48472017

Smallest eigenvalues:
 [1]  0.33017882  0.30439988  0.25462496  0.14442313  0.08664877 -0.10384253
 [7] -0.38191603 -0.76665602 -1.02315666 -2.35168057

Largest  eigenvalues:
 [1] 60659072 57300087 54802718 53135060 52313831 50969051 49852052 49624595
 [9] 49228522 48956059

Smallest eigenvalues:
 [1]  0.38678808  0.33526306  0.25149170  0.22455124  0.20537057  0.18122629
 [7]  0.16304496  0.15331019 -0.01762924 -0.63827793

Largest  eigenvalues:
 [1] 58650368 56081763 53885697 52084119 51838137 50309065 49100318 48646062
 [9] 48206745 47629981

Smallest eigenvalues:
 [1]  0.4192507  0.4077064  0.3410043  0.2778001  0.2420358  0.1973463
 [7]  0.1821753 -0.2229754 -0.2744616 -0.3177189

Largest  eigenvalues:
 [1] 61295454 57380062 54827144 53551655 52053652 50370018 49821364 49495813
 [9] 49242921 48759885

Smallest eigenvalues:
 [1]  0.5406579  0.5003668  0.4597957  0.3588029  0.3325741  0.2955678
 [7]  0.2885041  0.1619238  0.1482223 -0.5074862

Largest  eigenvalues:
 [1] 60648032 56391887 54156534 52793418 51839235 50258124 49055121 49007539
 [9] 48820880 48108566

Smallest eigenvalues:
 [1]  0.39419785  0.38617724  0.35403919  0.32741738  0.27403111  0.14424427
 [7]  0.05499041 -0.03401287 -0.29777416 -1.10073036

Largest  eigenvalues:
 [1] 60434190 56346286 54118193 52494278 51492292 50169993 49270240 48798722
 [9] 48647031 48152355

Smallest eigenvalues:
 [1]  0.38417510  0.25461163  0.15015650  0.11758328  0.02145941 -0.15609713
 [7] -0.18551911 -0.22016006 -0.24563160 -1.23551217

Largest  eigenvalues:
 [1] 58207034 56804866 53781407 52206470 51645930 50808063 49681354 49334507
 [9] 48109531 47896795

Smallest eigenvalues:
 [1]  0.45020860  0.42148541  0.39601853  0.39064089  0.28288552  0.23227884
 [7]  0.15824238  0.07447579 -3.45277610 -5.36635851

Largest  eigenvalues:
 [1] 60470924 56931249 54290099 52522916 52275227 50989538 49158590 48917650
 [9] 48659855 48006792

Smallest eigenvalues:
 [1]   0.4493032   0.4367285   0.2364430   0.2357436   0.1747338   0.1639817
 [7]  -0.1398297  -0.4956277  -2.2292221 -31.6300210

Largest  eigenvalues:
 [1] 59271412 55618053 52939937 51837217 50974396 49415680 48393000 48187862
 [9] 47931640 47348080

Smallest eigenvalues:
 [1]  0.45520751  0.44566280  0.36639149  0.33807235  0.28932723  0.28607987
 [7]  0.21986350  0.07265161 -0.12066180 -0.43917277

Largest  eigenvalues:
 [1] 62076583 57348636 54810443 53495467 52413427 50972769 50250282 49846613
 [9] 49161942 49111304

Smallest eigenvalues:
 [1]   0.3116315   0.2985958   0.2871249   0.2391888   0.2326053   0.2211436
 [7]  -0.1189162  -2.1527048 -10.2022640 -15.7198921

Largest  eigenvalues:
 [1] 60593942 56992457 54224791 53125538 51979463 50501563 50069517 49366892
 [9] 48930593 48831956

Smallest eigenvalues:
 [1]  0.4637383  0.3875362  0.3301318  0.2892344  0.2820832  0.2593836
 [7]  0.2095194  0.1601700 -0.2305081 -0.4285403

Largest  eigenvalues:
 [1] 62408624 56984729 54590720 53932155 51960671 50212923 50102465 49810097
 [9] 48814719 48749993

Smallest eigenvalues:
 [1]  0.31122110  0.28234665  0.23652225  0.23010392  0.17719528  0.14485532
 [7]  0.06963547  0.03707936 -1.55130328 -4.38862773

Largest  eigenvalues:
 [1] 61294421 57763937 54278776 53411392 53007977 51060737 50456862 49703703
 [9] 49090437 49070834

Smallest eigenvalues:
 [1]  0.31366395  0.28779193  0.27916411  0.24767994  0.22439651  0.21275749
 [7]  0.15779675  0.08882063 -1.10278569 -1.14502976

Largest  eigenvalues:
 [1] 61540134 56823891 54110758 53551240 52145753 50563925 49898067 49203197
 [9] 49176370 48357032

Smallest eigenvalues:
 [1]  0.4239849  0.3787170  0.3426921  0.3340188  0.3292710  0.2816513
 [7]  0.1806327  0.1670743  0.1197871 -0.3233019

Largest  eigenvalues:
 [1] 59294884 57280967 53962863 52768297 52422402 50688091 49636928 49368825
 [9] 48854023 48719733

Smallest eigenvalues:
 [1]  0.53632004  0.46766716  0.32272287  0.29422753  0.26218855  0.18913284
 [7]  0.12784040  0.03740815 -0.11563543 -0.15722049

Largest  eigenvalues:
 [1] 63588265 57286165 55147282 54505526 52110461 50832131 50384325 49853217
 [9] 49189206 49093302

Smallest eigenvalues:
 [1]  0.35841713  0.33638821  0.20826792  0.19129876  0.16507549  0.09396055
 [7]  0.07613675 -0.11048022 -0.18615755 -4.83928957

Largest  eigenvalues:
 [1] 61516881 57581489 54263179 53087709 52536261 50816299 50240767 49403849
 [9] 49221385 48935756

Smallest eigenvalues:
 [1]   0.34046528   0.33256557   0.31434083   0.22799051   0.22051705
 [6]   0.09986872   0.02859728  -0.20648966  -5.30970348 -18.88088698

Largest  eigenvalues:
 [1] 61782066 57001518 54513637 53373497 52257559 50727866 49774420 49369805
 [9] 49126714 48242476

Smallest eigenvalues:
 [1]   0.131836792   0.114257089   0.112506727   0.088245789   0.007450638
 [6]  -0.065298361  -0.079313230  -0.303015051  -0.662625046 -45.443338720

Largest  eigenvalues:
 [1] 59777862 57230779 54286339 52482457 52385233 50805631 49781313 49119615
 [9] 48788159 48309467

Smallest eigenvalues:
 [1]  0.38120530  0.36685662  0.23840016  0.20976964  0.01806366 -0.09285273
 [7] -0.16190265 -0.46711971 -3.26255291 -4.09162112

Largest  eigenvalues:
 [1] 60262404 56386364 53664445 52634765 51387077 49639793 48727195 48675675
 [9] 48549349 47737914

Smallest eigenvalues:
 [1]  0.42006515  0.36833810  0.33483251  0.24318105  0.19474352  0.11196651
 [7]  0.09266439 -0.02891082 -0.24740555 -4.33810300

Largest  eigenvalues:
 [1] 61866681 56369224 53871255 52974701 51612440 50223763 49265588 49070255
 [9] 48805484 48308821

Smallest eigenvalues:
 [1]  0.299382605  0.217246401  0.145785694  0.073617206  0.040811053
 [6]  0.008976005 -0.231941334 -0.932579108 -5.780782534 -6.075570333

Largest  eigenvalues:
 [1] 62270949 57024164 54580720 53973783 52193056 50776080 50211366 49566862
 [9] 49345149 48727551

Smallest eigenvalues:
 [1]  0.52510958  0.46386520  0.43481311  0.40614587  0.40539473  0.26241105
 [7]  0.19934583  0.13273229 -0.09821225 -1.01697121

Largest  eigenvalues:
 [1] 61677524 57558413 54460142 53911845 52499116 50906807 50024470 49984054
 [9] 49663677 48918989

Smallest eigenvalues:
 [1]  0.4470429  0.4406437  0.3791411  0.3089484  0.2675828  0.2110227
 [7]  0.1948143 -0.2029869 -0.6959014 -5.2934709

Largest  eigenvalues:
 [1] 60741843 56743899 53977441 52665908 52016223 50466602 49292414 49085745
 [9] 48941822 48330784

Smallest eigenvalues:
 [1]  0.5962806  0.5433250  0.5403848  0.4712882  0.4210564  0.3237574
 [7]  0.3231302  0.2507061  0.2016491 -0.1337087

Largest  eigenvalues:
 [1] 59196366 57238096 54414183 52277223 52083932 50751619 49429863 49249267
 [9] 48560001 48367544

Smallest eigenvalues:
 [1]  0.527343213  0.481449902  0.423630479  0.324562346  0.262447993
 [6]  0.206552456  0.196993330  0.060195356 -0.009826601 -0.136721059

Largest  eigenvalues:
 [1] 61957631 57471215 54939933 53535837 52456145 51057611 50020727 49683250
 [9] 49498419 48875414

Smallest eigenvalues:
 [1]  0.391163738  0.382259313  0.343626069  0.287187744  0.275968097
 [6]  0.180612419  0.107215566  0.001730944 -0.556919588 -1.131280687

Largest  eigenvalues:
 [1] 61726541 57586045 54679741 53656176 52770492 51261118 50260220 49835977
 [9] 49674111 49086230

Smallest eigenvalues:
 [1]  0.4751794  0.4338979  0.4164889  0.3890979  0.2893370  0.2746776
 [7]  0.2686471  0.1301998  0.1110316 -0.4758231

Largest  eigenvalues:
 [1] 61150740 57743222 54043375 53499419 52462492 50582257 50109155 49664654
 [9] 49145916 48999559

Smallest eigenvalues:
 [1]  0.49659695  0.44345113  0.40898821  0.40401861  0.32115636  0.24469731
 [7]  0.23460340 -0.09529336 -0.20894937 -0.73934099

Largest  eigenvalues:
 [1] 61233436 57696352 55401904 53233292 52387413 51253901 49716474 49627250
 [9] 49584811 48976749

Smallest eigenvalues:
 [1]  0.37830869  0.31966236  0.30634410  0.27922753  0.25206800  0.21332421
 [7]  0.20623868  0.03177369 -0.93030296 -2.13165514

Largest  eigenvalues:
 [1] 60131929 57123889 53869652 52792703 52313405 50558798 49934771 49016179
 [9] 48800604 48519326

Smallest eigenvalues:
 [1]  0.5779883  0.5686235  0.5313749  0.4413090  0.3697106  0.3662736
 [7]  0.2101569  0.1770587 -0.2119506 -0.4446801

Largest  eigenvalues:
 [1] 61064834 56439896 54259904 52653783 51742894 50269188 49078852 49014789
 [9] 48715133 48031810

Smallest eigenvalues:
 [1]  0.4675412  0.4595034  0.4328221  0.4230367  0.3068548  0.2733584
 [7]  0.2115269  0.1533303 -0.5148192 -2.9466759

Largest  eigenvalues:
 [1] 61579485 56737883 53661362 52720961 51882712 50159515 49280457 49016488
 [9] 48996516 48595741

Smallest eigenvalues:
 [1]  0.52616720  0.50713439  0.45627493  0.42524232  0.40009670  0.38532158
 [7]  0.32059081  0.18087486 -0.01600144 -1.32009883

Largest  eigenvalues:
 [1] 61265775 57302480 54302502 53455540 52715597 51086075 49822837 49747269
 [9] 49160030 48570112

Smallest eigenvalues:
 [1]  0.3163779  0.2987390  0.2489280  0.2009231  0.1518982  0.1413334
 [7] -0.2353368 -0.8320955 -1.0596978 -9.5906019

Largest  eigenvalues:
 [1] 61810896 56957060 54080754 53295011 51751553 50360668 49617946 49189582
 [9] 49149829 48380777

Smallest eigenvalues:
 [1]  0.417872184  0.403019014  0.364067618  0.337982843  0.290507968
 [6]  0.279985342  0.236833596 -0.004323992 -0.133306996 -0.369669761

Largest  eigenvalues:
 [1] 60447917 56681275 54724851 52614048 51798426 50386741 49074974 48875089
 [9] 48756814 48094715

Smallest eigenvalues:
 [1]  0.37349604  0.36088349  0.23645661  0.22665584  0.22509863  0.05008246
 [7] -0.36080667 -0.41968590 -0.54381151 -8.92759856

Largest  eigenvalues:
 [1] 61983406 56656327 54488032 52511666 51746071 50598475 49336981 49157373
 [9] 48984410 48689319

Smallest eigenvalues:
 [1]   0.4926747   0.4342801   0.4030166   0.2890331   0.2013994   0.1692464
 [7]   0.0922654  -0.0961822  -0.2861295 -52.7433798

Largest  eigenvalues:
 [1] 59997502 57076895 53725770 52590533 52534512 50544623 49605270 49176419
 [9] 48766401 48246012

Smallest eigenvalues:
 [1]  0.4846577  0.4776786  0.3926871  0.3765648  0.3363943  0.2955917
 [7]  0.2859804  0.2493600  0.1338946 -1.6125203

Largest  eigenvalues:
 [1] 60844613 57006572 53867081 53086884 52633446 50888256 49784471 49409578
 [9] 49321366 48582918

Smallest eigenvalues:
 [1]  0.52063058  0.49071241  0.43844052  0.31826751  0.31201550  0.27687431
 [7]  0.25807263  0.08091928 -0.08009682 -0.17197054

Largest  eigenvalues:
 [1] 61761887 56697977 53585685 53217948 51660392 49978722 49515666 48884065
 [9] 48699347 48099059

Smallest eigenvalues:
 [1]  0.43143328  0.42081522  0.38255488  0.37397894  0.21358025  0.17653139
 [7]  0.12875449  0.09876649  0.06042186 -0.16757353

Largest  eigenvalues:
 [1] 60142246 57028270 54040533 52541064 52069059 50862415 49578240 49307527
 [9] 48538281 48317690

Smallest eigenvalues:
 [1]  0.53236544  0.52229172  0.46827748  0.45091960  0.44155349  0.25063813
 [7]  0.22134283  0.16196824  0.02279001 -1.39751865

Largest  eigenvalues:
 [1] 61795617 57682652 54353487 53569345 52828995 51019963 49920253 49793590
 [9] 49288927 48723896

Smallest eigenvalues:
 [1]  0.33459310  0.30177519  0.28950235  0.18515476  0.16697755  0.12515452
 [7]  0.07882004  0.04177229 -1.07230525 -2.16296592

Largest  eigenvalues:
 [1] 63009171 57270557 54374982 54318009 52111760 50660720 50545413 49775390
 [9] 49659164 49025458

Smallest eigenvalues:
 [1]  0.3766376  0.3342775  0.2827166  0.2507207  0.2166431  0.1833937
 [7]  0.1232313 -0.2659694 -0.9294953 -2.9583220

Largest  eigenvalues:
 [1] 61446362 56257324 54274426 52862441 51720310 50529734 49246249 49147229
 [9] 49038530 48479967

Smallest eigenvalues:
 [1]  0.3940590  0.3460800  0.3145156  0.2921522  0.2898588  0.2738630
 [7]  0.2231340  0.2111581 -0.4894491 -0.5228936

Largest  eigenvalues:
 [1] 61440268 56787905 54767623 53117186 52333125 51120774 49397788 49212010
 [9] 48967295 48156013

Smallest eigenvalues:
 [1]  -0.3163597  -0.6939889  -0.7659704  -0.7754386  -0.8826546  -0.9936103
 [7]  -1.1966426  -1.5837540  -1.9660663 -19.7337128

Largest  eigenvalues:
 [1] 59412987 57479798 54417275 53557253 52350330 51591238 49525984 49255752
 [9] 48637686 48093344

Smallest eigenvalues:
 [1]  0.32228367  0.30971945  0.26693085  0.23240276  0.15581570  0.13989633
 [7]  0.02781956 -0.10424959 -0.56899945 -9.05945639

Largest  eigenvalues:
 [1] 58960537 55965503 53058445 51654979 51611142 49955888 48543266 48133884
 [9] 47862213 47391663

Smallest eigenvalues:
 [1]  0.3772123  0.3471470  0.3191515  0.2843143  0.2758321  0.2657427
 [7]  0.2196151  0.1244580 -0.1827859 -0.1829246

Largest  eigenvalues:
 [1] 61852968 57208998 55069446 53296113 52169107 50732193 49821493 49775096
 [9] 49270942 49136606

Smallest eigenvalues:
 [1]  0.31785035  0.31085821  0.30367631  0.21060792  0.18652539  0.15123288
 [7]  0.06660781 -0.13874761 -0.24155226 -2.07494894

Largest  eigenvalues:
 [1] 62231200 56783743 54414742 53546615 51801063 50427583 49903020 49108168
 [9] 48831898 48186435

Smallest eigenvalues:
 [1]  0.40166168  0.27431137  0.26692210  0.24752077  0.18908565  0.12970148
 [7]  0.07432295  0.06915576 -0.83508196 -2.35804652

Largest  eigenvalues:
 [1] 62350627 56766381 54232385 53729722 51792384 50211696 50067820 49561446
 [9] 48946111 48680879

Smallest eigenvalues:
 [1]  0.48478048  0.45058904  0.42070936  0.31416544  0.28338867  0.20771669
 [7]  0.10266092  0.03606486 -0.07390494 -3.77561209

Largest  eigenvalues:
 [1] 62175800 57023364 54241390 53422437 51789982 50164244 49724218 49138137
 [9] 48758167 48258077

Smallest eigenvalues:
 [1]   0.28823548   0.13120189   0.05069389   0.00408220  -0.32397746
 [6]  -0.34911872  -1.22364367  -8.95925401 -12.45242650 -47.71906666

Largest  eigenvalues:
 [1] 59238381 55374048 52696385 51248966 51188979 49415805 48335904 47878619
 [9] 47544906 47215742

Smallest eigenvalues:
 [1]  0.43537886  0.42626241  0.42558254  0.38778306  0.32259139  0.30761260
 [7]  0.28655907  0.02376902 -0.00350010 -4.17533949

Largest  eigenvalues:
 [1] 61693631 56388556 53624361 53598524 51415772 49815492 49721569 48807710
 [9] 48598894 48022968

Smallest eigenvalues:
 [1]  0.528402876  0.504690579  0.483229260  0.437236375  0.331888613
 [6]  0.271730618  0.212058671  0.198478455 -0.004638645 -3.014639638

Largest  eigenvalues:
 [1] 63044161 57587430 54951859 53988999 52632465 50585442 50421876 50063718
 [9] 49374428 49283781

Smallest eigenvalues:
 [1]   0.5429344   0.5400139   0.4455596   0.3792661   0.3225131   0.2837928
 [7]   0.2724103   0.2358099   0.1790095 -31.2524015

Largest  eigenvalues:
 [1] 60305527 57326450 54258940 52758191 52621490 51164619 49502746 49291942
 [9] 48858767 48630233

Smallest eigenvalues:
 [1]   0.41592808   0.37538020   0.28915192   0.27235868   0.16884168
 [6]   0.08135910  -0.03725051  -0.07324944  -0.15500263 -24.97457371

Largest  eigenvalues:
 [1] 61025066 56289089 54098951 53004421 51561830 50032786 49357652 48882956
 [9] 48813166 47796571

Smallest eigenvalues:
 [1]  0.4800195  0.3453841  0.3337500  0.2895167  0.2734345  0.2709365
 [7]  0.2561887  0.1324717 -0.2744279 -2.4728586

Largest  eigenvalues:
 [1] 60952975 57415870 53805027 53783453 52201526 50603387 49860958 49329266
 [9] 49168398 48153359

Smallest eigenvalues:
 [1]   0.40921446   0.40397521   0.27914442   0.12461639  -0.02411838
 [6]  -0.18149470  -0.84962043  -1.96712799  -3.27651210 -16.03066299

Largest  eigenvalues:
 [1] 60591084 56640958 53805669 52724716 51816426 50481682 49012521 48907727
 [9] 48851078 47920877

Smallest eigenvalues:
 [1]   0.4851435   0.4172960   0.4037480   0.3575174   0.3405694   0.3084201
 [7]   0.2842711   0.1924449   0.1661641 -11.0310101

Largest  eigenvalues:
 [1] 60882537 57100704 54178649 53206124 52162797 50696490 49374607 49264912
 [9] 49134633 48327263

Smallest eigenvalues:
 [1]   0.3449633   0.2689929   0.2674617   0.2532790   0.1776660   0.1523659
 [7]  -0.2797336  -0.3920454  -0.8037189 -12.2217481

Largest  eigenvalues:
 [1] 62412328 56863309 54430964 53348900 52215404 50907064 49666601 49456788
 [9] 49326453 48992279

Smallest eigenvalues:
 [1]  0.5546884  0.5304329  0.4600697  0.4453827  0.4184473  0.2976896
 [7]  0.2439453  0.2091047  0.1222638 -0.9256579

Largest  eigenvalues:
 [1] 61373557 57508826 54132224 53580008 52449120 50704965 49780165 49528277
 [9] 49394693 48416793

Smallest eigenvalues:
 [1]  0.3289948  0.3113222  0.2808730  0.2697081  0.2452006  0.2312575
 [7]  0.1598467 -0.7246084 -1.5851729 -2.8434746

Largest  eigenvalues:
 [1] 62005266 56656775 53867168 53685584 51963274 50470540 49986043 49073156
 [9] 49051945 48283946

Smallest eigenvalues:
 [1]   0.41752964   0.37106945   0.34187507   0.18355867   0.12485874
 [6]   0.07246263  -0.31926985  -0.44166161  -1.88560506 -23.47400888

Largest  eigenvalues:
 [1] 62279555 57133149 54331339 53736978 52161907 50544436 49920653 49726454
 [9] 49170419 48957030

Smallest eigenvalues:
 [1]   0.25783768   0.22892593   0.11862846   0.07350162  -0.08815636
 [6]  -0.16910272  -1.87276111  -2.82019062  -7.89382940 -16.13772410

Largest  eigenvalues:
 [1] 61358524 56939037 53929578 53656457 51878887 50561444 49739572 48995935
 [9] 48986162 47974483

Smallest eigenvalues:
 [1]  0.3979987  0.3897463  0.3386844  0.2668677  0.2152867  0.1308378
 [7]  0.1151779 -0.2860246 -0.5770757 -1.9045157

Largest  eigenvalues:
 [1] 62714832 57274377 54911869 54351494 52246432 50679153 50629560 50216029
 [9] 49261716 49166051

Smallest eigenvalues:
 [1]  0.3981241  0.3946529  0.3399019  0.2819012  0.2321022  0.2229595
 [7]  0.2087211  0.1320222  0.1046734 -0.3699108

Largest  eigenvalues:
 [1] 59591231 57485727 54561632 53029139 52468101 51217426 49983685 49487861
 [9] 48738127 48491944

Smallest eigenvalues:
 [1]  0.5382623  0.4622930  0.3846954  0.3065558  0.2956224  0.2714992
 [7]  0.2713373  0.1914231 -0.1185494 -0.4422132

Largest  eigenvalues:
 [1] 61568879 56897333 54721006 53744201 51875400 50347067 49960426 49463599
 [9] 48877622 48525676

Smallest eigenvalues:
 [1]  0.43224575  0.43049092  0.39011711  0.38555291  0.35974162  0.22007268
 [7]  0.08723876 -0.22985422 -0.70185850 -0.77115855

Largest  eigenvalues:
 [1] 61021389 57021717 54164000 52991550 52013998 50392699 49310606 49300105
 [9] 49257627 48506422

Smallest eigenvalues:
 [1]  0.53123464  0.45400270  0.38853981  0.34032142  0.28921702  0.22092215
 [7]  0.19417337  0.18182406  0.05407943 -0.27718053

Largest  eigenvalues:
 [1] 60535856 56772481 54264677 52799728 52262534 50813447 49410257 49107292
 [9] 49006730 48295221

Smallest eigenvalues:
 [1]  0.3251987  0.3240275  0.2435386  0.1884451  0.1285746  0.0297709
 [7] -0.3280108 -0.4136464 -0.7648452 -6.6254925

Largest  eigenvalues:
 [1] 61309277 56879541 54438797 52933980 52395909 50981418 49906869 49342329
 [9] 49128068 48991347

Smallest eigenvalues:
 [1]   0.40744323   0.38594542   0.37049259   0.33299996   0.25690749
 [6]   0.23174785   0.21793333   0.01873293  -0.22821150 -15.87033079

Largest  eigenvalues:
 [1] 61282060 56946330 54536333 52962157 52355819 50871982 49462342 49396166
 [9] 49361133 48549042

Smallest eigenvalues:
 [1]   0.3327716   0.3172897   0.3092849   0.2179291   0.1811371   0.1765268
 [7]   0.1705095   0.1663353  -6.5427572 -13.3171176

Largest  eigenvalues:
 [1] 60831360 57582799 54238753 53256687 52436851 50583648 49897262 49550533
 [9] 48894170 48745150

Smallest eigenvalues:
 [1]   0.25498578   0.23364338   0.13061187  -0.02730126  -0.04535112
 [6]  -0.13105671  -2.10816812  -2.88635458  -9.57463125 -11.82811023

Largest  eigenvalues:
 [1] 61955807 57459405 54190115 53258930 52676653 51177849 49813211 49565304
 [9] 49389243 48942024

Smallest eigenvalues:
 [1]  0.38546920  0.30569562  0.30030786  0.26002536  0.21383642  0.19672300
 [7]  0.14461593  0.13388213 -0.01131249 -1.19477367

Largest  eigenvalues:
 [1] 60252027 56813001 54075367 52698201 52328171 50688661 49089982 49037739
 [9] 48936679 48113873

Smallest eigenvalues:
 [1]  0.45367019  0.43445248  0.42952376  0.41406225  0.38693280  0.38419472
 [7]  0.21247798  0.17721839  0.16056121 -0.08294111

Largest  eigenvalues:
 [1] 59339938 57213532 54058812 52690104 52190405 51094308 49779580 49317891
 [9] 48546323 48361160

Smallest eigenvalues:
 [1]  0.38933909  0.33158133  0.31827045  0.28651238  0.22930725  0.20056563
 [7]  0.15686031 -0.08093246 -0.38597245 -1.60641760

Largest  eigenvalues:
 [1] 58959123 57150030 54529056 53057044 51362061 51322568 49483293 49236092
 [9] 48120370 48097236

Smallest eigenvalues:
 [1]   0.47190154   0.43160214   0.36294626   0.32577114   0.28373129
 [6]   0.22782944   0.08724500   0.02268298  -0.17287610 -14.33659303

Largest  eigenvalues:
 [1] 60283899 56899936 54201877 52455388 52133001 51041042 49559396 49425902
 [9] 48607089 48455280

Smallest eigenvalues:
 [1]  0.52793212  0.48299634  0.42974987  0.41490155  0.40683390  0.29647934
 [7]  0.22853794  0.20801019  0.06818744 -0.56743580

Largest  eigenvalues:
 [1] 61779020 57655715 54685028 53684488 52959879 51374148 50221128 50020364
 [9] 49372916 48610143

Smallest eigenvalues:
 [1]  0.4730599  0.4717637  0.3615370  0.3419566  0.3260494  0.3083615
 [7]  0.3048087  0.2761801  0.1620163 -0.6846015

Largest  eigenvalues:
 [1] 61052588 57156497 54003069 53070905 52503631 50772913 49447274 49244168
 [9] 49224751 48206476

Smallest eigenvalues:
 [1]   0.2432103   0.2042841   0.1903342   0.1882352   0.1730858   0.1585371
 [7]   0.1117303  -0.2387666  -1.9121208 -10.7276031

Largest  eigenvalues:
 [1] 60839558 56841852 54091943 52879792 51691711 50492207 49269888 49132674
 [9] 48801021 48437122

Smallest eigenvalues:
 [1] -0.2696201 -0.3727248 -0.3788205 -0.4570900 -0.6134132 -0.6791791
 [7] -0.7341080 -0.7653298 -1.0638922 -4.5525826

Largest  eigenvalues:
 [1] 61249629 57373168 54754658 53738211 52289608 50855535 50082869 49791995
 [9] 49748500 49080676

Smallest eigenvalues:
 [1]  0.3480784  0.3447809  0.3313652  0.1913536  0.1560704  0.1549315
 [7]  0.1533832  0.0837505 -0.7286488 -4.5450232

Largest  eigenvalues:
 [1] 58561301 56768384 54097729 53174506 51522943 51342637 50011980 48628074
 [9] 48123200 47842270

Smallest eigenvalues:
 [1]  0.5071886  0.5015757  0.4135469  0.3983790  0.3665902  0.3568987
 [7]  0.2124301  0.2057271  0.1084625 -1.1570186

Largest  eigenvalues:
 [1] 62247415 57058741 54476567 53931551 52134275 50358685 50204042 49912211
 [9] 48855532 48795747

Smallest eigenvalues:
 [1]  0.42785338  0.40991571  0.31931309  0.21454428  0.20518782  0.18802414
 [7]  0.15642693  0.12044481  0.04126479 -0.42067914

Largest  eigenvalues:
 [1] 60388500 57064767 54108616 53020923 52463295 50968304 49728652 49221389
 [9] 49004809 48275749

Smallest eigenvalues:
 [1]   0.41330351   0.40559825   0.40473311   0.34158786   0.25602342
 [6]   0.15615590   0.08797451  -0.01980880  -0.12654621 -13.30518877

Largest  eigenvalues:
 [1] 61366525 56288727 53940964 52746219 51694424 50334335 49227619 48935295
 [9] 48627800 48473263

Smallest eigenvalues:
 [1]  0.3959002  0.3204508  0.3110198  0.2999301  0.2348817  0.2235670
 [7]  0.1817805  0.1618775 -0.4135727 -4.3768149

Largest  eigenvalues:
 [1] 62658909 56957554 54603616 53736673 51792794 50558848 50115207 49336673
 [9] 48899175 48475231

Smallest eigenvalues:
 [1]  0.379457665  0.372975888  0.348872313  0.304811643  0.219146347
 [6]  0.209685033  0.150282101  0.130195426  0.001570124 -0.565892613

Largest  eigenvalues:
 [1] 61620522 56725366 54687385 53331012 51877531 50704748 49518229 49425580
 [9] 49261703 48876598

Smallest eigenvalues:
 [1]   0.36935093   0.31771957   0.23440516   0.19006310   0.13045937
 [6]   0.11594599  -0.01740653  -0.15036296  -0.23063087 -16.71050452

Largest  eigenvalues:
 [1] 62255940 57259544 55156386 53809178 52156098 50474094 50064938 49760301
 [9] 49558586 49118973

Smallest eigenvalues:
 [1]  0.4592252  0.3960161  0.3907904  0.2754517  0.2725689  0.2012916
 [7]  0.1589252 -0.8958183 -3.1459340 -6.3225859

Largest  eigenvalues:
 [1] 60969701 57858837 54547430 53445002 53055612 51647798 50136085 49634044
 [9] 49617119 49065534

Smallest eigenvalues:
 [1]   0.44399706   0.37413541   0.32789273   0.28192023   0.13027950
 [6]   0.02438023  -0.14169085  -1.00391922  -2.25966768 -21.68333434

Largest  eigenvalues:
 [1] 59760738 56290745 53424249 51747287 51581109 50003698 48890451 48383647
 [9] 48073702 47869110

Smallest eigenvalues:
 [1]  0.46364936  0.43245097  0.42137884  0.36380742  0.32807721  0.27976022
 [7]  0.17171699  0.02672438 -0.14106341 -0.29644418

Largest  eigenvalues:
 [1] 60302527 56887940 53706597 52505492 52006556 50110546 49135126 48950790
 [9] 48738630 48425788

Smallest eigenvalues:
 [1]  0.47885996  0.40594506  0.37135664  0.35409861  0.28420595  0.21555298
 [7]  0.15433303  0.01568441 -0.07605173 -0.23954093

Largest  eigenvalues:
 [1] 61589138 57129127 54621903 53042185 52109356 50606057 49530142 49392942
 [9] 49301839 48645402

Smallest eigenvalues:
 [1]  0.45289183  0.33440655  0.29009562  0.24337142  0.21230066  0.12913549
 [7]  0.12111591  0.08851302 -0.12093250 -0.33073563

Largest  eigenvalues:
 [1] 63158916 56725744 54661894 53996640 51466756 50485073 50034376 49040198
 [9] 48521533 48311398

Smallest eigenvalues:
 [1]  0.49212726  0.48062993  0.40814546  0.36575238  0.35853317  0.19818619
 [7]  0.08774666  0.05650257  0.04859625 -0.70186176

Largest  eigenvalues:
 [1] 58983405 56300006 53965883 52038112 51626391 50595374 49361194 48711540
 [9] 48007252 47836242

Smallest eigenvalues:
 [1]  0.47667699  0.41938755  0.40378262  0.38983456  0.37903303  0.34624521
 [7]  0.22082671  0.11190574  0.07797660 -0.01977828

Largest  eigenvalues:
 [1] 61550357 56989421 54450523 53467352 51847246 50437230 49796454 49066163
 [9] 48979601 48167486

Smallest eigenvalues:
 [1]  0.4885390  0.4846938  0.4571574  0.4312058  0.4024464  0.2792770
 [7]  0.2688315  0.1947389  0.1497939 -3.4510884

Largest  eigenvalues:
 [1] 62205630 57056923 54607655 53999425 51758137 50314188 50062747 49331340
 [9] 48677501 48485298

Smallest eigenvalues:
 [1]  0.36462231  0.35327929  0.28350234  0.24705952  0.19057182  0.18695790
 [7]  0.06751266 -0.02855174 -0.78793673 -0.92900799

Largest  eigenvalues:
 [1] 60144317 57284923 54437308 52542849 52220423 50981973 49483403 48930381
 [9] 48786875 48005571

Smallest eigenvalues:
 [1]  0.509699566  0.499210893  0.493274718  0.313215092  0.308651687
 [6]  0.269909674  0.219491072  0.121951435 -0.001762749 -0.557237561

Largest  eigenvalues:
 [1] 60443609 56612325 53755304 52999593 51916863 50170434 49485113 49094541
 [9] 49061023 48208853

Smallest eigenvalues:
 [1]   0.35147446   0.29824333   0.28052950   0.22664488   0.14067093
 [6]   0.11483106   0.09997084  -1.41880538 -10.02786331 -16.44646890

Largest  eigenvalues:
 [1] 62191545 57044858 54548043 53477790 52437264 51048699 49823587 49739679
 [9] 49223746 48561789

Smallest eigenvalues:
 [1]  0.3279844  0.2991115  0.2698473  0.2378653  0.2251274  0.1667304
 [7]  0.1622551  0.1189911 -1.1584352 -2.4698089

Largest  eigenvalues:
 [1] 62239701 57127395 54138015 54040755 51911031 50406159 50256535 50164845
 [9] 49312946 49075471

Smallest eigenvalues:
 [1]  0.3659295  0.3421568  0.2951490  0.2925708  0.2535854  0.1406956
 [7] -0.3748997 -2.6932590 -4.3399124 -5.7460369

Largest  eigenvalues:
 [1] 60277942 57082654 54376451 52959072 52366349 50936439 49401047 49381065
 [9] 49216547 48463521

Smallest eigenvalues:
 [1]   0.399893373   0.353066423   0.338472467   0.258965240   0.167474525
 [6]   0.147212355   0.120959737   0.002822353  -0.869214549 -32.777625035

Largest  eigenvalues:
 [1] 59605894 57585507 54733801 53154730 52434702 51539808 50281980 49465738
 [9] 48702462 48612311

Smallest eigenvalues:
 [1]  0.54906439  0.53156309  0.33387275  0.32732769  0.23542289  0.13170213
 [7]  0.07899525  0.06431167 -2.94163934 -6.91226047

Largest  eigenvalues:
 [1] 61877072 56688735 53743941 53629148 51822700 50132489 49847353 49105202
 [9] 49043280 48112413

Smallest eigenvalues:
 [1]  0.4208114  0.3616818  0.3394315  0.3288885  0.2170461  0.1611744
 [7]  0.1574711  0.1501619 -0.2156835 -2.1166502

Largest  eigenvalues:
 [1] 60763529 57079062 54329312 52774700 52107272 50608086 49266020 49123501
 [9] 48845401 48446712

Smallest eigenvalues:
 [1]  0.48840637  0.48073097  0.35830665  0.31868349  0.29251419  0.25716255
 [7]  0.23017513 -0.01698269 -1.13667987 -3.97184048

Largest  eigenvalues:
 [1] 61703796 56739081 54272210 53413440 51847579 50622004 49681663 49505028
 [9] 48878280 48626037

Smallest eigenvalues:
 [1]   0.5400668   0.4987775   0.4686579   0.4039596   0.3551848   0.3360950
 [7]   0.3229468   0.3211843   0.3027462 -11.0153712

Largest  eigenvalues:
 [1] 59863314 56809338 54115721 52542099 52051026 50359947 49079458 48870127
 [9] 48757291 47912532

Smallest eigenvalues:
 [1]  0.37521739  0.30393826  0.30054082  0.26336103  0.24939871  0.24933361
 [7] -0.02240462 -0.42562209 -0.42902856 -6.82831809

Largest  eigenvalues:
 [1] 59532698 56919266 53701565 52410448 51576889 50148486 49222111 49086122
 [9] 48609733 48190065

Smallest eigenvalues:
 [1]  0.45414194  0.45199362  0.31376597  0.31229278  0.28865897  0.25861197
 [7]  0.18071507  0.09284467 -0.55858617 -0.73468635

Largest  eigenvalues:
 [1] 60452815 57563361 54470302 52959108 52226397 50811989 49710658 49695853
 [9] 49285855 48833670

Smallest eigenvalues:
 [1]  0.56146567  0.55036863  0.40428437  0.37013852  0.35820852  0.33638605
 [7]  0.30441905  0.03823034 -0.26899933 -0.33000762

Largest  eigenvalues:
 [1] 60326108 56806088 54196788 52571399 52127741 50668999 49281899 49218269
 [9] 48894051 48237014

Smallest eigenvalues:
 [1]  0.57941655  0.48703107  0.46775732  0.39251795  0.38746004  0.31962709
 [7]  0.30162716  0.11235960  0.08714428 -0.20076717

Largest  eigenvalues:
 [1] 61811355 57514874 54415628 53278997 52748178 51148507 49678991 49587016
 [9] 49338970 48431143

Smallest eigenvalues:
 [1]  0.32608451  0.30830041  0.26864895  0.19430569  0.11891875  0.09719704
 [7] -0.96127199 -1.79953920 -4.32634773 -5.05157534

Largest  eigenvalues:
 [1] 59884673 56301374 53975555 52421083 51478565 50508127 49355445 49159692
 [9] 48592923 48428867

Smallest eigenvalues:
 [1]  0.48844241  0.43597832  0.38618662  0.32674637  0.26653503  0.22191069
 [7]  0.17814152  0.11152074  0.02005887 -2.94665620

Largest  eigenvalues:
 [1] 60804714 57540239 54805088 53188095 52875449 51321678 49722599 49703147
 [9] 49448897 48511838

Smallest eigenvalues:
 [1]  0.4386887  0.4053393  0.3588944  0.2880324  0.2868159  0.2693010
 [7]  0.1667450  0.1383977 -0.5005862 -8.0270663

Largest  eigenvalues:
 [1] 59818272 56336863 53878643 51973226 51846216 50318762 49173017 48578878
 [9] 48192085 47906586

Smallest eigenvalues:
 [1]  0.40926731  0.30920097  0.30316277  0.27090417  0.25586102  0.20864753
 [7]  0.08453194  0.06568759 -0.54045309 -2.78669978

Largest  eigenvalues:
 [1] 59565900 55900474 53740271 52011794 51576491 50190542 48912567 48740052
 [9] 48311396 47688261

Smallest eigenvalues:
 [1]  0.59845895  0.52519853  0.44738907  0.37773856  0.32485333  0.31060168
 [7]  0.27368305  0.10865708  0.04605266 -0.35481314

Largest  eigenvalues:
 [1] 62157653 57470764 54671850 53968258 52533768 50702156 50253415 49769042
 [9] 49270694 48643134

Smallest eigenvalues:
 [1]  0.48769512  0.48183869  0.45220765  0.30329599  0.24960013  0.24710339
 [7]  0.20352193 -0.07782453 -0.20082527 -0.95011384

Largest  eigenvalues:
 [1] 61152685 57130845 54563595 53185029 52457838 50730424 49786354 49528412
 [9] 49421951 48750696

Smallest eigenvalues:
 [1]  0.45516370  0.39900609  0.32624053  0.31239373  0.28330105  0.27626319
 [7]  0.17141732  0.15069993 -0.07127875 -0.39237906

Largest  eigenvalues:
 [1] 60005810 57580883 54322838 53009894 52752272 51281597 50485985 49673654
 [9] 49113713 48890834

Smallest eigenvalues:
 [1]  -0.3192497  -0.3641236  -0.4968987  -0.8589310  -1.0168099  -1.6923999
 [7]  -1.9993637  -4.5486783  -5.7714185 -10.0224569

Largest  eigenvalues:
 [1] 62495286 57852974 54195462 53751984 53187535 51301262 50355306 50029893
 [9] 49254273 49238548

Smallest eigenvalues:
 [1]  0.4256595  0.4249179  0.3292673  0.3150990  0.2659408  0.2630464
 [7]  0.2552083  0.2297464 -0.1943231 -0.2452156

Largest  eigenvalues:
 [1] 60293924 57268540 54682456 53154643 52840129 51220434 50228679 49418340
 [9] 49384070 48803976

Smallest eigenvalues:
 [1]  0.22011203  0.18798333  0.15779337  0.15514424  0.15281943  0.05838464
 [7]  0.01548702 -0.04863282 -0.96672203 -5.86800189

Largest  eigenvalues:
 [1] 60516965 56887730 54064219 52410118 52038234 50935653 49745473 49457403
 [9] 48850775 48510924

Smallest eigenvalues:
 [1]  0.4076317  0.3723512  0.3203764  0.2399224  0.2284312  0.2201157
 [7]  0.2116526  0.1723039 -0.0704165 -0.1743759

Largest  eigenvalues:
 [1] 61538541 56888785 54443621 53587385 51549521 50457291 49865581 48995861
 [9] 48747354 48169791

Smallest eigenvalues:
 [1]  0.41360861  0.36553079  0.36282850  0.35830358  0.29282790  0.28285776
 [7]  0.27078392  0.12435801 -0.01842499 -0.07970028

Largest  eigenvalues:
 [1] 59026314 56788655 54055834 52284969 51658931 50932441 49670126 48725607
 [9] 48105610 47883918

Smallest eigenvalues:
 [1]   0.223536041   0.209044986   0.157704090   0.019773038  -0.006674767
 [6]  -0.145668639  -0.420577499  -1.263644141 -20.112173550 -32.659189916

Largest  eigenvalues:
 [1] 59074398 56271541 53475535 52347983 51336692 50378005 48972234 48493258
 [9] 47940532 47489942

Smallest eigenvalues:
 [1]  0.52754077  0.50219463  0.46807168  0.43741845  0.33066532  0.25540185
 [7]  0.10614152  0.09639581 -0.06711066 -3.54062598

Largest  eigenvalues:
 [1] 60547244 56560485 53770132 52656924 51396958 49726432 48920049 48675448
 [9] 48281023 47857967

Smallest eigenvalues:
 [1]  0.47735944  0.41078339  0.37843947  0.35803626  0.29761180  0.20522432
 [7]  0.13184251  0.12391783  0.09118706 -0.13078051

Largest  eigenvalues:
 [1] 62425372 57401852 54395876 53685400 52213850 50694101 49918282 49518451
 [9] 49457340 48832971

Smallest eigenvalues:
 [1]  0.38983414  0.35792073  0.34871948  0.19969289  0.19651135  0.17916727
 [7]  0.11795739 -0.07157888 -0.89234300 -2.03223132

Largest  eigenvalues:
 [1] 61260120 57133965 54435384 53682793 52511969 51121295 49899671 49829460
 [9] 49753065 48811847

Smallest eigenvalues:
 [1]  0.39260729  0.34849456  0.30559180  0.16623647  0.14326479  0.03781588
 [7] -0.15828144 -0.30750267 -0.71101095 -2.82616200

Largest  eigenvalues:
 [1] 60832080 56750314 53956501 53698570 52137649 50438047 49996888 49675003
 [9] 49527288 48546269

Smallest eigenvalues:
 [1]  0.33423317  0.26690670  0.22564015  0.20650699  0.20601109  0.17192209
 [7]  0.16859454  0.02264137 -0.71646835 -9.78735965

Largest  eigenvalues:
 [1] 60236409 57035158 54464520 52758290 52526787 51091224 49947556 49011971
 [9] 48739854 48299666

Smallest eigenvalues:
 [1]  0.50608003  0.47083322  0.42990666  0.38215378  0.31678071  0.29517903
 [7]  0.28292218  0.21902721  0.12034255 -0.09583888

Largest  eigenvalues:
 [1] 59348467 56260959 53913254 52204857 51830694 50208551 48734010 48721058
 [9] 48479070 47829128

Smallest eigenvalues:
 [1]  0.4824399  0.4334597  0.4152391  0.4010560  0.3940131  0.2397180
 [7]  0.2307609  0.1763561 -0.1117882 -0.4902346

Largest  eigenvalues:
 [1] 61019381 56854456 54156747 53220262 51798630 50159320 49405626 49283799
 [9] 49085575 48501027

Smallest eigenvalues:
 [1]  0.5541878  0.5088885  0.4538716  0.3557807  0.3277846  0.2744693
 [7]  0.2498319  0.2354386  0.1793992 -0.1429816

Largest  eigenvalues:
 [1] 60761809 56630163 54098377 52687375 51945304 50456321 49078680 48754690
 [9] 48694956 47773306

Smallest eigenvalues:
 [1]   0.38384570   0.33748294   0.33582867   0.22210700   0.16861759
 [6]  -0.05969512  -0.22860554  -0.30205247 -11.69326564 -37.12660551

Largest  eigenvalues:
 [1] 60331005 56943597 53991377 52260707 52241744 50657442 49637865 49055659
 [9] 48668251 48500366

Smallest eigenvalues:
 [1]  0.4771165  0.3352665  0.3167202  0.3091691  0.2261011  0.2152673
 [7]  0.2035332 -0.4584838 -1.0208242 -1.2885227

Largest  eigenvalues:
 [1] 61566724 56811436 54128848 53413875 51948826 50240380 50160702 49713132
 [9] 49072941 48970454

Smallest eigenvalues:
 [1]  0.4773682  0.4564842  0.4076168  0.3897601  0.3219099  0.2810229
 [7]  0.2171431  0.1746532  0.0824828 -0.6441086

Largest  eigenvalues:
 [1] 60113984 57484918 54604711 52693266 52228135 51081808 49953712 49280052
 [9] 48742620 48522219

Smallest eigenvalues:
 [1]   0.41147860   0.39156071   0.33777490   0.30948373   0.23749989
 [6]   0.23474789   0.21187758   0.19680293  -0.09878452 -14.40866374

Largest  eigenvalues:
 [1] 60192228 56138128 53851640 52381968 51438382 49828385 48786468 48689249
 [9] 48290936 47640258

Smallest eigenvalues:
 [1]  0.54781296  0.49634563  0.43891840  0.42307954  0.40809411  0.34451431
 [7]  0.30747788  0.28867788  0.01535167 -0.27393333

Largest  eigenvalues:
 [1] 60501619 57163123 54007422 53096330 52156689 50391565 49392966 49273626
 [9] 48934477 48235407

Smallest eigenvalues:
 [1]   0.5397361   0.5056801   0.4704349   0.4340496   0.3608806   0.3172314
 [7]   0.2590753   0.2303959   0.1301523 -11.8721330

Largest  eigenvalues:
 [1] 59441764 56635373 53636954 52070935 52010209 50364590 48840737 48509207
 [9] 48322556 47643090

Smallest eigenvalues:
 [1]  0.39158197  0.37335006  0.33914636  0.23048811  0.22776263  0.15186533
 [7]  0.08310912 -0.07700362 -0.16661063 -4.96153420

Largest  eigenvalues:
 [1] 61476769 56831381 54287026 53029567 52311815 50572861 50151925 49365179
 [9] 49117231 49017698

Smallest eigenvalues:
 [1]   0.38036553   0.37152004   0.35666276   0.33803615   0.20750919
 [6]  -0.07292445  -0.24837107  -0.69346397  -5.95487597 -22.75342217

Largest  eigenvalues:
 [1] 61151055 56664328 53924411 53156101 51883729 50335920 49348319 49315922
 [9] 49283773 48483517

Smallest eigenvalues:
 [1]   0.07577418  -0.21466705  -0.80276743  -1.04089999  -1.28523696
 [6]  -4.19222702  -6.14341317 -35.38397038 -44.10755822 -50.37978452

Largest  eigenvalues:
 [1] 62053488 56577695 53863048 53671280 51631677 50302780 49788265 48843989
 [9] 48535956 47824579

Smallest eigenvalues:
 [1]   0.48197926   0.45779312   0.42735592   0.39283497   0.32399117
 [6]   0.14864271   0.09961016   0.09402510  -2.56466915 -17.16193423

Largest  eigenvalues:
 [1] 59189670 57440199 53854906 52863953 52168213 51110600 49502680 49258602
 [9] 48442500 48312142

Smallest eigenvalues:
 [1]  0.38710375  0.37450667  0.34751638  0.15844434  0.14583332  0.13750541
 [7]  0.13374282  0.09455328  0.08635825 -6.86735816

Largest  eigenvalues:
 [1] 59418875 56763049 54045013 53051160 51776665 51172946 49471493 49386918
 [9] 48396710 48116334

Smallest eigenvalues:
 [1]  0.52220613  0.49976495  0.39012587  0.37743679  0.24325199  0.15265113
 [7]  0.01739840 -0.02228364 -0.07452527 -0.37205984

Largest  eigenvalues:
 [1] 59345634 55983428 52863386 51756343 51336084 49499447 48280924 48181841
 [9] 47978973 47332216

Smallest eigenvalues:
 [1]  0.3929610  0.3363814  0.2984957  0.2780176  0.1736340  0.1501597
 [7]  0.1298350  0.1242632 -0.3122030 -1.1081691

Largest  eigenvalues:
 [1] 62020636 56153875 54079564 53091072 51687563 50180569 49487543 48959604
 [9] 48802904 48210560

Smallest eigenvalues:
 [1]  0.5587650  0.5264955  0.4698078  0.4420742  0.3405764  0.3388369
 [7]  0.2949213  0.2914038  0.2736783 -1.3461873

Largest  eigenvalues:
 [1] 62290247 56902855 54371533 54094611 52052228 50592095 50295511 49466567
 [9] 49361659 48542137

Smallest eigenvalues:
 [1]  0.4752313  0.4436238  0.4340575  0.4214729  0.3229614  0.2888121
 [7]  0.1898384 -0.1613281 -0.4425740 -0.9114261

Largest  eigenvalues:
 [1] 62206266 57442697 55069937 53629692 52575521 50894514 50509986 50033434
 [9] 49741461 49377361

Smallest eigenvalues:
 [1]  0.3815545  0.3279717  0.2834949  0.2297587  0.1894288  0.1820309
 [7]  0.1486541  0.1016408 -0.9774141 -2.3506032

Largest  eigenvalues:
 [1] 62931338 56282551 53738838 53648638 51576647 50149474 49914005 49149828
 [9] 48883186 48390438

Smallest eigenvalues:
 [1]  0.31348797  0.30360753  0.18797860  0.17671321  0.05684698 -0.23179085
 [7] -0.38546890 -0.56174680 -1.32425900 -3.37321892

Largest  eigenvalues:
 [1] 61646927 56729868 53689765 53252176 51317982 49854692 49437141 48861746
 [9] 48770798 48134419

Smallest eigenvalues:
 [1]  0.4841052  0.4193218  0.3923431  0.3057651  0.2709355  0.2601504
 [7]  0.2349510  0.2039716 -0.1188956 -6.7275196

Largest  eigenvalues:
 [1] 61317034 56707393 54090274 53352835 51971258 50320290 49576067 48955930
 [9] 48772378 48148988

Smallest eigenvalues:
 [1]  0.54228172  0.39314691  0.38089776  0.32935447  0.27219198  0.24777976
 [7]  0.18488296  0.09721208 -0.20356037 -1.86484850

Largest  eigenvalues:
 [1] 61527409 56407189 54484164 53269211 51475941 50072593 49659020 48810976
 [9] 48689091 47931595

Smallest eigenvalues:
 [1]  0.3819995  0.3601517  0.3065941  0.2670016  0.2356865  0.1774529
 [7]  0.1384545  0.1029310 -0.0569955 -3.0960319

Largest  eigenvalues:
 [1] 62096124 57371873 55068231 53084927 52289762 51140254 49647876 49553263
 [9] 49429086 48483318

Smallest eigenvalues:
 [1]   0.3035512   0.2846392   0.2784677   0.2495718   0.2280931   0.1592669
 [7]   0.1108972  -1.6677846 -26.0709358 -29.7145504

Largest  eigenvalues:
 [1] 61941290 56831751 53904231 53442662 52064254 50558867 49667690 49376225
 [9] 49355993 48554151

Smallest eigenvalues:
 [1]  0.26817372  0.21613537  0.16008748  0.15473738  0.15468351  0.12539758
 [7] -0.01979232 -0.17147172 -2.24627954 -6.42266699

Largest  eigenvalues:
 [1] 61602922 56295380 53325376 53120608 51596460 50170049 49273322 49210284
 [9] 48898335 48355808

Smallest eigenvalues:
 [1]   0.4113670   0.3558879   0.3353538   0.3324130   0.3131391   0.2607270
 [7]   0.2573398   0.1865885 -21.8868949 -30.5379340

Largest  eigenvalues:
 [1] 61600007 57223793 54583426 53559112 52451316 50977889 49834643 49476184
 [9] 49241755 48474938

Smallest eigenvalues:
 [1]   0.3058565   0.2856233   0.1442651   0.1324406  -0.2394078  -0.5051559
 [7]  -0.8675156  -2.3548078  -9.0872581 -12.9552366

Largest  eigenvalues:
 [1] 61990282 57226962 54442876 53388940 52517162 51015780 49624707 49574833
 [9] 49457448 48556360

Smallest eigenvalues:
 [1]  0.4422177  0.4025370  0.2687712  0.2523224  0.2242800  0.1216324
 [7] -0.4747098 -0.6980977 -0.7821793 -1.1210840

Largest  eigenvalues:
 [1] 58968854 56764323 53994311 52459130 51871717 50802980 49708885 49053154
 [9] 48346188 48207035

Smallest eigenvalues:
 [1]   0.3040017   0.3004577   0.2935229   0.2375510   0.1253672   0.1207880
 [7]  -0.1988924  -0.6151019 -10.0334810 -11.4427705

Largest  eigenvalues:
 [1] 61552360 56949953 54222085 53171265 52229733 50622436 49699683 49481798
 [9] 48758118 48318276

Smallest eigenvalues:
 [1]  0.54632893  0.43498110  0.42193335  0.40157459  0.29895170  0.28580287
 [7]  0.24782916  0.13022041  0.07982283 -0.58466648

Largest  eigenvalues:
 [1] 61852433 57602766 54342438 53857976 52655873 50926724 50033431 49942961
 [9] 49437166 48849458

Smallest eigenvalues:
 [1]  0.37030557  0.36345061  0.34044548  0.29822409  0.29137453  0.19394862
 [7]  0.11360659  0.10202595  0.03597045 -0.49789658

Largest  eigenvalues:
 [1] 61781339 57617699 54820106 53789424 52985643 51455199 50235519 49973526
 [9] 49738732 48983300

Smallest eigenvalues:
 [1]  0.53636312  0.46215688  0.42610568  0.40954671  0.33387113  0.31294576
 [7]  0.28635439  0.23393347  0.06121316 -0.06926746

Largest  eigenvalues:
 [1] 61139434 57852125 55508894 52916197 52806366 51543942 50255621 49794031
 [9] 49443629 49209031

Smallest eigenvalues:
 [1]  0.48783834  0.42537067  0.41551393  0.40304681  0.33162491  0.20686126
 [7]  0.16086673  0.09628232 -0.23160070 -0.74427166

Largest  eigenvalues:
 [1] 61438458 57353553 54735099 52997283 52529005 51187004 49713390 49657580
 [9] 49357598 48784493

Smallest eigenvalues:
 [1]   0.28306653   0.27932696   0.23600699   0.21272961  -0.02656672
 [6]  -0.19260834  -1.50265164  -1.60179973  -3.65170328 -14.35110598

Largest  eigenvalues:
 [1] 61491928 56396876 53638232 52781549 51746549 50154303 49195509 48853716
 [9] 48205090 47422630

Smallest eigenvalues:
 [1]   0.38834741   0.31839170   0.26605727   0.20116019   0.10626607
 [6]   0.07590181  -0.03330955  -0.82290678  -1.73999865 -15.06702094

Largest  eigenvalues:
 [1] 61682431 57647525 54596848 54162091 52229512 50205145 50160327 49317020
 [9] 49231521 48441467

Smallest eigenvalues:
 [1]   0.172457000   0.148723048   0.128129017   0.103360963   0.004761457
 [6]  -0.066728737  -2.601409463  -3.467904983  -8.325014639 -28.689920892

Largest  eigenvalues:
 [1] 58798269 56840296 54493930 52253399 51461909 50981691 49229165 49167213
 [9] 48343378 47922761

Smallest eigenvalues:
 [1]  0.47385309  0.43401749  0.42805676  0.24616559  0.22671502  0.18030622
 [7] -0.07844261 -0.51682237 -1.67005688 -3.03589807

Largest  eigenvalues:
 [1] 61932204 57680368 54663648 53759726 52839868 51205075 50411408 49964241
 [9] 49644135 49194110

Smallest eigenvalues:
 [1]   0.30259554   0.28994283   0.26862911   0.18359397   0.13819175
 [6]   0.12950282   0.04996976  -0.18276856  -1.25025447 -14.12026107

Largest  eigenvalues:
 [1] 59864097 56567945 53714984 52478983 52130039 50521713 49521373 48982791
 [9] 48685565 48261501

Smallest eigenvalues:
 [1]  0.57065696  0.53574787  0.49979061  0.42744591  0.40950185  0.38802542
 [7]  0.34914624  0.30842700  0.26156400 -0.01251103

Largest  eigenvalues:
 [1] 60116328 57050509 54108077 53066707 52394654 50570264 49494918 49440518
 [9] 49142881 48327251

Smallest eigenvalues:
 [1]  0.2895363  0.2563151  0.1966756  0.1881640  0.1848180  0.1554454
 [7] -1.1603565 -1.2872661 -1.9470245 -5.5679466

Largest  eigenvalues:
 [1] 60551750 56336313 54197717 53265190 51573299 50286018 49418518 48920567
 [9] 48819324 48043436

Smallest eigenvalues:
 [1]  0.56508567  0.56207102  0.48860797  0.37273905  0.36083905  0.35521123
 [7]  0.30850582  0.29998902  0.24122011 -0.02714331

Largest  eigenvalues:
 [1] 60151865 56746937 53891798 52664443 51741823 50122637 48999536 48920248
 [9] 48710497 48143317

Smallest eigenvalues:
 [1]  0.44465788  0.43987401  0.42858930  0.39992520  0.38387856  0.32356597
 [7]  0.24267266  0.17422714 -0.06217521 -1.19356981

Largest  eigenvalues:
 [1] 60953730 56368411 53853615 53410136 51967798 50391442 49489517 49251777
 [9] 49189172 48271343

Smallest eigenvalues:
 [1]   0.44119654   0.39131675   0.38728820   0.35376936   0.27617680
 [6]   0.18339429   0.07624087  -0.20614322  -0.27756319 -11.43942765

Largest  eigenvalues:
 [1] 61875192 56747669 54502470 53314430 51820384 50387912 49672659 49299752
 [9] 49043326 48381023

Smallest eigenvalues:
 [1]  0.22339787  0.22134696  0.15646319  0.13019136  0.10010082  0.01947175
 [7] -0.34159411 -1.74831268 -6.41307044 -7.52728200

Largest  eigenvalues:
 [1] 60016969 56695393 53578928 52688013 51563646 50130459 49107948 48909911
 [9] 48900766 48312064

Smallest eigenvalues:
 [1]  0.4612909  0.4002415  0.3923534  0.3666081  0.3566948  0.2464878
 [7]  0.2409846  0.2011406 -0.0263149 -0.1909707

Largest  eigenvalues:
 [1] 60533083 56698441 54613439 53064588 51528422 50171593 49327114 49168701
 [9] 48842945 48456318

Smallest eigenvalues:
 [1]  0.31737785  0.29272011  0.28897271  0.28040345  0.20116880  0.18586698
 [7]  0.12955417  0.08284158 -0.54475810 -0.90491526

Largest  eigenvalues:
 [1] 59619831 56419246 54095015 52282466 52244351 50770008 49488236 48580249
 [9] 48521481 47876922

Smallest eigenvalues:
 [1]  0.3693455  0.3642734  0.3201752  0.3174283  0.2946600  0.2799460
 [7]  0.2787288  0.2637924  0.1909357 -0.1348770

Largest  eigenvalues:
 [1] 61558481 57205574 54628314 54008712 51847271 50563339 50178399 49596483
 [9] 48905541 48631371

Smallest eigenvalues:
 [1]  0.5271368524  0.4741773739  0.4333002800  0.3675921899  0.2671287581
 [6]  0.2649786561  0.1678971055  0.0119868750  0.0002818979 -0.0628815243

Largest  eigenvalues:
 [1] 59144020 56499688 53738906 52250791 52133302 50445487 49422779 49063038
 [9] 48453415 48144389

Smallest eigenvalues:
 [1]   0.36297860   0.34727825   0.24700489   0.24089456   0.09709237
 [6]  -0.10668919  -0.30814681  -0.41429732  -7.51970850 -20.31708983

Largest  eigenvalues:
 [1] 61630029 56174956 53830725 52732088 51540313 50319512 48958422 48835100
 [9] 48662306 48150370

Smallest eigenvalues:
 [1]  0.53869546  0.48056094  0.45035212  0.44573638  0.31247488  0.27269191
 [7]  0.22162558  0.12995192 -0.01726772 -0.04677941

Largest  eigenvalues:
 [1] 61937046 57439918 54585286 53715359 52289789 50602612 50131137 50058928
 [9] 49209737 49128508

Smallest eigenvalues:
 [1]  0.44547142  0.41387134  0.29987522  0.24375112  0.23204446  0.19388214
 [7]  0.19020763  0.09565894  0.03561604 -0.07021743

Largest  eigenvalues:
 [1] 61567136 57274383 54329186 53524660 52405985 50777084 49793879 49624414
 [9] 49400897 48606429

Smallest eigenvalues:
 [1]   0.38548747   0.30487165   0.28867506   0.27946251   0.24096028
 [6]   0.02429095  -0.23250330  -2.24828979  -9.51773309 -14.71480035

Largest  eigenvalues:
 [1] 61080790 57050739 54268924 52847648 52276760 50850797 49355132 49327305
 [9] 49179867 48710827

Smallest eigenvalues:
 [1]   0.26647409   0.19324602   0.18885614   0.14735052   0.03939683
 [6]  -0.02467086  -1.03561656  -1.19542613  -2.32074277 -73.40258345

Largest  eigenvalues:
 [1] 61141104 57256965 54246565 53324909 52870692 51303563 49823714 49783885
 [9] 49370239 48993906

Smallest eigenvalues:
 [1]  0.46300648  0.45557774  0.42832519  0.34085195  0.31232123  0.27599119
 [7]  0.26405735  0.23342092  0.20452771 -0.01802679

Largest  eigenvalues:
 [1] 59546564 57245973 54147896 52398575 52390603 50976094 49823820 48912399
 [9] 48610248 48205363

Smallest eigenvalues:
 [1]  0.50062859  0.48837669  0.39642986  0.35683514  0.34523069  0.27775410
 [7]  0.21936403  0.08395141 -0.02366618 -0.04937289

Largest  eigenvalues:
 [1] 62332001 56909209 54085368 53355921 52403245 50540532 49817606 49731396
 [9] 48926245 48741208

Smallest eigenvalues:
 [1]   0.37681955   0.36493948   0.26909130   0.18361298   0.13927241
 [6]   0.10381980   0.05969520  -0.03304384  -1.00761888 -17.10390106

Largest  eigenvalues:
 [1] 60649874 56301226 52904908 52480053 51649141 49746915 48792840 48667711
 [9] 48507041 47767190

Smallest eigenvalues:
 [1]   0.4124631   0.4098655   0.3233414   0.2964143   0.2234228   0.1953904
 [7]   0.1213895   0.0520657  -0.5757630 -17.4404497

Largest  eigenvalues:
 [1] 60885862 57374007 53953401 52936241 52884529 51338008 50044490 49412016
 [9] 49101023 48641929

Smallest eigenvalues:
 [1]   0.43164167   0.22046006   0.09325817   0.03929236  -0.05626717
 [6]  -0.99473745  -1.88958691  -5.80751659 -14.64264489 -22.88452554

Largest  eigenvalues:
 [1] 60441921 56118704 53510023 52497539 51523290 50048199 49248453 48571185
 [9] 48486482 47881590

Smallest eigenvalues:
 [1]  0.5242968  0.4528744  0.3746077  0.3455156  0.3402478  0.3007240
 [7]  0.2589339  0.2261131  0.1472645 -0.6581062

Largest  eigenvalues:
 [1] 61382895 56709406 53667663 53050308 51898674 50250288 49396877 49294944
 [9] 48760144 48456545

Smallest eigenvalues:
 [1]  0.4201678  0.4028160  0.3920768  0.3638857  0.3117124  0.2972377
 [7]  0.2738566  0.0977866 -0.2117887 -2.5852988

Largest  eigenvalues:
 [1] 60150716 56576310 54328097 52193411 51745869 50090661 48831211 48710835
 [9] 48467786 48013986

Smallest eigenvalues:
 [1]  0.4372878  0.3848718  0.3637617  0.3120119  0.2936867  0.2790229
 [7]  0.1821967  0.1196975 -0.3971291 -0.5749063

Largest  eigenvalues:
 [1] 61397146 57127042 54283921 53456001 52271714 50789616 49746434 49214191
 [9] 49155783 48212280

Smallest eigenvalues:
 [1]   0.38396514   0.35275432   0.34273141   0.29702799   0.28621115
 [6]   0.18679149   0.11656280   0.11566745  -0.07280567 -23.86415052

Largest  eigenvalues:
 [1] 58236601 56180004 53491873 51842028 50959753 49952364 48589909 48014547
 [9] 47430043 47253997

Smallest eigenvalues:
 [1]  0.3499243  0.3401431  0.3043064  0.2784503  0.2751097  0.2715228
 [7]  0.2291704  0.1625926  0.1335382 -0.1403669

Largest  eigenvalues:
 [1] 59072660 56313172 53644513 52078899 51743484 50285819 48857162 48538227
 [9] 48300442 47763889

Smallest eigenvalues:
 [1]   0.360613783   0.323130503   0.318246571   0.299944839   0.288143593
 [6]   0.235345048   0.006906573  -0.812772341  -1.427933394 -20.591254506

Largest  eigenvalues:
 [1] 61317990 57215128 54439692 53562591 52290323 50516522 49752892 49514081
 [9] 49366966 48338894

Smallest eigenvalues:
 [1]   0.23082779   0.22115176   0.14329393   0.08710430   0.05316245
 [6]  -0.63465479  -1.55515696  -3.15623118  -3.70854008 -83.91631335

Largest  eigenvalues:
 [1] 61586236 56815213 53571923 53454194 52034857 50330133 49597756 49381184
 [9] 49161485 48316484

Smallest eigenvalues:
 [1]  0.56105578  0.50005169  0.43948868  0.38133509  0.37739006  0.29505879
 [7]  0.14999177  0.10860312  0.07121852 -0.55846771

Largest  eigenvalues:
 [1] 60341622 57037962 54266686 52774785 52179892 51153188 49570772 49262602
 [9] 48610246 48359665

Smallest eigenvalues:
 [1]  0.4885337  0.4756377  0.3834402  0.3171454  0.3114576  0.2950203
 [7]  0.2612420  0.2195895  0.1433516 -0.6745835

Largest  eigenvalues:
 [1] 61028552 56764938 54638327 53018301 52599658 51153114 49717386 49377774
 [9] 49264609 48669142

Smallest eigenvalues:
 [1]  0.297182294  0.279255894  0.251438357  0.246735560  0.146237809
 [6]  0.137491756  0.120208607  0.005428975 -0.288284578 -1.759612351

Largest  eigenvalues:
 [1] 57968528 56089613 53787178 52012557 51212653 50361814 49391920 48627944
 [9] 48317579 47559226

Smallest eigenvalues:
 [1]  0.39839590  0.39024635  0.30199555  0.29454206  0.26859548  0.24846861
 [7]  0.24023214  0.15597442 -0.09065493 -3.54881474

Largest  eigenvalues:
 [1] 61363975 56944719 54012880 53383415 52008125 50355178 49710541 49158760
 [9] 48803316 48149158

Smallest eigenvalues:
 [1]  0.39575540  0.38113141  0.34057457  0.31013803  0.22541344  0.20147078
 [7]  0.14257764  0.08941422  0.03110219 -1.29263491

Largest  eigenvalues:
 [1] 62314791 57060318 54599269 53887650 52306832 50997897 50223097 49317388
 [9] 49202467 48245040

Smallest eigenvalues:
 [1]  0.3493131  0.3337269  0.2892494  0.2790288  0.1456771  0.1367938
 [7]  0.1336202  0.1079044 -0.2040339 -4.9093716

Largest  eigenvalues:
 [1] 59957923 57766656 54341010 52943339 52698578 51312901 50488776 49544527
 [9] 49417220 48952436

Smallest eigenvalues:
 [1]  0.37031519  0.29918059  0.26861681  0.26708867  0.18239568  0.07326837
 [7] -0.03395980 -0.80969851 -1.19417260 -7.33038375

Largest  eigenvalues:
 [1] 60417828 57238649 54257278 52903385 52590871 51270691 50035910 49286354
 [9] 48921411 48791047

Smallest eigenvalues:
 [1]  0.5724432  0.5099677  0.3935385  0.3727481  0.3646484  0.3273439
 [7]  0.2934019  0.2258051  0.1920886 -0.8042753

Largest  eigenvalues:
 [1] 60676086 56639147 54265734 52603868 52099194 50644840 49422653 49252502
 [9] 48904174 48479882

Smallest eigenvalues:
 [1]  0.4394855  0.3930451  0.3731450  0.3277383  0.2728043  0.1536384
 [7] -0.2665673 -0.6577459 -1.4074642 -1.9658887

Largest  eigenvalues:
 [1] 61798382 57250550 54206667 53158306 52216831 50435516 50061143 49521000
 [9] 49004291 48748349

Smallest eigenvalues:
 [1]   0.20093558   0.15460809   0.13328035  -0.07004664  -7.47491582
 [6] -10.70352272 -20.09395665 -43.02253978 -44.97379173 -45.95386369

Largest  eigenvalues:
 [1] 61547035 57134313 54835580 53100195 52471936 50441494 50020841 49418394
 [9] 49317138 49138187

Smallest eigenvalues:
 [1]  0.4143698  0.3806197  0.3135725  0.2040917 -0.1067484 -0.1894938
 [7] -0.2142496 -0.8897743 -1.9223137 -4.1271353

Largest  eigenvalues:
 [1] 61173013 56668337 53684685 53180369 51499805 49930818 49308129 49105274
 [9] 48900996 48157744

Smallest eigenvalues:
 [1]   0.28545951   0.19944245   0.15408568   0.12990053   0.06990041
 [6]  -0.02217001  -0.05417481  -1.03266822  -1.23043281 -13.97373361

Largest  eigenvalues:
 [1] 58892516 57101321 54110963 52736352 51178775 50992355 49716348 48845087
 [9] 48163084 47997955

Smallest eigenvalues:
 [1]  0.51832438  0.51507136  0.45420674  0.34648149  0.31458839  0.29901368
 [7]  0.26688667  0.15831286  0.07129153 -1.24245670

Largest  eigenvalues:
 [1] 60204605 56780793 54477655 52298566 52007679 50563799 49377963 48977901
 [9] 48720247 48439724

Smallest eigenvalues:
 [1]  0.41322221  0.39338438  0.37107515  0.36334885  0.19780196  0.14254834
 [7]  0.07378896 -0.11313841 -0.74888843 -6.98703687

Largest  eigenvalues:
 [1] 60721206 56834018 54112195 52738184 51863020 50470663 49724841 48969018
 [9] 48892822 48858791

Smallest eigenvalues:
 [1]  0.54591136  0.50654662  0.48657837  0.46342706  0.43598210  0.38736118
 [7]  0.19360581  0.13999623 -0.05302026 -1.96955349

Largest  eigenvalues:
 [1] 61199503 56741589 54024763 53137348 51763829 50024161 49401172 49059275
 [9] 48825928 48223430

Smallest eigenvalues:
 [1]   0.3272388   0.3246140   0.3173594   0.3019645   0.2500908   0.1790376
 [7]   0.1590405  -0.2673127  -2.1435318 -79.2884765

Largest  eigenvalues:
 [1] 58794868 56647315 53235773 52022350 51882109 50143769 49312022 48572327
 [9] 48076312 47773235

Smallest eigenvalues:
 [1]  0.4532039  0.3173140  0.2911425  0.2896573  0.2710577  0.2588845
 [7]  0.2491383  0.2421482 -1.0094096 -4.5310353

Largest  eigenvalues:
 [1] 61708217 56946595 53801549 53666780 52176716 50425284 49913675 49864820
 [9] 49065139 48863600

Smallest eigenvalues:
 [1]  0.39679018  0.38660264  0.38023324  0.32847708  0.23307124  0.11450474
 [7] -0.05277803 -0.10585854 -1.01667002 -8.74651736

Largest  eigenvalues:
 [1] 60739205 56997130 54461853 52932866 51766857 50356992 49285656 49205664
 [9] 49073906 48568607

Smallest eigenvalues:
 [1]  0.3120734  0.2941493  0.2534024  0.2440380  0.2180089  0.2036373
 [7]  0.1805841  0.1540712 -2.2935465 -3.6227514

Largest  eigenvalues:
 [1] 60653776 56260279 53517988 52922639 51568009 50210136 49052244 49001388
 [9] 48329438 47684613

Smallest eigenvalues:
 [1]  0.31730278  0.25919321  0.19504488  0.18417382  0.13995289  0.13903878
 [7]  0.09889956  0.03181261 -1.33762613 -3.36781480

Largest  eigenvalues:
 [1] 60094802 57453702 54652613 52698534 52380950 50956872 50220778 49536135
 [9] 49221512 48996771

Smallest eigenvalues:
 [1]  0.41150342  0.33247941  0.22278490  0.21309265  0.12719062  0.09354510
 [7] -0.03535945 -0.09758639 -0.30314502 -0.78720884

Largest  eigenvalues:
 [1] 60042898 57127595 54229095 52659602 52172143 51132953 49754673 49318136
 [9] 48543119 48425180

Smallest eigenvalues:
 [1]  0.44338776  0.41362992  0.35318634  0.30466279  0.26667000  0.25482162
 [7]  0.22816601  0.14097607  0.10474068 -0.05674704

Largest  eigenvalues:
 [1] 61960536 57886505 54593802 53936775 52738638 50950323 50295944 50096029
 [9] 49212570 49194850

Smallest eigenvalues:
 [1]   0.39121354   0.37162867   0.33972715   0.32680376   0.32138827
 [6]   0.28735921   0.19829199   0.06800142  -0.73075199 -16.10605955

Largest  eigenvalues:
 [1] 59718387 56529420 53501898 52482975 51771887 50298326 49003071 48957125
 [9] 48648563 48204881

Smallest eigenvalues:
 [1]  0.3526066  0.3507056  0.3134071  0.2590029  0.1843413  0.1634195
 [7]  0.1312385 -0.1255664 -0.3285346 -0.8120371

Largest  eigenvalues:
 [1] 62748369 56956047 54994044 54007649 51660796 50314810 50278299 49508750
 [9] 48911643 48839504

Smallest eigenvalues:
 [1]  0.319983374  0.300000898  0.254501530  0.119615021  0.113519606
 [6]  0.059834421 -0.006232157 -0.017940569 -0.688933599 -3.888730173

Largest  eigenvalues:
 [1] 60378308 58045797 54940966 52835474 52374078 51468403 49757373 49591505
 [9] 48834942 48620984

Smallest eigenvalues:
 [1]  0.50245197  0.45552756  0.38713084  0.29643347  0.27147716  0.25563625
 [7]  0.21358564  0.20242045 -0.05923261 -1.52209947

Largest  eigenvalues:
 [1] 61961958 57624283 54501346 53592991 53031319 51561553 49924439 49891516
 [9] 49852105 49066525

Smallest eigenvalues:
 [1]  0.50945474  0.45949625  0.43348907  0.41162968  0.37600245  0.35225360
 [7]  0.31695458  0.22013719  0.05430134 -4.31971382

Largest  eigenvalues:
 [1] 60396581 56802729 54316866 52870955 52490264 50915854 49439475 49151497
 [9] 49089597 48257240

Smallest eigenvalues:
 [1]  0.5067116  0.4882665  0.4587631  0.3324501  0.2643893  0.2493352
 [7]  0.2370293  0.1847793  0.1490126 -0.3964830

Largest  eigenvalues:
 [1] 61651615 56834934 53535493 53414688 51811509 49877342 49643430 49076728
 [9] 48715673 48160009

Smallest eigenvalues:
 [1]  0.55523608  0.51193463  0.48189558  0.47297097  0.38096002  0.33766157
 [7]  0.26751359  0.18549163  0.08537344 -0.07110883

Largest  eigenvalues:
 [1] 60587990 56885078 53941420 52469831 52155481 50832458 49377738 49142591
 [9] 48598537 48375000

Smallest eigenvalues:
 [1]  0.352340229  0.318895494  0.310571759  0.286896633  0.278908360
 [6]  0.262222897  0.145422568 -0.008028557 -0.318559858 -2.348658348

Largest  eigenvalues:
 [1] 59423147 56443162 53866278 51603018 51499804 50117359 48857407 48570309
 [9] 48247994 48025113

Smallest eigenvalues:
 [1]  0.40138169  0.35776456  0.35306231  0.30936662  0.27418108  0.21536110
 [7]  0.21118826 -0.09033148 -0.50737412 -1.11713563

Largest  eigenvalues:
 [1] 63139919 57762741 55678891 54354070 52541074 51234928 50755089 50180148
 [9] 49860520 49284360

Smallest eigenvalues:
 [1]  0.4211715  0.4023504  0.3518663  0.3006542  0.2128347  0.1604205
 [7]  0.1553507 -0.3554280 -4.4385515 -4.9015903

Largest  eigenvalues:
 [1] 61463994 57169402 54130358 52936705 52116766 50384854 49843861 49356458
 [9] 48920157 48626112

Smallest eigenvalues:
 [1]  0.570667115  0.530390643  0.446296336  0.402871329  0.369543654
 [6]  0.270166149  0.246221198  0.217548477  0.031254285 -0.008525335

Largest  eigenvalues:
 [1] 60746020 56775452 53971209 52737085 51989532 50207362 49048428 49023984
 [9] 48830299 48031823

Smallest eigenvalues:
 [1]  0.48696248  0.46901752  0.37464827  0.36839085  0.32457018  0.31402224
 [7]  0.21421051  0.18324177  0.08788199 -0.01711724

Largest  eigenvalues:
 [1] 60826367 56567913 54073064 52451666 51991334 50397200 49265360 48812338
 [9] 48593141 47865304

Smallest eigenvalues:
 [1]   0.3446097   0.2342628   0.2137899   0.1726198   0.1709127   0.0599499
 [7]  -0.1088735  -0.2380491  -0.4730524 -43.7756924

Largest  eigenvalues:
 [1] 60765318 56377373 53856517 52982169 51681701 50026833 49269223 49221962
 [9] 48570182 47788285

Smallest eigenvalues:
 [1]  0.389996851  0.388665667  0.380638452  0.302766248  0.295507205
 [6]  0.192248361  0.169694273  0.099483633  0.078357169 -0.002984752

Largest  eigenvalues:
 [1] 60187204 57232853 54045583 52622569 52279310 50635337 49229791 49047894
 [9] 48953545 48166016

Smallest eigenvalues:
 [1]   0.2323943   0.1803474   0.1559938   0.1543501   0.1129005  -0.0170259
 [7]  -0.8926041  -2.0052744 -22.5802806 -27.2139183

Largest  eigenvalues:
 [1] 62018768 56713334 54300650 53420467 51692689 50181949 49926220 49682450
 [9] 49210217 49085559

Smallest eigenvalues:
 [1]   0.4191048   0.4059177   0.3613530   0.2784968   0.2550466   0.2523693
 [7]   0.2048876   0.1292614  -1.2633721 -10.1475183

Largest  eigenvalues:
 [1] 62104274 56741119 54348837 53894958 51531314 50184170 50164886 49063441
 [9] 49030355 48440976

Smallest eigenvalues:
 [1]  0.55093988  0.45502096  0.43261036  0.38253711  0.33331661  0.26418454
 [7]  0.26143995  0.18230047  0.07955738 -0.98473366

Largest  eigenvalues:
 [1] 62003087 57400460 54568826 54094394 52385757 50700515 50348928 49611419
 [9] 49381415 48527018

Smallest eigenvalues:
 [1]  0.4686639  0.4428894  0.4131769  0.4010316  0.3833951  0.3781866
 [7]  0.2669119  0.2629616  0.1993791 -1.2637632

Largest  eigenvalues:
 [1] 60746057 56994746 54035540 53244785 52154585 50677185 49646097 49405260
 [9] 48925752 48239667

Smallest eigenvalues:
 [1]  0.33870225  0.23295839  0.22717611  0.22266403  0.05789483  0.04414513
 [7] -0.19269129 -0.57604365 -3.73696129 -8.76516412

Largest  eigenvalues:
 [1] 62492146 56220773 53855788 53109211 51075263 49637714 49483061 48741247
 [9] 48334356 47926246

Smallest eigenvalues:
 [1]   0.14870438   0.08592403   0.07063419  -0.02909018  -0.45170093
 [6]  -1.10159584 -10.55233598 -12.70571969 -14.15854413 -22.67339065

Largest  eigenvalues:
 [1] 60367311 56277435 54103852 52672242 51954518 50541009 49007426 48890297
 [9] 48808356 47826437

Smallest eigenvalues:
 [1]   0.30899428   0.30178321   0.24706514   0.21582513   0.14186291
 [6]  -0.03332608  -0.08916350  -0.90197917 -10.79833658 -30.69525042

Largest  eigenvalues:
 [1] 60198454 56811515 53517310 52940683 52089814 50254431 49466473 49097650
 [9] 48811175 48274654

Smallest eigenvalues:
 [1]  0.4402253  0.3916358  0.3751367  0.3474146  0.3228600  0.2984106
 [7]  0.2783365  0.2410652  0.1970938 -1.2124872

Largest  eigenvalues:
 [1] 60979968 56859207 54166834 52659687 52358726 50957406 49745216 49100748
 [9] 48970575 48473078

Smallest eigenvalues:
 [1]  0.5022565  0.4686686  0.4478753  0.3324490  0.2986369  0.2545173
 [7]  0.2426628  0.1964309  0.1367384 -5.4439030

Largest  eigenvalues:
 [1] 61958040 57494988 54593364 53279515 52193737 50510558 49661317 49289540
 [9] 49212552 48514519

Smallest eigenvalues:
 [1]  0.5191223  0.4472410  0.4247659  0.4069959  0.3527973  0.3309592
 [7]  0.2826756  0.2612016 -0.1483051 -0.1896565

Largest  eigenvalues:
 [1] 59166487 57268163 54061885 52646363 52241324 50526829 49474294 49091182
 [9] 48720102 48088746

Smallest eigenvalues:
 [1]  0.44968389  0.43432879  0.40906025  0.39239648  0.33937191  0.33800952
 [7]  0.27115871  0.06571163  0.03748450 -2.54345639

Largest  eigenvalues:
 [1] 60372076 56832892 54150163 52357135 52244339 50886593 49387341 49030093
 [9] 48651890 48286813

Smallest eigenvalues:
 [1]  0.37939189  0.33035289  0.28030219  0.27701635  0.19823506  0.15960168
 [7]  0.06599043 -1.13891870 -5.24297476 -9.68681075

Largest  eigenvalues:
 [1] 60346221 57076310 53423067 52711666 52352463 50659526 49543529 49031844
 [9] 48912666 48442002

Smallest eigenvalues:
 [1]  0.47169350  0.45233755  0.43849730  0.38436059  0.30823527  0.17881341
 [7]  0.09078722  0.09067441 -0.10587495 -5.14037157

Largest  eigenvalues:
 [1] 61513831 57026664 54651941 53240050 51934637 50750195 49498216 49407813
 [9] 49178214 48564903

Smallest eigenvalues:
 [1]  0.4026326  0.3262625  0.2760441  0.2740694  0.2618078  0.2183853
 [7]  0.1862497 -0.1569601 -0.9577239 -1.1340502

Largest  eigenvalues:
 [1] 61484915 56725264 54686696 53149814 52161967 51039096 49511113 49413140
 [9] 49348716 48665306

Smallest eigenvalues:
 [1]  0.30603775  0.30372261  0.28550123  0.26858160  0.26080426  0.10958037
 [7]  0.09244892  0.08269669 -0.17257367 -1.58484947

Largest  eigenvalues:
 [1] 59027861 56939841 53791804 52641193 51989672 50659761 49077095 48700673
 [9] 48292973 47709077

Smallest eigenvalues:
 [1]   0.4157076   0.3363701   0.2576163   0.2502222   0.2389831   0.1891671
 [7]  -0.3655199  -3.1680631 -10.0106360 -25.8209726

Largest  eigenvalues:
 [1] 60814808 57680611 54055451 53388703 52897826 51222156 49867051 49624917
 [9] 48946368 48439592

Smallest eigenvalues:
 [1]  0.46179115  0.43091411  0.38895157  0.35488317  0.34359584  0.09974296
 [7] -0.03913103 -0.29992946 -1.80821907 -9.79633723

Largest  eigenvalues:
 [1] 61192193 56397696 54012562 52428399 51669393 50043891 48791408 48714580
 [9] 48669419 47975152

Smallest eigenvalues:
 [1]  0.53165372  0.40274175  0.37970943  0.27570791  0.27474707  0.25022044
 [7]  0.23796668 -0.09176933 -0.52908367 -5.49580617

Largest  eigenvalues:
 [1] 60660559 56662652 53948650 52425478 52412288 50902938 49480409 49052044
 [9] 48771877 48198535

Smallest eigenvalues:
 [1]  0.3290764  0.3056106  0.2771728  0.2441116  0.2112559  0.1934479
 [7]  0.1732795  0.1391931 -0.1784300 -0.7168688

Largest  eigenvalues:
 [1] 59811706 57156843 54205675 52937283 51932780 50742214 49136205 49115554
 [9] 48998019 48101083

Smallest eigenvalues:
 [1]  0.3535318  0.3010332  0.2495670  0.2407851  0.2318093  0.1746198
 [7]  0.1161130 -0.9635806 -1.7498247 -3.7730808

Largest  eigenvalues:
 [1] 62457967 56585112 54173203 53981067 51696984 50458942 50281188 48971679
 [9] 48898288 48292036

Smallest eigenvalues:
 [1]  0.389161840  0.294135147  0.276181395  0.249251539  0.248513695
 [6]  0.201425852 -0.007060416 -1.223195952 -1.796170225 -1.940858347

Largest  eigenvalues:
 [1] 61823959 56763772 54737222 53714683 51762128 50441648 49962827 49574370
 [9] 48972858 48837303

Smallest eigenvalues:
 [1]  0.5333120  0.4943729  0.3641004  0.3394227  0.2585095  0.2451496
 [7]  0.2381711  0.2263346 -1.0795920 -2.2828445

Largest  eigenvalues:
 [1] 60207307 56552626 54044672 52538586 52203970 50875552 49407573 49219719
 [9] 48741937 48290640

Smallest eigenvalues:
 [1]  0.54300585  0.52855008  0.46517011  0.38818401  0.29381276  0.18122202
 [7]  0.09600804  0.09125548 -0.73885152 -1.40737678

Largest  eigenvalues:
 [1] 59934450 56415927 53634732 52123061 51958120 50651059 49141220 48779745
 [9] 48276692 47720549

Smallest eigenvalues:
 [1]   0.4622443   0.3987063   0.3268634   0.2664115   0.2073778   0.1719860
 [7]   0.1390684  -0.3547308  -2.0553737 -14.2249814

Largest  eigenvalues:
 [1] 59999368 56657248 53956445 52452366 52382571 51055864 49932155 49231752
 [9] 48548217 48331561

Smallest eigenvalues:
 [1]  0.5670198  0.5387322  0.5113118  0.4674800  0.4201758  0.3639382
 [7]  0.3160560  0.2994868  0.2619558 -0.2471928

Largest  eigenvalues:
 [1] 59556190 56602918 54059429 52230358 52168173 50346138 49735111 48823509
 [9] 48547204 48394857

Smallest eigenvalues:
 [1]  0.38173914  0.22578431  0.20074961  0.17087987  0.13405107  0.09380402
 [7]  0.03224086  0.02125660 -1.40048360 -4.76001401

Largest  eigenvalues:
 [1] 61030199 56458948 54280698 52348756 52149585 50662041 49188369 49023181
 [9] 48785063 48180627

Smallest eigenvalues:
 [1]  0.41086374  0.35681446  0.30963847  0.26814350  0.26112175  0.25628568
 [7]  0.10071607  0.04015024 -0.03995307 -0.28022370

Largest  eigenvalues:
 [1] 60126168 56893231 54189104 52625688 52421343 50822456 50036258 49258788
 [9] 49044573 48864545

Smallest eigenvalues:
 [1]  0.4289359  0.3950907  0.3783711  0.3623820  0.3018641  0.2955898
 [7]  0.2551930  0.1559691 -0.6305254 -0.7333129

Largest  eigenvalues:
 [1] 61624897 56357237 53571311 53259126 51808629 50150503 49611461 48629333
 [9] 48479690 47592252

Smallest eigenvalues:
 [1]  0.4803209  0.4512281  0.4127469  0.3534740  0.3221978  0.2529718
 [7]  0.2088123  0.1907809  0.1873931 -0.1172393

Largest  eigenvalues:
 [1] 60690141 57087520 54299232 53266609 52177041 50790105 49449469 49244176
 [9] 49093247 48448566

Smallest eigenvalues:
 [1]  0.4439649  0.3898715  0.2998521  0.2723315  0.2550672  0.1711473
 [7]  0.1499616  0.1457232  0.1103189 -1.2177641

Largest  eigenvalues:
 [1] 62223994 57237675 54586785 53757813 52415362 51049153 50091368 49659331
 [9] 49644504 48704613

Smallest eigenvalues:
 [1]   0.24992155   0.19821666   0.19260588   0.18687583   0.11574283
 [6]  -0.03853566  -2.26150403 -15.72113414 -18.38973391 -46.48648778

Largest  eigenvalues:
 [1] 60373788 57530577 54027671 53095311 52775686 51732321 49979533 49676520
 [9] 48973736 48822051

Smallest eigenvalues:
 [1]   0.40785164   0.39404390   0.34082493   0.23993409   0.21004917
 [6]   0.15616988   0.02025404  -0.36702657 -10.89062299 -14.50229837

Largest  eigenvalues:
 [1] 60818780 56915523 54586793 52665118 52215509 50922098 49555519 49448950
 [9] 48886226 48587448

Smallest eigenvalues:
 [1]  0.4913620  0.4497253  0.4466122  0.4314280  0.3721452  0.3597995
 [7]  0.3243416  0.1857508  0.1837245 -0.2520058

Largest  eigenvalues:
 [1] 59847039 56924084 54337872 52468450 52435675 50634228 50019776 48937318
 [9] 48906332 48796638

Smallest eigenvalues:
 [1]  0.5703175  0.5303038  0.4822052  0.3749495  0.3192475  0.3177358
 [7]  0.2815970  0.2529439  0.1763980 -0.1400922

Largest  eigenvalues:
 [1] 60005139 56684094 53846553 52552444 51848262 50347014 49092614 48806902
 [9] 48798014 48104824

Smallest eigenvalues:
 [1]   0.3732083   0.3505868   0.3315426   0.2623437   0.2133517   0.1668389
 [7]  -0.4053639  -1.8686760  -4.7956924 -11.8713398

Largest  eigenvalues:
 [1] 60433290 55894671 53472007 52550915 51260404 49916482 48929245 48800799
 [9] 48651553 47891150

Smallest eigenvalues:
 [1]  0.26101253  0.25076085  0.22821208  0.22544798  0.22407172  0.04044592
 [7] -0.63766012 -1.24328673 -2.12339934 -4.60049209

Largest  eigenvalues:
 [1] 59424317 56930881 53627549 52186769 52145530 50532870 49605107 48901926
 [9] 48502486 48325570

Smallest eigenvalues:
 [1]   0.31564260   0.21367931   0.20749078   0.19863209   0.18929329
 [6]   0.18214824  -0.09996127  -0.51840553  -6.91026109 -34.81725336

Largest  eigenvalues:
 [1] 60853237 57461701 54399792 53620915 53038309 51470595 50053943 49731810
 [9] 49547624 48977440

Smallest eigenvalues:
 [1]  0.4972782  0.4747164  0.4432018  0.4296695  0.3994533  0.3916961
 [7]  0.2882557  0.1920210  0.1031796 -0.3680169

Largest  eigenvalues:
 [1] 60358874 56608381 53316529 52460314 51933329 50301306 49205233 48853540
 [9] 48678082 48120183

Smallest eigenvalues:
 [1]   0.4376309   0.4268220   0.3714861   0.3418039   0.2994845   0.2720832
 [7]   0.2540180   0.1969878   0.1785853 -43.1808457

Largest  eigenvalues:
 [1] 59845261 57351419 54428275 53186790 52374251 51614581 49837484 49004533
 [9] 48660578 48207361

Smallest eigenvalues:
 [1]  0.4255473  0.4123912  0.3521531  0.3219596  0.2894944  0.2311587
 [7]  0.2092418 -0.6280675 -1.3918889 -1.7768789

Largest  eigenvalues:
 [1] 62565590 56789323 54106725 54043798 51660856 50365049 50083385 49749188
 [9] 48658638 48561693

Smallest eigenvalues:
 [1] -0.1390819 -0.2170049 -0.3323154 -0.5326482 -0.6168624 -0.6742931
 [7] -0.8621925 -0.8709568 -1.0180588 -1.2162951

Largest  eigenvalues:
 [1] 59831312 56404945 53548153 52506619 52100424 50289192 49225035 49121773
 [9] 48655367 48161106

Smallest eigenvalues:
 [1]   0.36371888   0.32185477   0.25653160   0.25411209   0.19994200
 [6]   0.19687083   0.09628776  -0.54192461  -0.77546351 -17.07839671

Largest  eigenvalues:
 [1] 62233714 57786110 54935747 54203205 52440786 50331466 50244035 50149106
 [9] 49223045 49103326

Smallest eigenvalues:
 [1]  0.5580760  0.4939797  0.4922788  0.4126050  0.3790359  0.2819348
 [7]  0.2765272  0.1390174  0.0327105 -1.2835989

Largest  eigenvalues:
 [1] 60055542 57089761 54091674 52439503 52100195 50422442 49187750 48980912
 [9] 48724080 48316289

Smallest eigenvalues:
 [1]  0.44012583  0.35307503  0.27568932  0.26065686  0.22184490  0.19663255
 [7]  0.15724436 -0.08638441 -0.28698729 -1.21350044

Largest  eigenvalues:
 [1] 60412182 57025739 54601193 53006969 52673138 51144169 49828632 49441164
 [9] 49243910 48611841

Smallest eigenvalues:
 [1]  0.54945647  0.39558115  0.37765923  0.32760085  0.29121211  0.27650916
 [7]  0.12815696  0.07123199 -0.02304807 -0.21196796

Largest  eigenvalues:
 [1] 61305480 57203925 54333730 53006388 52385503 50714894 49554707 49382795
 [9] 49030651 48321000

Smallest eigenvalues:
 [1]  0.4471790  0.4468151  0.3706218  0.3090550  0.3081898  0.2316257
 [7]  0.1304340 -0.2240167 -0.7994059 -5.1780936

Largest  eigenvalues:
 [1] 60452341 56482856 53851217 52493420 51737298 50057187 49058702 48695860
 [9] 48627866 47948721

Smallest eigenvalues:
 [1]  0.3841541  0.3589080  0.3148786  0.2399918  0.2255127  0.2132834
 [7]  0.1350854  0.1239517 -1.1252585 -4.0426740

Largest  eigenvalues:
 [1] 60600586 57752544 54659578 53182707 53103503 51699364 50090454 49970623
 [9] 49283784 48818003

Smallest eigenvalues:
 [1]  0.3114201  0.2796522  0.2356031  0.2103930  0.1597068 -0.2842413
 [7] -0.3221553 -1.5569055 -1.8706072 -3.1528805

Largest  eigenvalues:
 [1] 60473768 56415909 54212450 51917381 51735732 50245517 49468047 48571256
 [9] 48476005 48410191

Smallest eigenvalues:
 [1]  0.43168236  0.42504436  0.40896166  0.38808241  0.33410139  0.31714291
 [7]  0.21878530  0.06689256 -0.17149900 -0.55398932

Largest  eigenvalues:
 [1] 61588155 57289505 54613751 53446355 52271833 50521755 49855045 49838530
 [9] 48803633 48342970

Smallest eigenvalues:
 [1]  0.47138063  0.45650980  0.45500700  0.41787431  0.35809832  0.34194951
 [7]  0.21248448  0.10051370  0.09703461 -0.04463957

Largest  eigenvalues:
 [1] 60013585 57357053 54242350 52356724 52235184 50821791 49459613 49141697
 [9] 48644061 48444619

Smallest eigenvalues:
 [1]  0.54671661  0.46792009  0.40153316  0.36887710  0.31562460  0.28257160
 [7]  0.17169124  0.10448762  0.07140511 -0.22071932

Largest  eigenvalues:
 [1] 61659931 56422074 53860824 52870848 51564574 50032360 49209159 48700471
 [9] 48665787 48084182

Smallest eigenvalues:
 [1]  0.34835336  0.32663927  0.27187825  0.23542007  0.16776220  0.07968264
 [7] -0.03345215 -0.77837593 -5.90228931 -9.23992327

Largest  eigenvalues:
 [1] 60910785 56641751 53836067 53111589 52322494 50796633 49242446 49228065
 [9] 49063831 48395203

Smallest eigenvalues:
 [1]   0.17662191   0.14701573   0.14649222   0.10347165   0.07814492
 [6]   0.05710740  -0.70549348  -1.82760890  -6.34490195 -32.51025849

Largest  eigenvalues:
 [1] 62944964 57089649 54483648 53947707 52423586 50872967 50365958 50321588
 [9] 49477911 48997101

Smallest eigenvalues:
 [1]  0.3176975  0.2823086  0.2509452  0.2043332  0.1858994  0.1692234
 [7] -0.1271624 -0.1859470 -0.5507800 -0.8548960

Largest  eigenvalues:
 [1] 62527511 56632378 54485810 53989127 51459639 50287804 50051946 48759354
 [9] 48675418 48160534

Smallest eigenvalues:
 [1]  0.5162945  0.4511005  0.4385022  0.4009457  0.2869997  0.2591677
 [7]  0.2196847  0.1921336 -0.2971061 -2.5016950

Largest  eigenvalues:
 [1] 61493261 56697859 54251552 53049877 51688169 49972951 49705693 49445785
 [9] 48878473 48690327

Smallest eigenvalues:
 [1]   0.41535924   0.40812665   0.39807359   0.34445798   0.32794427
 [6]   0.29240453   0.02002087  -0.02918034 -16.60262717 -36.07439184

Largest  eigenvalues:
 [1] 60557788 56827046 54157762 52210247 52164056 50793135 49250690 49046916
 [9] 48544317 48458460

Smallest eigenvalues:
 [1]  0.4266901  0.4055665  0.3727555  0.2985601  0.2802720  0.1518603
 [7]  0.1222462 -0.1000245 -0.3731731 -0.9471946

Largest  eigenvalues:
 [1] 59982663 56654977 54574897 52480810 52061028 51223902 49627939 49102761
 [9] 48414196 48261435

Smallest eigenvalues:
 [1]  0.4068204  0.4009320  0.3762176  0.3381411  0.3079746  0.2763121
 [7]  0.2255566  0.1730536  0.1615744 -0.4189887

Largest  eigenvalues:
 [1] 61765482 57643524 54693149 53828687 52540377 51037725 50083958 49984245
 [9] 49443775 48646642

Smallest eigenvalues:
 [1]  0.50735683  0.50713093  0.41962333  0.31519830  0.29439871  0.26235806
 [7]  0.22445070  0.17373163  0.07618286 -0.12460078

Largest  eigenvalues:
 [1] 60981741 57058200 54397488 53169725 52264623 50570973 50296596 49534610
 [9] 48876111 48802405

Smallest eigenvalues:
 [1]  0.4240886  0.4165069  0.3742436  0.2854681  0.2121542  0.1946346
 [7]  0.1450766  0.1419572 -0.3662326 -6.4153035

Largest  eigenvalues:
 [1] 60649173 57171478 54716914 52864166 52592305 51339458 49872373 49812053
 [9] 48918500 48735103

Smallest eigenvalues:
 [1]  0.3695670  0.3548248  0.3500379  0.3246229  0.2488123  0.1844365
 [7]  0.1656266  0.1568008  0.1339524 -0.8944041

Largest  eigenvalues:
 [1] 60117208 56716287 53993213 52120908 51842030 50159961 48493505 48453238
 [9] 48212275 47330846

Smallest eigenvalues:
 [1]   0.4089921   0.4073233   0.3547962   0.3108988   0.2454954   0.2390874
 [7]  -1.0227305  -1.1333625  -3.9568769 -14.4350513

Largest  eigenvalues:
 [1] 62196725 56786965 54104297 53772645 51952737 49962935 49940587 49663923
 [9] 48835501 48496093

Smallest eigenvalues:
 [1]   0.3147089   0.2691223   0.2551160   0.2485574   0.2235012   0.2190282
 [7]   0.2085586   0.2046603  -0.7633386 -11.1113128

Largest  eigenvalues:
 [1] 60150171 56226284 53567587 52579483 51878059 50424135 49305834 48777236
 [9] 48263560 47601906

Smallest eigenvalues:
 [1]  0.42191679  0.41483440  0.35077710  0.28367138  0.26105530  0.22739990
 [7]  0.11722243  0.06569049 -0.04358547 -2.77606260

Largest  eigenvalues:
 [1] 59750129 56056589 53323082 51819652 51535432 49878817 49100399 48236444
 [9] 48169070 48049494

Smallest eigenvalues:
 [1]  0.499231791  0.440008579  0.418095418  0.401997353  0.311957781
 [6]  0.307089010  0.231114788  0.147381575  0.137940294 -0.004165697

Largest  eigenvalues:
 [1] 60814897 56820649 54296278 53101644 51875864 50402499 49326352 49121693
 [9] 49088459 48374843

Smallest eigenvalues:
 [1]   0.3910972   0.3254893   0.3204014   0.2910008   0.2647446   0.2378803
 [7]  -0.1787452  -0.5617049  -1.1635131 -16.4891594

Largest  eigenvalues:
 [1] 60378344 56312114 53776659 52413283 52011193 50499427 49027468 48847216
 [9] 48746072 47927949

Smallest eigenvalues:
 [1]  0.439499735  0.396451408  0.360217018  0.340929618  0.312705953
 [6]  0.200430848  0.171564137  0.083689198 -0.004879004 -0.564904759

Largest  eigenvalues:
 [1] 61905507 57990558 54494612 53774053 52710946 51069457 50076060 49984080
 [9] 49642822 49093538

Smallest eigenvalues:
 [1]  0.3969204  0.3510861  0.3302470  0.3083795  0.2345656  0.2248264
 [7]  0.2018016  0.0804707 -1.5454891 -3.0450980

Largest  eigenvalues:
 [1] 59589090 56493623 54125406 52834144 51759232 51087430 49640188 48569031
 [9] 48102181 47844745

Smallest eigenvalues:
 [1]  0.4536524  0.3685705  0.3475585  0.3172027  0.2820355  0.2300680
 [7]  0.2043613 -0.1605662 -0.7447793 -0.9546099

Largest  eigenvalues:
 [1] 62732873 57582517 54991170 54402441 52407132 50711778 50701529 50210614
 [9] 49333069 49031926

Smallest eigenvalues:
 [1]  0.5520704  0.5448518  0.4112108  0.3746011  0.3153940  0.2825629
 [7]  0.2572838  0.1301782 -0.1497266 -0.5291301

Largest  eigenvalues:
 [1] 60819202 57034914 54356302 53328852 52128264 50434897 49603230 49530212
 [9] 49157756 48701862

Smallest eigenvalues:
 [1]  0.55300944  0.53405229  0.36639161  0.36362757  0.35401949  0.33323917
 [7]  0.26615738  0.18628319 -0.05703658 -0.21817642

Largest  eigenvalues:
 [1] 60684636 56318185 53709856 52712446 51867130 50374714 48909748 48898454
 [9] 48579262 47795086

Smallest eigenvalues:
 [1]   0.3343917   0.2569268   0.2326976   0.2087988   0.1745439   0.1523458
 [7]   0.1456388   0.1332859  -0.1943149 -18.0702373

Largest  eigenvalues:
 [1] 59762373 56016769 53803644 52344934 51481891 49991848 48739492 48667669
 [9] 48625799 48059891

Smallest eigenvalues:
 [1]   0.2366141   0.2085159   0.1861823   0.1588452   0.1235713  -0.6508953
 [7]  -2.8090842 -14.2662866 -16.4916976 -26.7953621

Largest  eigenvalues:
 [1] 60820010 55818597 53495864 52105190 51615599 50196661 49034030 48766494
 [9] 48520197 48028894

Smallest eigenvalues:
 [1]   0.31745225   0.30649946   0.23084139   0.16257985   0.15427284
 [6]  -0.02641795  -0.57626254  -1.10627634  -8.19919001 -27.84661070

Largest  eigenvalues:
 [1] 60003448 56110090 53267627 52676044 51340431 49806059 48869123 48379053
 [9] 48058181 47166258

Smallest eigenvalues:
 [1]   0.2970569   0.2238655   0.2010375   0.1659331   0.1605131  -0.1098398
 [7]  -0.4973454  -1.5010336 -14.8695651 -43.2579018

Largest  eigenvalues:
 [1] 61738072 56675809 53699647 53255058 52045488 50490070 49460487 49432170
 [9] 49156956 48646518

Smallest eigenvalues:
 [1]  0.4937931  0.3797228  0.3312952  0.3309922  0.2847543  0.2343620
 [7]  0.1875436 -0.1631735 -0.2138261 -0.3478553

Largest  eigenvalues:
 [1] 62130410 56699044 54527331 53724895 51707202 50028865 49911759 49451783
 [9] 48965321 48765848

Smallest eigenvalues:
 [1]  0.4806181  0.4624442  0.4238570  0.2627189  0.2240836  0.1977554
 [7]  0.1870243  0.1830931  0.1267200 -0.8954530

Largest  eigenvalues:
 [1] 58061088 56552048 53763418 52336739 50941736 50540209 48885622 48762779
 [9] 47926680 47538050

Smallest eigenvalues:
 [1]  0.159178732  0.009386789 -0.098827629 -0.233465977 -0.295322587
 [6] -0.431743797 -0.573295139 -1.293248266 -1.545804191 -2.061804181

Largest  eigenvalues:
 [1] 60087397 56995240 53719790 52781376 52483943 50659500 49462741 49040369
 [9] 48994992 48296913

Smallest eigenvalues:
 [1]  0.4602684  0.4455640  0.4038406  0.3679004  0.3488780  0.2877631
 [7]  0.2540486  0.1715845 -0.3514743 -7.2217864

Largest  eigenvalues:
 [1] 60558884 56918813 54302667 52711773 52497467 51256125 49721367 49573576
 [9] 48823974 48552749

Smallest eigenvalues:
 [1]  0.40174318  0.39038637  0.37460023  0.29341706  0.28539993  0.17156788
 [7]  0.14909510  0.06605809  0.03272562 -2.19620856

Largest  eigenvalues:
 [1] 61428556 56651872 53953030 52719585 51929654 50286100 49052974 48949175
 [9] 48917280 48337116

Smallest eigenvalues:
 [1]  0.39200316  0.36513878  0.35120954  0.31525517  0.29361319  0.26342386
 [7]  0.21066937  0.14889299 -0.02671328 -0.28138865

Largest  eigenvalues:
 [1] 58848291 56327839 54140006 52021989 51733893 50627917 49193028 48423560
 [9] 48130500 47710759

Smallest eigenvalues:
 [1]  0.36661718  0.35880548  0.29746880  0.26332123  0.12297637 -0.07308289
 [7] -0.37239779 -1.19361192 -1.89481121 -8.60750358

Largest  eigenvalues:
 [1] 61897164 57015226 54311511 53521909 51896503 50077519 49843360 49144885
 [9] 48920826 48473019

Smallest eigenvalues:
 [1]   0.4705004   0.3947833   0.3364615   0.3305103   0.3187152   0.2197134
 [7]  -0.1535119  -0.2164121  -0.9195204 -10.6409927

Largest  eigenvalues:
 [1] 61393207 56657195 54098691 53223888 52051359 50171540 49482777 49378477
 [9] 48853519 48306208

Smallest eigenvalues:
 [1]  0.42588232  0.37955921  0.37568724  0.29979840  0.20818049  0.19855462
 [7] -0.07359839 -0.08140830 -0.60399217 -0.66676398

Largest  eigenvalues:
 [1] 60790173 56180495 53884491 52519517 51513187 49824244 48907293 48855882
 [9] 48558386 48104679

Smallest eigenvalues:
 [1]  0.3875242  0.3607722  0.3542732  0.3491930  0.3373780  0.2605059
 [7]  0.2056434  0.2049081 -0.1167760 -0.5538089

Largest  eigenvalues:
 [1] 60999558 56286611 53783757 52834510 51730539 50129936 49165203 48668855
 [9] 48387832 47537487

Smallest eigenvalues:
 [1]  0.4227196  0.3925881  0.3707511  0.2749182  0.2390396  0.1883664
 [7]  0.1858637  0.1554571  0.1203926 -1.2167088

Largest  eigenvalues:
 [1] 61802304 57154877 54672945 53999036 52125030 50843809 50230655 49170785
 [9] 48788895 48050858

Smallest eigenvalues:
 [1]  0.5580718  0.4813434  0.4756031  0.4389980  0.4108176  0.3367040
 [7]  0.2817007  0.2623414  0.1046230 -0.2389845

Largest  eigenvalues:
 [1] 60220114 56975564 54220607 52279020 52265113 50605537 49293656 48826488
 [9] 48715647 47946281

Smallest eigenvalues:
 [1]  0.35447580  0.34934731  0.33113164  0.25465531  0.25264764  0.24747485
 [7]  0.20829666  0.08355711 -0.09107919 -0.83898856

Largest  eigenvalues:
 [1] 61671484 56834140 54312267 53482233 52471377 50877057 49651453 49487737
 [9] 48922173 48645474

Smallest eigenvalues:
 [1]  0.51257920  0.44957028  0.43721844  0.33349725  0.29252488  0.19255276
 [7]  0.16481403  0.10570990 -0.02914557 -0.27503378

Largest  eigenvalues:
 [1] 61391218 57242473 54265797 52960897 52143770 50711601 49436822 49310663
 [9] 49173034 48655507

Smallest eigenvalues:
 [1]   0.41413222   0.33301498   0.32848325   0.29382472   0.27898602
 [6]   0.22579549   0.19905472   0.05521943  -0.71269817 -37.85904742

Largest  eigenvalues:
 [1] 60434609 57066515 54008978 53018985 52312753 50820888 49405612 49181116
 [9] 49088032 48280753

Smallest eigenvalues:
 [1]  0.3248489  0.2826673  0.2597613  0.2399535  0.2010673  0.1897887
 [7]  0.1243988 -2.3242182 -4.3734430 -8.5131688

Largest  eigenvalues:
 [1] 61901139 57900738 54384919 54226329 53107283 51395179 50461277 49791579
 [9] 49434558 48688952

Smallest eigenvalues:
 [1]  0.4136482  0.3770308  0.3576600  0.2933905  0.2543331  0.2460215
 [7]  0.2165575 -0.3080185 -0.4171580 -0.5490019

Largest  eigenvalues:
 [1] 59681303 56212059 53704806 51929347 51721745 50150165 49029644 48654891
 [9] 48400692 48196375

Smallest eigenvalues:
 [1]  0.5232527  0.5151313  0.5075324  0.3945570  0.3913021  0.2788334
 [7]  0.2784558  0.2104368  0.1613865 -0.1665843

Largest  eigenvalues:
 [1] 61432044 57332683 54685553 52737564 52641299 50883309 49381475 49343808
 [9] 49279577 48386850

Smallest eigenvalues:
 [1]   0.4146894   0.2931616   0.2741223   0.2701020   0.2343389   0.2297259
 [7]  -0.2542258  -0.2833549  -0.9194391 -15.5219621

Largest  eigenvalues:
 [1] 60678627 56437749 53905953 52672472 51855729 50041635 49015051 48852103
 [9] 48808432 48132048

Smallest eigenvalues:
 [1]  0.48394620  0.43965886  0.39786691  0.38425004  0.33497993  0.31980896
 [7]  0.20160213  0.18608163  0.08693398 -0.65186771

Largest  eigenvalues:
 [1] 59565798 56980428 53815465 52501342 52195091 50691688 49397047 49317538
 [9] 48715760 48411507

Smallest eigenvalues:
 [1]  0.36203016  0.35139501  0.33360260  0.30218734  0.26849243  0.25804722
 [7]  0.12708800 -0.03147284 -0.40261943 -3.04388181

Largest  eigenvalues:
 [1] 60507507 57148441 54472354 52967071 52041069 50691881 49307167 49247603
 [9] 49221163 48458873

Smallest eigenvalues:
 [1]  0.33941021  0.23822724  0.16821041  0.11469921 -0.04501172 -0.32298686
 [7] -0.80100980 -1.50782981 -1.96247650 -4.83001963

Largest  eigenvalues:
 [1] 61193021 57386215 54097537 54095279 52525917 50507598 50040747 50018617
 [9] 49405306 48648078

Smallest eigenvalues:
 [1]   0.3954332   0.2639436   0.2593385   0.2372815   0.1945548   0.1805734
 [7]   0.1079849  -1.1482784  -1.2031355 -67.9996430

Largest  eigenvalues:
 [1] 59967957 55941968 53373855 52270754 51846331 50315039 49126061 48721111
 [9] 48453667 48002982

Smallest eigenvalues:
 [1]  0.5095137  0.4679926  0.3942853  0.3122799  0.2719831  0.2697274
 [7]  0.2053577 -0.1299356 -0.4848006 -2.9449581

Largest  eigenvalues:
 [1] 61785375 56280212 53711880 53004639 51643303 49941259 49305600 48872952
 [9] 48793748 47977484

Smallest eigenvalues:
 [1]  0.42178225  0.40868595  0.33012645  0.31262087  0.26496476  0.21882746
 [7]  0.18523890  0.01204778 -1.85513784 -5.05620358

Largest  eigenvalues:
 [1] 60269686 57243208 54731308 52743760 52003643 51317946 49412102 49378419
 [9] 48517112 48359413

Smallest eigenvalues:
 [1]  0.36968155  0.34138465  0.27757725  0.23688959  0.20693207  0.09448451
 [7]  0.06079864  0.05061530 -1.15838416 -4.96608575

Largest  eigenvalues:
 [1] 61954665 56499096 53701703 53483094 51830502 50243642 49677164 49324153
 [9] 48495623 48445700

Smallest eigenvalues:
 [1]   0.32309284   0.21005326   0.18017066   0.16016262   0.07738761
 [6]   0.06086700  -0.06452118  -1.79371967 -10.87460485 -15.97641340

Largest  eigenvalues:
 [1] 60107059 57017553 53939313 52597031 51989780 51027536 49718388 49659270
 [9] 48794972 48431083

Smallest eigenvalues:
 [1]  0.55864955  0.54356446  0.41104668  0.40577362  0.39437248  0.32488028
 [7]  0.30957986  0.25658556  0.18261240 -0.07195788

Largest  eigenvalues:
 [1] 60376740 56362003 54169819 52252216 51870522 50477751 49072086 48728482
 [9] 48603240 48044460

Smallest eigenvalues:
 [1]  0.26573334  0.22690222  0.12901061  0.07454859 -0.05466274 -0.30103262
 [7] -0.46403007 -0.92394236 -1.08706770 -3.80218258

Largest  eigenvalues:
 [1] 60276272 55703685 53301393 52718096 50944922 49533448 48837772 48360915
 [9] 48323088 47389914

Smallest eigenvalues:
 [1]   0.431867741   0.372614473   0.267122477   0.227364940   0.182068131
 [6]   0.139920660  -0.008522181  -2.132147476  -3.747067491 -23.279231912

Largest  eigenvalues:
 [1] 60904712 56581981 53586356 52660736 52070099 50689199 49334951 49249119
 [9] 48893386 48336414

Smallest eigenvalues:
 [1] -0.08802358 -0.09412573 -0.22002134 -0.30140960 -0.34476998 -0.42181532
 [7] -0.54625285 -1.35448529 -2.90772791 -7.04167338

Largest  eigenvalues:
 [1] 61990771 57487979 54249336 53843505 52956721 51307424 50009083 49934875
 [9] 49573599 49009580

Smallest eigenvalues:
 [1]  0.48394273  0.45743958  0.41790292  0.31572695  0.26416957  0.20078505
 [7]  0.16933878  0.16764347  0.08503126 -0.06902037

Largest  eigenvalues:
 [1] 61632929 56981466 54360548 53476149 52212436 50558300 50080607 49733207
 [9] 49335067 49087324

Smallest eigenvalues:
 [1]  0.356654058  0.349521877  0.341194408  0.314330352  0.303301185
 [6]  0.240079953  0.201519934  0.097892396 -0.006077542 -0.174273599

Largest  eigenvalues:
 [1] 61666707 56399899 53719762 52816827 51369343 49926122 49335619 49047406
 [9] 48406112 48208360

Smallest eigenvalues:
 [1]  0.36019327  0.29663626  0.26120413  0.23845004  0.15468699  0.06598445
 [7] -1.05582334 -1.83997886 -3.53585996 -3.66530156

Largest  eigenvalues:
 [1] 61582605 57178036 53979749 53129124 52451416 50706384 49851493 49543538
 [9] 48882829 48560221

Smallest eigenvalues:
 [1]  0.5044813  0.4828255  0.4419376  0.3659268  0.3548451  0.2703001
 [7]  0.2696013  0.2465577  0.2251820 -0.4896558

Largest  eigenvalues:
 [1] 60418738 56481699 54096546 52604776 51668351 50312685 49126026 48907108
 [9] 48884759 48384148

Smallest eigenvalues:
 [1]   0.3722600   0.3184194   0.2580759   0.2331599   0.2022322   0.1429425
 [7]  -0.3171552  -0.8617764 -10.8614376 -20.2505700

Largest  eigenvalues:
 [1] 60366721 56866995 54087795 52782614 52401237 51342176 49759356 49155271
 [9] 48641789 48435916

Smallest eigenvalues:
 [1]  0.4965561  0.4044152  0.3447775  0.3285556  0.2796134  0.2449597
 [7]  0.2142338  0.1501360  0.1162406 -0.3276573

Largest  eigenvalues:
 [1] 59097536 57134438 53809783 52242966 52184861 50632559 48992897 48903971
 [9] 48405743 47919183

Smallest eigenvalues:
 [1]   0.26118717   0.25914742   0.25063944   0.16602732   0.07823036
 [6]   0.07236635  -0.27423246  -1.04475096  -4.73173522 -20.16313290

Largest  eigenvalues:
 [1] 62797678 56904649 54990856 54323788 51790645 50673761 49909294 49813715
 [9] 48863822 48644868

Smallest eigenvalues:
 [1]  0.48791362  0.47760226  0.46780066  0.39482623  0.35959547  0.32187561
 [7]  0.26866625  0.09457191 -0.62546352 -7.61497821

Largest  eigenvalues:
 [1] 60170017 57393001 54117725 53022143 52200098 50474729 49584718 49252941
 [9] 48687534 48296292

Smallest eigenvalues:
 [1]  0.5215488  0.4470798  0.4151331  0.3600295  0.3449611  0.3102762
 [7]  0.2349280  0.2200590  0.1834186 -0.2201999

Largest  eigenvalues:
 [1] 60425352 56654518 54319369 52343425 52310133 50768711 49307536 49065594
 [9] 48703065 48388378

Smallest eigenvalues:
 [1]   0.23551207   0.23258500   0.20657833   0.08828505   0.03713145
 [6]  -0.16128231  -0.45311228  -3.71039893 -10.23069146 -13.38582639

Largest  eigenvalues:
 [1] 61836741 57181904 54732182 53823834 52288816 50717147 50131533 49642596
 [9] 49315722 48723066

Smallest eigenvalues:
 [1]  0.43992125  0.42094593  0.30971952  0.29868932  0.16415782  0.13015577
 [7]  0.08285453 -0.08290483 -0.11926624 -4.88819655

Largest  eigenvalues:
 [1] 61519957 56763027 54404152 53135439 51941171 50426976 49487104 49460561
 [9] 48881666 48475901

Smallest eigenvalues:
 [1]  0.41577326  0.39713697  0.37830078  0.19544009  0.19480598  0.08698267
 [7]  0.05714332 -0.72629843 -1.24119140 -8.69483774

Largest  eigenvalues:
 [1] 60255801 56781713 53671719 52281972 51883190 50401785 49176092 48859176
 [9] 48595168 48409135

Smallest eigenvalues:
 [1]  0.3663924  0.3627366  0.3508961  0.3258831  0.2362026  0.1413982
 [7]  0.1040180 -0.3007408 -1.2295748 -8.3170534

Largest  eigenvalues:
 [1] 61295945 56699364 54082553 53121324 51887758 50392919 49546996 49444161
 [9] 49140496 48679536

Smallest eigenvalues:
 [1]   0.07050201   0.05718619  -0.04248789  -0.07866189  -1.19862286
 [6]  -2.78179726  -5.08194630  -7.92995027 -44.76202018 -45.08175498

Largest  eigenvalues:
 [1] 61609484 56705800 53600573 53063060 52137387 50405722 49800486 49363823
 [9] 48625217 48472253

Smallest eigenvalues:
 [1]  0.53286784  0.44794487  0.38540445  0.34780048  0.31179227  0.29277845
 [7]  0.21403901  0.12105206  0.06529864 -0.14125647

Largest  eigenvalues:
 [1] 61711029 57990496 55041661 53592729 53096614 51715270 50181507 50092692
 [9] 49870359 49156558

Smallest eigenvalues:
 [1]  0.5452084  0.4777621  0.4543715  0.4279139  0.3519336  0.3353493
 [7]  0.2977777  0.2767443  0.1339215 -2.5822400

Largest  eigenvalues:
 [1] 61754279 57105566 54164338 53309853 52218843 50679567 49596993 49358115
 [9] 48950155 48476574

Smallest eigenvalues:
 [1]   0.4187649   0.3830171   0.3197251   0.3067155   0.2941940   0.1953803
 [7]   0.1656330   0.1288161  -0.5412452 -11.7839864

Largest  eigenvalues:
 [1] 59965415 56233825 53781525 52240001 52190440 50649267 49047305 48620363
 [9] 48502291 47632999

Smallest eigenvalues:
 [1]  0.5171943  0.3932629  0.3835900  0.2943932  0.2851526  0.1931129
 [7]  0.1339003 -0.0333617 -1.0402600 -7.1688060

Largest  eigenvalues:
 [1] 61531845 57021322 54387228 52763500 52722512 51104017 49644047 49374079
 [9] 49056311 48901314

Smallest eigenvalues:
 [1]  0.3723298  0.3474942  0.3100412  0.2710962  0.2659115  0.1807546
 [7]  0.1197395  0.0674782 -0.2711414 -0.9392399

Largest  eigenvalues:
 [1] 60701728 57262422 53810744 53298945 52103618 50529611 49437223 49061446
 [9] 49053304 48327546

Smallest eigenvalues:
 [1]  0.4783583  0.4248015  0.3739803  0.3688025  0.3563851  0.1712337
 [7]  0.0268449 -0.1548360 -0.5643596 -4.3257666

Largest  eigenvalues:
 [1] 59825360 56295231 53970897 51922871 51707342 50565349 48965807 48583088
 [9] 48127366 47859037

Smallest eigenvalues:
 [1]   0.11824586   0.11779102   0.09272212  -0.50310614  -0.55833461
 [6]  -1.75756728 -15.05611061 -23.00087490 -26.07882653 -42.94884800

Largest  eigenvalues:
 [1] 62443147 57570500 54821995 54333135 52990771 51393081 50382605 50352961
 [9] 49455795 49163795

Smallest eigenvalues:
 [1]  0.56233224  0.45486657  0.45283725  0.40255552  0.30229992  0.25099012
 [7]  0.18845315  0.01365011 -0.10530342 -0.38169700

Largest  eigenvalues:
 [1] 60846156 56621275 53631496 52882109 51866463 49929002 49073006 48767133
 [9] 48467844 47516722

Smallest eigenvalues:
 [1]  0.48890983  0.46499137  0.43140000  0.38461842  0.27781239  0.20255095
 [7]  0.17857041  0.06436231 -0.05042630 -2.14027136

Largest  eigenvalues:
 [1] 60993197 57168839 54349768 53277235 51890212 50594430 49527234 49108062
 [9] 48840042 47968026

Smallest eigenvalues:
 [1]   0.36720582   0.36618929   0.35050856   0.25330771   0.25068227
 [6]   0.18522255   0.13247165  -0.03035573  -5.08119620 -14.49139855

Largest  eigenvalues:
 [1] 60161611 56597206 54535032 52128515 52003755 50755728 49546417 48710910
 [9] 48448726 48137986

Smallest eigenvalues:
 [1]  0.3900543  0.3876171  0.3579453  0.3352295  0.2923148  0.2685221
 [7]  0.2453548  0.1630981 -0.1616682 -0.6827609

Largest  eigenvalues:
 [1] 61801490 57375249 54379707 53489468 52757416 51054022 49997297 49879177
 [9] 49283839 48739162

Smallest eigenvalues:
 [1]  0.44475212  0.41275753  0.39298752  0.36153024  0.32331346  0.30908240
 [7]  0.27205324  0.17709786 -0.04148515 -0.27171112

Largest  eigenvalues:
 [1] 61078556 57238729 54782249 53328502 52745365 51407756 49960847 49728965
 [9] 49530043 49005638

Smallest eigenvalues:
 [1]   0.39985673   0.34901062   0.33594935   0.33277216   0.22183412
 [6]   0.12357724   0.00794805  -0.57480741  -8.19465506 -11.90813206

Largest  eigenvalues:
 [1] 61349118 56385395 53759997 52916261 51826942 50229325 49197898 49182063
 [9] 48733925 47897788

Smallest eigenvalues:
 [1]  0.4823605  0.4550646  0.4122300  0.3563737  0.3211078  0.2681999
 [7]  0.2043704  0.1467183 -0.2499244 -0.7559955

Largest  eigenvalues:
 [1] 61673721 56941260 54129133 53040569 52160730 50748522 49387268 49285551
 [9] 49165283 48290356

Smallest eigenvalues:
 [1]  0.4623288  0.4380419  0.3252336  0.3176281  0.2688846  0.2637597
 [7]  0.1930479 -0.1021357 -0.4267492 -4.5724210

Largest  eigenvalues:
 [1] 60593578 56814359 54223193 53192548 52151391 51469860 50021884 48914074
 [9] 48516757 48126797

Smallest eigenvalues:
 [1]  0.41497254  0.34453026  0.33394633  0.32185247  0.31511965  0.22658572
 [7]  0.18295444  0.15329198  0.03361928 -0.44209410

Largest  eigenvalues:
 [1] 59637525 56033717 53739716 52259451 51607122 50612132 49210546 48714120
 [9] 48048074 47836842

Smallest eigenvalues:
 [1]   0.25729410   0.24200477   0.21027044   0.12193439   0.05099067
 [6]  -0.07301389  -0.21492613  -6.33637916 -13.40809126 -15.22904798

Largest  eigenvalues:
 [1] 62385880 56085247 53888280 53664941 51125959 49867043 49488249 49309741
 [9] 48556288 48477103

Smallest eigenvalues:
 [1]  0.4030718  0.3686695  0.3439895  0.2843486  0.2030892  0.1288293
 [7]  0.1008753 -0.1112656 -0.2212221 -4.1230713

Largest  eigenvalues:
 [1] 61278040 56990122 54432030 52939944 52504690 50827187 49627907 49588661
 [9] 49367781 48804409

Smallest eigenvalues:
 [1]  0.435137846  0.397301393  0.381047404  0.370238558  0.352072968
 [6]  0.329283724  0.202330205  0.187266226  0.108106251 -0.007852709

Largest  eigenvalues:
 [1] 61393191 56865161 54702324 53432474 52246819 50701281 49628665 49560001
 [9] 49214880 48522921

Smallest eigenvalues:
 [1]  0.4902092  0.4639326  0.4167734  0.3228402  0.3099322  0.2943941
 [7]  0.2312352  0.1952533 -0.1542093 -0.9407169

Largest  eigenvalues:
 [1] 61595888 56726223 54219921 53195644 52212842 50900610 49351581 49258212
 [9] 49218237 48486341

Smallest eigenvalues:
 [1]  0.39022089  0.33305672  0.30101112  0.28017426  0.27944535  0.25540180
 [7]  0.20333862  0.14687396  0.08815677 -0.19402103

Largest  eigenvalues:
 [1] 60605900 56959782 54216068 52667601 52554914 50680708 49035259 48952041
 [9] 48829301 48257816

Smallest eigenvalues:
 [1]   0.39045039   0.33140119   0.30005425   0.23326185   0.09299865
 [6]   0.07927156   0.07824957   0.03982120  -0.05397127 -11.65603366

Largest  eigenvalues:
 [1] 62342596 57172371 54574527 53298354 52033727 50712343 49734315 49661818
 [9] 49074305 48960146

Smallest eigenvalues:
 [1]  0.36755025  0.36350692  0.35912693  0.28536110  0.27257565  0.19600893
 [7]  0.13662145  0.05402214  0.00227399 -7.03035510

Largest  eigenvalues:
 [1] 59506087 57325516 53978917 52683020 52420361 50755030 49195136 49166998
 [9] 48828297 48398858

Smallest eigenvalues:
 [1]  0.4618625  0.4277725  0.3907306  0.3109066  0.2684919  0.2575722
 [7]  0.2215640  0.1513702 -0.2664108 -9.8046663

Largest  eigenvalues:
 [1] 58828981 56061908 53441399 52011533 51411303 49731052 49032194 48268485
 [9] 48249742 47654758

Smallest eigenvalues:
 [1]  0.331949456  0.262705755  0.223931293  0.170245022  0.144538711
 [6]  0.084785249 -0.004901921 -0.059570902 -0.352946329 -9.400104338

Largest  eigenvalues:
 [1] 60732567 57648242 54286332 53123470 53055733 51133704 50012367 49156587
 [9] 49084147 49032944

Smallest eigenvalues:
 [1]   0.32393860   0.27415378   0.21484623   0.19364242   0.15815200
 [6]   0.12804334   0.08812595  -1.15372659  -2.66378935 -22.79358021

Largest  eigenvalues:
 [1] 60448234 56331068 54078631 52053030 52024089 50885393 49410882 49040669
 [9] 48486103 48329361

Smallest eigenvalues:
 [1]  0.5670946  0.5146144  0.4754313  0.4627517  0.4255053  0.3882429
 [7]  0.3355448  0.2812436  0.0279167 -4.9047624

Largest  eigenvalues:
 [1] 61667034 57370159 54455166 53509807 52617057 51149867 49775055 49635520
 [9] 49467332 48674709

Smallest eigenvalues:
 [1]  0.3946648  0.3564784  0.3338006  0.3080434  0.2917042  0.2123989
 [7]  0.1851480  0.1514834  0.1402906 -0.8055767

Largest  eigenvalues:
 [1] 60201397 57432839 54431355 52871503 52808836 51243920 49690355 49658709
 [9] 48977241 48614646

Smallest eigenvalues:
 [1]  0.4402191  0.3759932  0.2977007  0.2889548  0.2745540  0.2358266
 [7]  0.1821043 -0.0382577 -0.3797676 -5.5209038

Largest  eigenvalues:
 [1] 60751629 56023600 53263947 52400647 51723676 50127497 48691817 48652273
 [9] 48412865 47610050

Smallest eigenvalues:
 [1]  0.385131215  0.362520854  0.358572023  0.230147772  0.138420789
 [6]  0.134132088  0.001046094 -0.939758376 -1.731910192 -6.373648675

Largest  eigenvalues:
 [1] 59453998 56813973 53757123 52269748 52268110 50628625 49401632 49242839
 [9] 48250272 47963487

Smallest eigenvalues:
 [1]  0.48138738  0.44785107  0.44776696  0.42427035  0.38038804  0.28411955
 [7]  0.23894970  0.19963934  0.06156493 -2.73204631

Largest  eigenvalues:
 [1] 60723551 57227318 53785752 53281473 52528144 50777641 49398592 49358501
 [9] 48997651 48046187

Smallest eigenvalues:
 [1]  0.4652629  0.4402783  0.4357373  0.4192262  0.3423177  0.2740178
 [7]  0.2135654  0.2126790  0.1955623 -0.1722335

Largest  eigenvalues:
 [1] 60727817 56757227 54135162 52678469 52455991 50920550 49287607 49010341
 [9] 48945976 48187980

Smallest eigenvalues:
 [1]  0.44415345  0.40975772  0.35468509  0.32914204  0.31868858  0.27592037
 [7]  0.21120167  0.03306288 -0.58962323 -4.01139751

Largest  eigenvalues:
 [1] 60381543 56831372 54570687 52557294 52185154 50685202 49948382 48964507
 [9] 48941340 48763080

Smallest eigenvalues:
 [1]  0.29415346  0.21794766  0.17234694  0.15719172  0.09493242  0.08831225
 [7] -0.42407156 -0.80273419 -2.84317298 -7.83927846

Largest  eigenvalues:
 [1] 60741337 57447226 54906225 53363741 52577864 51391218 50079670 49883850
 [9] 49421404 48877115

Smallest eigenvalues:
 [1]  0.41107197  0.40760010  0.40447799  0.34883482  0.29710879  0.29397087
 [7]  0.27134827  0.14165099  0.08935935 -0.49468456

Largest  eigenvalues:
 [1] 61218801 57260191 54646281 52873685 52065030 50889159 49282202 49091617
 [9] 48944035 48251468

Smallest eigenvalues:
 [1]   0.1438057  -0.1288305  -0.1909403  -0.2716392  -1.6055091  -2.7424463
 [7]  -3.7736922  -5.6168819  -5.8237784 -31.1640356

Largest  eigenvalues:
 [1] 58927179 55964225 53261539 52009211 51700068 50146396 49057688 49017326
 [9] 47938924 47685416

Smallest eigenvalues:
 [1]  0.3554608  0.3111554  0.2814189  0.2773139  0.2154793  0.2112908
 [7]  0.1895101  0.1666524 -0.5421869 -1.4298095

Largest  eigenvalues:
 [1] 60475231 57317362 54774035 53295784 52561467 51265844 50171952 49614110
 [9] 49394458 49160218

Smallest eigenvalues:
 [1]  0.3621322  0.3293360  0.3174574  0.3107943  0.3090577  0.2037012
 [7]  0.1347536 -0.8186934 -2.6150792 -8.2109647

Largest  eigenvalues:
 [1] 60403040 56610658 53734115 52871482 51514687 50240041 49100258 48806661
 [9] 48612302 47951517

Smallest eigenvalues:
 [1]  0.42755345  0.36044127  0.31299401  0.29783375  0.27046879  0.20485714
 [7]  0.08744774 -0.15716369 -1.76536992 -2.51658944

Largest  eigenvalues:
 [1] 61181693 56490594 53714488 53543577 51458792 50108713 49710958 49151303
 [9] 48619385 48252980

Smallest eigenvalues:
 [1]  0.3753757  0.3722959  0.3701148  0.2774156  0.2754704  0.2327637
 [7]  0.1762103  0.1472211 -0.4350028 -0.7704539

Largest  eigenvalues:
 [1] 61418943 56860335 53992277 53177854 52238158 50648627 49528067 49472722
 [9] 49230244 48583948

Smallest eigenvalues:
 [1]   0.3173845   0.3047457   0.2511964   0.2210569   0.2024896  -0.1181932
 [7]  -0.6387505  -1.8540959  -8.1824464 -53.3303594

Largest  eigenvalues:
 [1] 63030011 57181051 54972313 54691051 51863559 50838233 50286222 49685288
 [9] 49288599 49112048

Smallest eigenvalues:
 [1]  0.53007287  0.42853930  0.39065401  0.38395514  0.35775705  0.28784991
 [7]  0.15103535  0.10393287  0.03757311 -0.12044170

Largest  eigenvalues:
 [1] 61935358 58027055 54734818 54089156 52961112 50841632 50383651 50281565
 [9] 49643515 49304655

Smallest eigenvalues:
 [1]  0.6046799  0.5745960  0.4964054  0.4098630  0.3970436  0.3781611
 [7]  0.3434390  0.2579412  0.1630675 -0.1363721

Largest  eigenvalues:
 [1] 60381197 56442479 53846773 52496918 51851036 50300049 49408781 48934477
 [9] 48796599 48421216

Smallest eigenvalues:
 [1]   0.4027470   0.3913490   0.3912340   0.3549024   0.3345217   0.2203419
 [7]   0.1646664   0.1471640  -1.5741631 -17.6398554

Largest  eigenvalues:
 [1] 60285641 56712810 53985092 52369038 52157164 50697908 48853087 48819044
 [9] 48681455 48038201

Smallest eigenvalues:
 [1]  0.4004761  0.3869652  0.3635221  0.3356740  0.3243954  0.2000877
 [7]  0.1476040 -0.1955125 -0.6150248 -4.2024429

Largest  eigenvalues:
 [1] 59812972 57092889 54203771 52368371 52307191 50603846 49535452 48843768
 [9] 48675241 48495198

Smallest eigenvalues:
 [1]  0.3741883  0.3529521  0.2865198  0.2237121  0.1821920  0.1820760
 [7]  0.1573903  0.1555990 -0.2084509 -1.2776487

Largest  eigenvalues:
 [1] 61180320 56600847 54224753 52760614 52020529 50594171 49424142 48972549
 [9] 48900138 48659975

Smallest eigenvalues:
 [1]   0.30522987   0.24206191   0.20856040   0.18958943   0.17792456
 [6]   0.14593476   0.12149449   0.09310473  -0.97997359 -20.22982331

Largest  eigenvalues:
 [1] 59445581 56502242 53819902 51890979 51829167 50194952 49100885 49045086
 [9] 48439754 48222412

Smallest eigenvalues:
 [1]  0.4330956  0.3805700  0.3575331  0.3215187  0.3122891  0.2919843
 [7]  0.1638085  0.1630907  0.0970133 -0.5891288

Largest  eigenvalues:
 [1] 61928111 56812792 54570889 53711681 51691880 50326287 49951928 49211543
 [9] 48741124 48327910

Smallest eigenvalues:
 [1]  0.3746639  0.3261630  0.2986129  0.2855983  0.2763041  0.2308618
 [7]  0.1617434  0.1291869 -1.3768379 -3.3911655

Largest  eigenvalues:
 [1] 61536822 57328995 54375096 53350174 52605998 51207740 49927757 49634134
 [9] 49504649 48528815

Smallest eigenvalues:
 [1]  0.37584788  0.37563116  0.30801611  0.28209525  0.24154831  0.15232508
 [7]  0.08178809  0.06403454 -0.09600118 -0.61170927

Largest  eigenvalues:
 [1] 59935746 56942657 54189239 52478243 52142814 50536525 49592028 48875859
 [9] 48775114 48125252

Smallest eigenvalues:
 [1]  0.3286931  0.2923529  0.2466297  0.1865464  0.1274534  0.1204055
 [7] -0.3336186 -1.9380959 -2.2669762 -7.7087225

Largest  eigenvalues:
 [1] 59117134 56474754 54155245 52622907 51533530 51070816 49804218 49392423
 [9] 48633976 48027668

Smallest eigenvalues:
 [1]  0.29346765  0.25949488  0.23008176  0.19551164  0.13151404  0.11307123
 [7] -0.06695442 -0.14504181 -3.19612657 -4.10930947

Largest  eigenvalues:
 [1] 60856879 56523720 54236215 53014689 51955050 50616992 49172279 48997313
 [9] 48878267 48429473

Smallest eigenvalues:
 [1]  0.37163535  0.31590923  0.27117154  0.23427003  0.23409090  0.16723556
 [7]  0.10481618  0.09935329  0.03574874 -5.14496972

Largest  eigenvalues:
 [1] 60582821 57365093 54610364 53202023 52616935 51062362 49778748 49541943
 [9] 49483622 48771969

Smallest eigenvalues:
 [1]  0.526958768  0.475773384  0.474013500  0.470767771  0.320339522
 [6]  0.263306778  0.223180161  0.184423444  0.134478689 -0.009004654

Largest  eigenvalues:
 [1] 61642439 56811724 54111425 53052201 51637509 49993573 49429580 48966249
 [9] 48832820 48288986

Smallest eigenvalues:
 [1]  0.42795890  0.36226957  0.35845374  0.32646872  0.31025624  0.30599406
 [7]  0.25427064 -0.02183352 -0.24942632 -4.59847699

Largest  eigenvalues:
 [1] 60294124 56554801 54163593 52530563 51730989 50120401 49086579 48951448
 [9] 48777579 48244995

Smallest eigenvalues:
 [1]  0.19873295  0.17806241  0.08600430  0.07799111 -0.06940455 -0.41468371
 [7] -0.58604974 -2.41330914 -2.80019782 -7.55021174

Largest  eigenvalues:
 [1] 62107000 57054980 54254144 53020101 52238964 50874691 49502221 49470183
 [9] 48896208 47839744

Smallest eigenvalues:
 [1]   0.3849546   0.3391538   0.1784226   0.1453718   0.0438147  -0.1038324
 [7]  -0.6407237  -1.6964340  -3.6561347 -21.0935763

Largest  eigenvalues:
 [1] 61325182 56777647 53838558 52921271 52038218 50397788 49330859 49206124
 [9] 48677509 48021891

Smallest eigenvalues:
 [1]   -0.6801403   -0.8250202   -1.8280455   -4.7721806   -8.6429795
 [6]  -42.0608876  -43.3148551  -45.6237067  -88.0467525 -144.4625258

Largest  eigenvalues:
 [1] 62698414 55913107 53637902 53411140 51193627 49690310 49529330 49266034
 [9] 48786510 48537575

Smallest eigenvalues:
 [1]   0.2262604   0.2216863   0.2053162   0.1238122   0.1109405   0.1104616
 [7]  -0.2601667  -0.4467474  -2.7332768 -18.5144519

Largest  eigenvalues:
 [1] 59395684 55710352 53096211 52074596 51137468 49706707 48690229 48285013
 [9] 48162105 47281996

Smallest eigenvalues:
 [1]  0.45958017  0.42323968  0.38100435  0.27113273  0.17136275  0.16110600
 [7]  0.13825267  0.02147330 -0.04946506 -4.39292346

Largest  eigenvalues:
 [1] 58767333 56693373 54048265 51907982 51712536 50379924 49223079 48936421
 [9] 48486101 48192022

Smallest eigenvalues:
 [1]  0.4460233  0.3324391  0.3306288  0.2896460  0.2675674  0.2463477
 [7]  0.2323300  0.1987867 -0.5104327 -0.7131444

Largest  eigenvalues:
 [1] 59822899 57008563 54132452 52641311 52312987 50816363 49319994 49205728
 [9] 48945765 48433414

Smallest eigenvalues:
 [1]  0.52399669  0.51852709  0.45419601  0.44204388  0.37564924  0.27643631
 [7]  0.18977572  0.02305043 -0.06354444 -0.46642052

Largest  eigenvalues:
 [1] 61620083 57477877 54842185 53167590 52225561 50797453 49642442 49538767
 [9] 49339365 48850474

Smallest eigenvalues:
 [1]  0.46220688  0.43345056  0.41204641  0.35985893  0.28472452  0.24642175
 [7]  0.19398944  0.12013317  0.06910627 -0.11376863

Largest  eigenvalues:
 [1] 61941747 57122879 54969705 53265729 52509792 50710966 49803154 49719131
 [9] 49205633 48664609

Smallest eigenvalues:
 [1]  0.4717943  0.4551337  0.3340419  0.3086120  0.2758056  0.2510398
 [7]  0.2151098  0.2072384  0.2050866 -0.2411751

Largest  eigenvalues:
 [1] 61597967 56706900 54559772 53267203 51687750 50466046 49657236 49078430
 [9] 48777874 48382915

Smallest eigenvalues:
 [1]  0.2630521  0.2595272  0.2189682  0.2146682  0.2020538 -0.2935609
 [7] -0.4503623 -0.8564189 -1.4259427 -7.2469401

Largest  eigenvalues:
 [1] 61879845 57268028 54625676 54103238 52217394 50678058 50343672 50070444
 [9] 48848681 48559730

Smallest eigenvalues:
 [1]   0.4698739   0.4416851   0.3713047   0.3238198   0.2898404   0.2850621
 [7]   0.1749582  -0.2354831  -3.9899517 -32.4261345

Largest  eigenvalues:
 [1] 60283815 56579684 53921454 52613024 52433231 50938210 49067516 48982943
 [9] 48799222 48265109

Smallest eigenvalues:
 [1]  0.45071049  0.44306643  0.41914692  0.36654760  0.32449349  0.29723858
 [7]  0.21437954  0.08412595 -0.05640778 -0.20523915

Largest  eigenvalues:
 [1] 60993718 57192905 54537919 52682157 51998353 50624117 49392022 49182895
 [9] 49037928 48619960

Smallest eigenvalues:
 [1]   0.4885786   0.4607187   0.3937427   0.3145667   0.2561769   0.2323242
 [7]   0.2177278   0.1845565  -0.2942461 -10.5128529

Largest  eigenvalues:
 [1] 61573701 56971220 54513295 53834944 52111309 50156357 50057324 49331684
 [9] 49067827 48367919

Smallest eigenvalues:
 [1]  0.4021701  0.3784051  0.2922592  0.2748855  0.2096465  0.1866577
 [7]  0.1498187  0.0583667 -0.1502983 -3.1108515

Largest  eigenvalues:
 [1] 59368971 57172142 54015351 52632929 52604459 51074285 49672880 49608468
 [9] 48781183 48575522

Smallest eigenvalues:
 [1]  0.39459183  0.36623610  0.26832882  0.26721891  0.20068006  0.07691399
 [7] -0.38678943 -0.52973956 -2.91451124 -3.32011068

Largest  eigenvalues:
 [1] 62363843 56857527 54812335 53449109 51930834 50941960 49824900 49569345
 [9] 49423267 48951640

Smallest eigenvalues:
 [1]  0.3903445  0.3901906  0.3393929  0.3160973  0.3000504  0.2731530
 [7]  0.1814825  0.1375826 -0.9476045 -3.0360224

Largest  eigenvalues:
 [1] 62428415 57468260 54785938 53996326 52469858 50592401 50331304 49530302
 [9] 49493212 48707229

Smallest eigenvalues:
 [1]   0.4465162   0.4355504   0.3443253   0.3088987   0.2951879   0.1100454
 [7]   0.1012690  -0.3946835  -0.5110460 -13.9277431

Largest  eigenvalues:
 [1] 61888831 56532540 53682788 52811733 51682143 50101369 49138148 49037133
 [9] 48644492 48093471

Smallest eigenvalues:
 [1]  0.436631473  0.427000005  0.368914047  0.312638306  0.289951990
 [6]  0.249490433  0.106535110  0.009602588 -0.182603810 -0.422015364

Largest  eigenvalues:
 [1] 60552591 56622673 54502925 53188939 51598308 50244902 49525267 49367824
 [9] 48802052 48725464

Smallest eigenvalues:
 [1]  0.55654102  0.50755541  0.46968907  0.38649047  0.38068972  0.35551759
 [7]  0.33565268  0.04322577 -0.11273736 -0.18183394

Largest  eigenvalues:
 [1] 61115955 57213539 54492847 53153258 52150857 50766730 49438822 49382438
 [9] 49229822 48288623

Smallest eigenvalues:
 [1]  0.260533983  0.163364417  0.158795517  0.146401631  0.069356093
 [6]  0.017175141  0.002324824 -0.033940530 -0.295170122 -2.055072540

Largest  eigenvalues:
 [1] 56852266 56656292 53964208 52532893 50810819 50565899 49346267 48731173
 [9] 47998609 47724181

Smallest eigenvalues:
 [1]   0.29118347   0.28489733   0.28026174   0.25999018   0.08777053
 [6]  -0.11785590  -0.70060267  -3.49331544 -13.64811248 -17.56523748

Largest  eigenvalues:
 [1] 58976104 56720752 53939609 52043243 51642946 50375582 49123811 48879845
 [9] 48363657 48273697

Smallest eigenvalues:
 [1]  0.48953567  0.45197409  0.42140663  0.40045530  0.39605595  0.36301187
 [7]  0.32425021  0.22670188  0.08065016 -0.29537116

Largest  eigenvalues:
 [1] 59845595 56507351 53564012 52372950 51937572 50406851 49445784 48538684
 [9] 48429256 47745555

Smallest eigenvalues:
 [1]  0.48596488  0.46292815  0.37398289  0.32645640  0.27524587  0.26239896
 [7]  0.19375040  0.07218173 -0.05151682 -0.24814098

Largest  eigenvalues:
 [1] 61402191 56538695 54325703 52784237 51753876 50290613 49302344 48650704
 [9] 48586047 47971453

Smallest eigenvalues:
 [1]  0.42433499  0.34175174  0.29165675  0.25529057  0.21170713  0.15614671
 [7]  0.14555489  0.09361946 -1.00763621 -5.28750324

Largest  eigenvalues:
 [1] 61347904 57101025 54869403 53008588 52416003 51169388 49722472 49443542
 [9] 49299307 48917797

Smallest eigenvalues:
 [1]   0.36643533   0.31333113   0.26496466   0.17868642   0.16239341
 [6]   0.05113204  -0.25285174  -1.04615977  -2.54992736 -29.31745335

Largest  eigenvalues:
 [1] 61505028 56710982 54331961 52863980 52323701 50474148 49793880 49205923
 [9] 49137344 48947432

Smallest eigenvalues:
 [1]  0.447639936  0.382680277  0.323319125  0.227768204  0.149650318
 [6]  0.001436324 -0.013990639 -0.458823225 -5.382201337 -7.052337114

Largest  eigenvalues:
 [1] 62318267 57039533 54314831 53945887 51779894 50227428 50128445 48899879
 [9] 48711076 47763870

Smallest eigenvalues:
 [1]   0.36210018   0.35904707   0.32408736   0.18341260  -0.05317542
 [6]  -0.16817783  -0.24250663  -1.23932180  -2.24377750 -18.99911887

Largest  eigenvalues:
 [1] 59100924 56062632 53765964 52065397 51670865 50619171 49030326 48639058
 [9] 47932294 47576607

Smallest eigenvalues:
 [1]  0.14366366  0.05681732 -0.11138906 -0.18001424 -0.19484689 -0.60424350
 [7] -0.64675070 -0.94448524 -1.16014157 -1.17947928

Largest  eigenvalues:
 [1] 62148907 56530898 54308376 53775302 51509585 50270909 50004280 49283108
 [9] 48849192 48536242

Smallest eigenvalues:
 [1]  0.4640112  0.4528071  0.3865665  0.2336814  0.1570571  0.1517641
 [7]  0.1281990 -0.2479216 -1.0852059 -6.7204959

Largest  eigenvalues:
 [1] 61332933 57424842 53955278 53464735 52700835 50780343 50032681 49500494
 [9] 49296992 48500308

Smallest eigenvalues:
 [1]  0.339175511  0.307912971  0.307208770  0.199144661  0.156294940
 [6]  0.139293495  0.130744065 -0.003598397 -0.196524446 -1.657573122

Largest  eigenvalues:
 [1] 58027611 56981897 53981192 52718677 50905419 50725588 49342560 48417841
 [9] 47780163 47688626

Smallest eigenvalues:
 [1]   0.2793720   0.2352363   0.1989567   0.1710637   0.1501798  -0.7099137
 [7]  -6.0949207  -6.3589111  -9.1482238 -39.2491201

Largest  eigenvalues:
 [1] 59811521 56491167 53820843 52899871 51765049 50076012 49412384 49096790
 [9] 48952380 48377946

Smallest eigenvalues:
 [1]  0.549759838  0.504900627  0.476635716  0.390003195  0.356372543
 [6]  0.347380444  0.325125089  0.316424075  0.266936507 -0.006116805

Largest  eigenvalues:
 [1] 60078706 56940455 54198162 52531248 52374660 50791948 49119881 48910229
 [9] 48826398 48013635

Smallest eigenvalues:
 [1]   0.38784599   0.32083920   0.26631119   0.14999510   0.03100831
 [6]  -0.61933901  -1.79219047  -3.25251313 -11.46399409 -19.10913050

Largest  eigenvalues:
 [1] 60285230 56358518 53753803 52551106 51980443 50499249 49518830 49193290
 [9] 48699352 48320638

Smallest eigenvalues:
 [1]   0.4435208   0.3520587   0.2974127   0.2551893   0.2288605   0.1443867
 [7]   0.0694762  -0.5085564  -1.1207016 -18.5116352

Largest  eigenvalues:
 [1] 60400168 56877356 53892888 52929407 52184277 50512210 49908089 49115168
 [9] 49044229 48802320

Smallest eigenvalues:
 [1]  0.5333649  0.4755432  0.4133360  0.4018409  0.3810956  0.3547434
 [7]  0.2703130  0.1411500  0.1136397 -0.0358267

Largest  eigenvalues:
 [1] 58584933 57411956 54424324 52959806 51450167 51146218 49551412 49371717
 [9] 48497421 47977790

Smallest eigenvalues:
 [1]  0.31764977  0.25853021  0.23470100  0.22189263  0.19157742  0.17745888
 [7]  0.06121566 -0.56323065 -0.81808028 -3.90698733

Largest  eigenvalues:
 [1] 61481185 57346391 54626891 53659179 52890198 51388639 49964974 49700971
 [9] 49411590 48659591

Smallest eigenvalues:
 [1]  0.47641663  0.35432400  0.32609368  0.28310366  0.27358396  0.27355493
 [7]  0.12530882 -0.07098368 -0.12279130 -5.72540601

Largest  eigenvalues:
 [1] 59093092 56266150 53498621 52142210 51349941 49879261 48881942 48558201
 [9] 48374190 48002228

Smallest eigenvalues:
 [1]   0.38390521   0.27367857   0.26061777   0.16204851   0.01257977
 [6]  -0.62844663  -1.20956883  -3.56087148 -20.59333590 -34.16226829

Largest  eigenvalues:
 [1] 60902431 56460794 53134343 53087743 51311845 49720924 49275072 48896458
 [9] 48739715 47947326

Smallest eigenvalues:
 [1]  0.4097731  0.4051816  0.3785287  0.3591862  0.2946844  0.2721150
 [7]  0.2589106  0.2406565  0.1819014 -1.1173823

Largest  eigenvalues:
 [1] 60077495 56297999 53688644 52418559 51691157 50284136 48864657 48717926
 [9] 48284317 47628659

Smallest eigenvalues:
 [1]  0.45047281  0.41015872  0.39756197  0.38943886  0.38160479  0.16588583
 [7]  0.16189752  0.09771213  0.06718701 -0.12993299

Largest  eigenvalues:
 [1] 61095825 57293261 54225411 53219838 52416428 50809656 49966312 49333671
 [9] 49323751 49052566

Smallest eigenvalues:
 [1]  0.54850374  0.53135245  0.50275939  0.44642900  0.44155686  0.36090623
 [7]  0.35871315  0.33571241  0.21521167 -0.05471739

Largest  eigenvalues:
 [1] 60420813 57286119 54628617 52673949 52630859 50879071 49732959 49123521
 [9] 49055113 48441678

Smallest eigenvalues:
 [1]  0.5447109  0.4878263  0.4863066  0.4268897  0.3568845  0.3309560
 [7]  0.3065167  0.2010307  0.1462200 -8.8785981

Largest  eigenvalues:
 [1] 60163228 56804659 54101596 52754821 52375271 50832973 49620835 49067479
 [9] 48890030 48151958

Smallest eigenvalues:
 [1]   0.26790295   0.23910157   0.22179608   0.07719870   0.03627669
 [6]   0.01945338  -0.90492194  -0.93704521  -0.94525045 -15.05997686

Largest  eigenvalues:
 [1] 58957316 56405039 53386010 52300613 51791320 50228594 49268228 49112759
 [9] 48278832 48103191

Smallest eigenvalues:
 [1]   0.3353948   0.2543446   0.2524597   0.2505750   0.2238432   0.1460797
 [7]  -0.1885191  -0.6325138  -5.3688326 -11.6301707

Largest  eigenvalues:
 [1] 60061773 56497743 53343176 52433954 52073134 50476958 49187085 48635308
 [9] 48386963 47721259

Smallest eigenvalues:
 [1]  0.48178706  0.45544995  0.40896900  0.38827427  0.29736962  0.19858588
 [7]  0.16091296  0.10801610 -0.09518595 -1.11474871

Largest  eigenvalues:
 [1] 60173019 56528922 54147633 52657320 51725081 50952280 49509551 49256941
 [9] 48353770 48146081

Smallest eigenvalues:
 [1]  0.43163787  0.38054631  0.33210746  0.32035137  0.31477398  0.28584600
 [7]  0.23353781  0.10434569 -0.05329913 -3.08974048

Largest  eigenvalues:
 [1] 62252324 57063421 54209754 53185784 52215329 50435998 49547412 48981006
 [9] 48797587 48412911

Smallest eigenvalues:
 [1]  0.42148238  0.40905621  0.27409166  0.26120059  0.21317944  0.20203543
 [7]  0.03471340 -0.02042252 -0.64588415 -1.91713842

Largest  eigenvalues:
 [1] 60673275 58062415 54138265 52962157 52929630 51230616 50343122 49207146
 [9] 49058611 48863892

Smallest eigenvalues:
 [1]  0.46095383  0.44457359  0.29982216  0.25504081  0.10874690  0.10403961
 [7] -0.05483162 -2.54237391 -2.73523559 -8.33702123

Largest  eigenvalues:
 [1] 59998629 56389740 53761474 52511336 51721979 50244670 49111109 48686836
 [9] 48538131 47732093

Smallest eigenvalues:
 [1]  0.47158431  0.45799175  0.33368068  0.30414562  0.26854217  0.24957315
 [7]  0.24324980  0.09508194  0.08057482 -1.01592687

Largest  eigenvalues:
 [1] 61781827 57089315 54482363 53956655 52401089 50941922 50175064 49782786
 [9] 49170977 48579451

Smallest eigenvalues:
 [1]  0.5098786  0.4465045  0.3879235  0.3078002  0.2615741  0.2552321
 [7]  0.2409576  0.1077741 -0.4290085 -1.4614653

Largest  eigenvalues:
 [1] 61925021 56411071 53542487 53396024 51439195 49716816 49614202 48849052
 [9] 48651802 48054131

Smallest eigenvalues:
 [1]   0.39622642   0.34405737   0.33027956   0.27819052   0.20873570
 [6]   0.07909117  -0.01269290  -1.02854220 -15.61452221 -19.39787167

Largest  eigenvalues:
 [1] 63061551 56864627 54809677 53896933 51631080 50248701 49790132 49552380
 [9] 48973727 48595372

Smallest eigenvalues:
 [1]  0.5423656  0.4910305  0.3444046  0.3069521  0.2680991  0.2579143
 [7]  0.2365904  0.2308456  0.1825648 -0.2020273

Largest  eigenvalues:
 [1] 62285603 56842489 54656757 53616303 52233999 50817500 50044193 49268544
 [9] 49118765 48343122

Smallest eigenvalues:
 [1]  0.56142911  0.53773567  0.52086709  0.49501931  0.42443595  0.30871022
 [7]  0.29925135  0.09509862  0.02037768 -0.32438306

Largest  eigenvalues:
 [1] 59509079 56572930 53618587 51829487 51728805 50057614 49029657 48471805
 [9] 48192120 47922658

Smallest eigenvalues:
 [1]   0.33949217   0.33803577   0.20666739   0.18366437   0.06969104
 [6]  -0.13261974  -0.40391647  -8.39635927 -16.78613768 -27.70082206

Largest  eigenvalues:
 [1] 60592441 56358036 53918962 52865285 51481458 50198923 49216932 49034845
 [9] 48785509 48315967

Smallest eigenvalues:
 [1]  0.5252320  0.4068926  0.3678924  0.2888089  0.2776018  0.2107020
 [7]  0.2004570 -0.2433275 -0.2588334 -0.4191841

Largest  eigenvalues:
 [1] 62757182 57525160 55160255 54666312 52396290 50883688 50766379 50096961
 [9] 49608110 49125633

Smallest eigenvalues:
 [1]  0.34200906  0.29045965  0.25533998  0.23016847  0.17769350  0.06670765
 [7] -0.01802079 -0.10795047 -1.09399591 -6.00853886

Largest  eigenvalues:
 [1] 60809287 56408096 53917298 52676513 51865352 50502337 49198363 48874516
 [9] 48798061 48242631

Smallest eigenvalues:
 [1]   0.2971786   0.2794462   0.2578279   0.2487571   0.1793941  -0.2017744
 [7]  -0.8718174  -1.6391411  -4.9906278 -11.6318728

Largest  eigenvalues:
 [1] 60985286 57102378 54525156 52964539 52720729 51316453 49969974 49646572
 [9] 49292600 48902220

Smallest eigenvalues:
 [1]  0.50971424  0.46053441  0.33399340  0.30219284  0.28981686  0.27723250
 [7]  0.24858656 -0.01027211 -0.32022824 -0.67075791

Largest  eigenvalues:
 [1] 60704998 57030454 54377220 52904816 52179012 50768238 49389217 49372898
 [9] 49226104 48435867

Smallest eigenvalues:
 [1]  0.4402515  0.4049418  0.3474676  0.2887192  0.2820669  0.2164072
 [7]  0.1234106  0.1167003 -0.4638426 -1.5059732

Largest  eigenvalues:
 [1] 59857237 57311806 54367127 52655927 52068086 50667817 49735715 49183565
 [9] 48969577 48828793

Smallest eigenvalues:
 [1]   0.314030622   0.285601403   0.259711788   0.239102235   0.161113736
 [6]   0.009876714  -0.605135381  -5.271492951  -6.617853614 -19.113927369

Largest  eigenvalues:
 [1] 61243047 56982822 54174588 52932402 52612589 50686177 49345786 49244404
 [9] 49207540 48460126

Smallest eigenvalues:
 [1]  0.31511518  0.24385121  0.23850909  0.20758819  0.18241314  0.15758979
 [7]  0.07120119 -0.46825107 -0.62621139 -3.16036797

Largest  eigenvalues:
 [1] 59349775 56280840 53975617 51986685 51807131 50408657 48898540 48694432
 [9] 48324891 48070235

Smallest eigenvalues:
 [1]  0.4508281  0.4423478  0.4225551  0.4146955  0.4090791  0.3148231
 [7]  0.3146502  0.2606874  0.2296801 -0.2237024

Largest  eigenvalues:
 [1] 60941272 56468751 53539636 52865900 51893150 50281783 49173924 48828301
 [9] 48637290 47919746

Smallest eigenvalues:
 [1]  0.4347725  0.3627567  0.3291757  0.3134036  0.3115428  0.2749950
 [7]  0.2477781  0.2199183  0.1421373 -0.2857909

Largest  eigenvalues:
 [1] 61271813 56815048 53730287 52875327 52038043 50337037 49246212 49037824
 [9] 48876943 48218396

Smallest eigenvalues:
 [1]  0.4910655  0.4890154  0.4360432  0.3191403  0.2616882  0.2271939
 [7]  0.2191214  0.1988822  0.1396233 -0.5111051

Largest  eigenvalues:
 [1] 60800877 57771715 54261069 53386073 52964523 51212364 50423100 49603599
 [9] 49378913 48774721

Smallest eigenvalues:
 [1]  0.56772685  0.53136156  0.48970770  0.36706839  0.32119377  0.28510216
 [7]  0.25532904  0.19250793  0.05833616 -0.14891229

Largest  eigenvalues:
 [1] 60343529 56827662 54024625 52544327 52150922 50289480 49491577 48943118
 [9] 48831098 48152604

Smallest eigenvalues:
 [1]   0.20834974   0.18960037   0.13656326   0.11928204   0.01317776
 [6]  -0.03442447  -1.30962481  -4.15751099 -26.22441190 -33.70775313

Largest  eigenvalues:
 [1] 60314777 57038021 54011562 52318541 51684195 50727284 49161274 48889373
 [9] 48664044 48015788

Smallest eigenvalues:
 [1]   0.41824215   0.38153962   0.31328214   0.25768773   0.16123829
 [6]   0.01464603  -0.26533252  -0.40173305  -0.51126494 -20.63714505

Largest  eigenvalues:
 [1] 63311846 57073473 54437712 53727916 51812577 50197060 50062158 49427953
 [9] 49100895 48927738

Smallest eigenvalues:
 [1]  0.30232228  0.26997100  0.26240753  0.23583639  0.23050949  0.21737139
 [7]  0.06163849 -0.32711451 -1.94496454 -7.87675623

Largest  eigenvalues:
 [1] 61675428 55956342 54015043 53329432 51169866 49693470 49598128 48877129
 [9] 48632746 48044227

Smallest eigenvalues:
 [1]   0.38916819   0.38684856   0.30577739   0.17589424   0.10741200
 [6]   0.08766567   0.04284418  -2.47324938  -9.63713136 -24.21626619

Largest  eigenvalues:
 [1] 59899175 57355085 54281021 52972183 51832365 51315424 49905177 49111614
 [9] 48574248 48382498

Smallest eigenvalues:
 [1]   0.348059043   0.301915751   0.300416857   0.270096223   0.112456101
 [6]   0.001729192  -0.539484795  -4.512547760 -51.909515872 -52.961187649

Largest  eigenvalues:
 [1] 60600196 56700310 54494119 53178318 52210746 50618606 49529498 49304286
 [9] 49229472 48636373

Smallest eigenvalues:
 [1]  0.3182713  0.3025223  0.2713749  0.2322011  0.2196419  0.1975188
 [7]  0.1891580 -0.7996352 -6.6101499 -9.0374399

Largest  eigenvalues:
 [1] 60563900 56957752 54282467 53076469 52388597 51463878 50076769 49232548
 [9] 48682014 48518212

Smallest eigenvalues:
 [1]  4.689397e-01  4.682354e-01  4.388693e-01  3.655827e-01  3.496670e-01
 [6]  2.934439e-01  8.185994e-02 -7.043162e-04 -7.767521e-01 -1.520887e+01

Largest  eigenvalues:
 [1] 60896387 56987225 53702324 52796052 52384080 50812435 49276830 49163470
 [9] 48970573 48409355

Smallest eigenvalues:
 [1]  0.40632874  0.40126512  0.29345013  0.22006015  0.16052347  0.06023394
 [7] -0.05025302 -0.21568122 -0.25433145 -2.88296807

Largest  eigenvalues:
 [1] 59378654 56147099 53547902 52031358 51495051 50205615 48842588 48823149
 [9] 48009829 47871754

Smallest eigenvalues:
 [1]   0.355797393   0.280437357   0.223174516   0.162479591   0.138431972
 [6]   0.007023788  -0.746266959  -1.523684331  -4.681798899 -34.868754382

Largest  eigenvalues:
 [1] 62585711 57130987 54848305 53964617 52260428 50449782 50322939 50267455
 [9] 49027184 48873772

Smallest eigenvalues:
 [1]  0.16607192  0.14306791  0.06301988  0.01136553 -0.02101099 -0.07411093
 [7] -0.93007851 -1.50250834 -4.21593645 -7.19805001

Largest  eigenvalues:
 [1] 61677328 56415181 53991103 52346626 51588008 50112759 48820152 48558262
 [9] 48382751 47950519

Smallest eigenvalues:
 [1]  0.4347337  0.3949646  0.3911517  0.3799328  0.3620830  0.3164204
 [7]  0.2842868  0.1541302  0.1387818 -0.2894760

Largest  eigenvalues:
 [1] 60013886 57072989 54464831 52281232 51953373 50776904 49274807 49122951
 [9] 48491688 48365570

Smallest eigenvalues:
 [1]   0.33410650   0.25496856   0.22934880   0.10244216   0.04663886
 [6]  -0.12400820  -0.38103637  -3.68947051  -9.56906650 -14.27356981

Largest  eigenvalues:
 [1] 61331244 55971884 53377388 53075800 51226343 49816550 49218873 49008289
 [9] 48884827 47991241

Smallest eigenvalues:
 [1]  0.4324697  0.4058812  0.3484058  0.3326332  0.3158235  0.2315195
 [7]  0.2125285  0.1788258  0.1565272 -3.4889222

Largest  eigenvalues:
 [1] 61479838 56841967 54310852 53269393 51996114 50515089 49602465 49256943
 [9] 49058740 48351937

Smallest eigenvalues:
 [1]  0.40652559  0.35255020  0.28946028  0.26758903  0.19425038  0.18984491
 [7]  0.17046889  0.14286037 -0.07237851 -0.93400345

Largest  eigenvalues:
 [1] 58816222 56240981 53505957 51957971 51552587 50241008 48691149 48223308
 [9] 47891293 47551007

Smallest eigenvalues:
 [1]  0.47522129  0.43065724  0.36815529  0.22724140  0.22029721  0.09921582
 [7]  0.05796817 -0.80382553 -1.17622260 -5.26424778

Largest  eigenvalues:
 [1] 62508304 57392133 54573662 53786971 52297792 50630489 50034398 49791413
 [9] 49655409 48938738

Smallest eigenvalues:
 [1]  0.52867667  0.47774386  0.44832935  0.41773423  0.38808711  0.30479910
 [7]  0.30193801  0.29348330  0.24325279 -0.03169598

Largest  eigenvalues:
 [1] 61745790 56680071 53775274 53295266 51836711 50216010 49592638 49221439
 [9] 48490832 47896045

Smallest eigenvalues:
 [1]  0.50762341  0.43790942  0.36605507  0.36128962  0.35702117  0.29127374
 [7]  0.22368624  0.05506251 -1.49015120 -3.46774518

Largest  eigenvalues:
 [1] 61920464 56915126 54709804 53262066 52066457 50586621 49688353 49412124
 [9] 49078386 48568808

Smallest eigenvalues:
 [1]  0.5373217  0.4921865  0.3911930  0.3160646  0.3155764  0.2851261
 [7]  0.2301770  0.2091235  0.1528929 -0.5387546

Largest  eigenvalues:
 [1] 59885236 56386070 53927796 52242904 51921123 50612544 49381455 48527053
 [9] 48433312 47765034

Smallest eigenvalues:
 [1]  0.3193982  0.2742213  0.2158687  0.1347838  0.1324331 -0.2499680
 [7] -0.3543204 -0.4550118 -5.3538463 -6.7993108

Largest  eigenvalues:
 [1] 61491672 56579458 53821945 53200254 51796781 50229421 49489024 49097235
 [9] 48448762 48111195

Smallest eigenvalues:
 [1]   0.43597619   0.35529175   0.33484908   0.29948128   0.26956299
 [6]   0.24300472   0.20844940   0.06841585  -1.14762635 -25.66460462

Largest  eigenvalues:
 [1] 60613711 57268413 54403456 53001567 52417993 51224446 49872351 49354218
 [9] 49190286 48623926

Smallest eigenvalues:
 [1]  0.4457120  0.4265161  0.3292969  0.3132624  0.3118756  0.2643701
 [7]  0.2409427  0.2384810  0.2046856 -0.3320168

Largest  eigenvalues:
 [1] 62088896 56185033 53272296 53206329 51522431 49739559 49527626 48785877
 [9] 48726901 48164591

Smallest eigenvalues:
 [1]  0.50525860  0.48665512  0.40186560  0.31861229  0.31623167  0.26425118
 [7]  0.17512966  0.17439243  0.06677018 -0.18584037

Largest  eigenvalues:
 [1] 58926610 56239984 53755090 51832699 51823323 50253530 48982801 48781276
 [9] 48187672 47839228

Smallest eigenvalues:
 [1]   0.30335962   0.27107458   0.22332071   0.12996096   0.12941904
 [6]   0.11065529   0.03322996  -3.18566404  -7.80800125 -11.10937003

Largest  eigenvalues:
 [1] 60015326 56087388 53942611 52558602 51751557 50119987 49036210 49007735
 [9] 48704744 48077439

Smallest eigenvalues:
 [1]   0.21849841   0.21006266   0.19585000   0.18335438   0.06734078
 [6]   0.06555411  -1.38074122  -2.68187884 -17.36305360 -22.25990004

Largest  eigenvalues:
 [1] 61614453 56736952 54078825 53895031 51404379 50131020 50093782 49155341
 [9] 48918451 48434383

Smallest eigenvalues:
 [1]  0.454075098  0.375293298  0.343175203  0.293986910  0.269019008
 [6]  0.170290433  0.126068577  0.008295461 -0.173063125 -1.066218434

Largest  eigenvalues:
 [1] 62443975 57213729 54764481 54107169 52154885 50570665 50394932 49512479
 [9] 49039240 48586900

Smallest eigenvalues:
 [1]  0.47654224  0.47405328  0.40542717  0.36764964  0.32185130  0.27098173
 [7] -0.02796257 -0.17387545 -0.18435590 -4.93877290

Largest  eigenvalues:
 [1] 59148813 56448666 53597542 51892494 51777076 50195110 48612268 48582809
 [9] 48191384 47694596

Smallest eigenvalues:
 [1]  0.39713474  0.34201073  0.32847861  0.27807093  0.14382892  0.11580935
 [7]  0.05878891  0.01022393 -0.10604584 -4.41011592

Largest  eigenvalues:
 [1] 62278253 56949902 54502763 53434316 51704548 50484321 49751664 49039133
 [9] 48821830 48448445

Smallest eigenvalues:
 [1]  0.3960974  0.3870214  0.3262925  0.3242616  0.2713724  0.2672649
 [7]  0.1985853  0.1914828  0.1416331 -0.9017774

Largest  eigenvalues:
 [1] 58484695 56931659 53890817 52249253 52170689 50633922 49059325 48957888
 [9] 48344596 47994280

Smallest eigenvalues:
 [1]  0.22984222  0.19473781  0.14173531  0.08821091  0.01332756 -0.05924591
 [7] -0.12893169 -0.75964906 -1.15871806 -1.75381416

Largest  eigenvalues:
 [1] 61932311 58385600 54770640 54085080 53457367 51722161 50337228 50198314
 [9] 50185155 49052813

Smallest eigenvalues:
 [1]   0.159957535   0.154988961   0.122071346   0.103456728   0.063762452
 [6]   0.009626203  -0.788769032 -13.226342707 -16.071954531 -77.367317742

Largest  eigenvalues:
 [1] 60568366 56202282 53647588 53571091 51687276 50271126 49650738 48838504
 [9] 48428981 47552671

Smallest eigenvalues:
 [1]   0.37639401   0.37411404   0.32809528   0.31800993   0.15742613
 [6]   0.15458086   0.05537723   0.02665379  -0.09724736 -21.76266455

Largest  eigenvalues:
 [1] 61970969 56900249 54184364 53280072 51803194 50154715 49581539 49298497
 [9] 48813472 48729453

Smallest eigenvalues:
 [1]  0.55835865  0.52289622  0.50149233  0.46242786  0.35588695  0.33479381
 [7]  0.11419346  0.07908370  0.07304577 -2.09408891

Largest  eigenvalues:
 [1] 60423281 56687405 53925098 52826634 51902484 50134608 49539128 49010750
 [9] 48854954 48421021

Smallest eigenvalues:
 [1]  0.4363871  0.4117852  0.3704457  0.2988169  0.2594690  0.2541040
 [7]  0.2472919  0.1106023 -0.3151061 -2.2463174

Largest  eigenvalues:
 [1] 62479444 56703453 54250297 53928835 51982903 50437601 50199427 49225524
 [9] 48735957 48305471

Smallest eigenvalues:
 [1]  0.39001993  0.34860670  0.32087413  0.18864156  0.15713521  0.13582955
 [7] -0.01219046 -0.11106249 -0.13627916 -4.26527530

Largest  eigenvalues:
 [1] 61128984 56732346 53992964 53217663 51869948 50121186 49515172 49379859
 [9] 48991461 48436081

Smallest eigenvalues:
 [1]  0.29914635  0.29173841  0.22432943  0.21983041  0.20580161  0.15986009
 [7]  0.11032136  0.06270175 -0.77642652 -5.48441529

Largest  eigenvalues:
 [1] 62649875 57155768 54490067 54333196 52636938 51381892 50331425 50040806
 [9] 49624009 48943595

Smallest eigenvalues:
 [1]  0.3409712  0.2995508  0.2935446  0.2316799  0.2293897  0.2238680
 [7]  0.1195191 -0.1214191 -1.7122432 -9.5012874

Largest  eigenvalues:
 [1] 62062317 56783429 54128018 53048092 51621695 50233678 49520405 48754257
 [9] 48727633 47854958

Smallest eigenvalues:
 [1]   0.23855246   0.23646101   0.19189648   0.09734688  -0.10149375
 [6]  -0.18790231  -0.18828343  -3.26314013  -4.40746644 -22.44208400

Largest  eigenvalues:
 [1] 61959735 57646600 55074580 53076393 53047418 51747009 50054201 49643340
 [9] 49520767 48609208

Smallest eigenvalues:
 [1]  0.54782995  0.50020943  0.46651002  0.40386465  0.26113576  0.22483265
 [7]  0.17237404 -0.03746588 -0.07045131 -0.52104164

Largest  eigenvalues:
 [1] 60706903 56869602 54595345 52467064 52329392 50918970 49807643 48991012
 [9] 48836898 48337336

Smallest eigenvalues:
 [1]  0.4107384  0.3703386  0.3533933  0.3300557  0.2686445  0.2315385
 [7] -0.1335953 -0.6894665 -0.6911723 -9.5687108

Largest  eigenvalues:
 [1] 61485116 57369993 54333168 53660042 52105644 50166396 50157911 49865260
 [9] 49127593 49011683

Smallest eigenvalues:
 [1]   0.29818195   0.28513261   0.25574607   0.17288593   0.13953916
 [6]   0.07527398   0.06827416  -2.79901952  -5.90286543 -19.79056468

Largest  eigenvalues:
 [1] 62092151 56285121 53498623 53488365 51552733 50158783 49607482 49283143
 [9] 48851897 48164440

Smallest eigenvalues:
 [1]   0.383494390   0.359194054   0.348828618   0.308043557   0.187171097
 [6]  -0.003795561  -0.131785008  -0.193868547  -2.548813603 -18.394154279

Largest  eigenvalues:
 [1] 59964097 55990257 53581110 51686824 51679979 50210190 48951708 48918447
 [9] 48063359 47914438

Smallest eigenvalues:
 [1]  0.480105662  0.470045790  0.460827249  0.336491777  0.243970141
 [6]  0.223312083  0.184523207  0.006941442 -0.150907437 -0.228801851

Largest  eigenvalues:
 [1] 63272550 57219429 54834797 54289989 52004004 50645927 50491490 49451821
 [9] 49283944 48787829

Smallest eigenvalues:
 [1]  0.37460795  0.35093166  0.33409953  0.33132392  0.31179075  0.24012342
 [7]  0.18126875  0.11475299  0.04580536 -0.01061992

Largest  eigenvalues:
 [1] 60249844 57321338 54270765 52964472 52243304 51189937 50310611 49404142
 [9] 49196141 48688708

Smallest eigenvalues:
 [1]  0.3954874  0.3369197  0.3149131  0.2860644  0.2648368  0.2517564
 [7]  0.2165180 -0.8853363 -1.4741663 -6.4369891

Largest  eigenvalues:
 [1] 61021795 56932466 54688868 53102247 52312690 50992720 49390527 49313578
 [9] 49245223 48589550

Smallest eigenvalues:
 [1]  0.46124141  0.34273903  0.30650608  0.27584418  0.25686014  0.22786718
 [7]  0.11179980  0.08336364 -0.09972070 -3.06198213

Largest  eigenvalues:
 [1] 60045626 56836281 54024820 52622129 52140874 50616641 49595008 48876672
 [9] 48803178 48009437

Smallest eigenvalues:
 [1]  0.38810326  0.32790431  0.32466401  0.30947199  0.22131191  0.21718657
 [7]  0.13572043  0.09753183 -0.05931946 -0.08945257

Largest  eigenvalues:
 [1] 61425016 57004572 54268286 53878091 51914423 50425227 50088409 49328219
 [9] 49103336 48302541

Smallest eigenvalues:
 [1]  0.4808768  0.4477533  0.3986728  0.3842572  0.3699377  0.2306832
 [7]  0.2297420  0.1736829  0.1178753 -1.0841523

Largest  eigenvalues:
 [1] 60813094 56710255 54238088 52724208 51944655 50254366 49223527 49171960
 [9] 49032194 48315009

Smallest eigenvalues:
 [1]  0.3535600  0.3408537  0.3101454  0.2916545  0.1873881  0.1350212
 [7] -0.2523438 -0.9252710 -0.9888521 -3.1518995

Largest  eigenvalues:
 [1] 61837632 57611809 54412002 53843953 53097169 51476929 50331822 49979942
 [9] 49617249 49335613

Smallest eigenvalues:
 [1]  0.5059704  0.4812803  0.4766706  0.4335792  0.3550847  0.3075314
 [7]  0.2778291  0.2522708  0.2293167 -0.3027754

Largest  eigenvalues:
 [1] 59948355 56610114 53505546 52558601 52029170 50214780 48870221 48821568
 [9] 48369744 47414848

Smallest eigenvalues:
 [1]  0.38034345  0.35545584  0.34592813  0.33273672  0.32648443  0.31745792
 [7]  0.28846999  0.16189176  0.13428060 -0.03288469

Largest  eigenvalues:
 [1] 61584032 56813073 54297019 52726826 52101652 50665274 49087892 49021156
 [9] 48847098 47902580

Smallest eigenvalues:
 [1]  0.33706078  0.21899162  0.18213287  0.17438290  0.16506014  0.15150083
 [7]  0.15115627  0.13450407  0.01476054 -1.25717332

Largest  eigenvalues:
 [1] 58541625 57066021 53970061 52817677 52019432 51050768 49665726 48799399
 [9] 48184684 47995465

Smallest eigenvalues:
 [1]   0.3190563   0.2938288   0.2856619   0.2089785   0.1863252   0.1368130
 [7]   0.1249840  -0.3696651  -0.5290861 -10.2357884

Largest  eigenvalues:
 [1] 60328162 56851709 54278718 52455654 52297597 50644645 49590427 49240832
 [9] 48855729 48538495

Smallest eigenvalues:
 [1]  0.4511547  0.3997581  0.3538266  0.3471897  0.3096604  0.3056124
 [7]  0.2294201  0.1702149 -1.8109910 -1.8842552

Largest  eigenvalues:
 [1] 62449256 57096866 54369385 54178792 52245220 50731708 50336783 49959531
 [9] 49613124 49275522

Smallest eigenvalues:
 [1]  0.34472456  0.33926289  0.32336987  0.30743851  0.25213531  0.22632663
 [7]  0.18835568  0.13517620  0.05189122 -0.36976699

Largest  eigenvalues:
 [1] 59460519 58011482 54661527 53432448 52696818 51740806 50578330 50086000
 [9] 49113356 48867280

Smallest eigenvalues:
 [1]   0.33114703   0.32095564   0.30484217   0.21789101   0.12444096
 [6]  -0.07116436  -0.26027412  -2.24406561  -6.45643860 -53.10448723

Largest  eigenvalues:
 [1] 57487998 56419185 53336004 52427585 50671607 50490045 49093795 48138150
 [9] 47392577 47308233

Smallest eigenvalues:
 [1]   0.2487038   0.1218874   0.0126370  -0.1063677  -0.3751204  -2.1610635
 [7]  -3.5344818 -10.5026740 -12.9080733 -38.4380439

Largest  eigenvalues:
 [1] 60011652 57027561 54132720 52829502 52394903 50931533 49920913 49542703
 [9] 48687130 48599236

Smallest eigenvalues:
 [1]  0.5043314  0.4674775  0.4438305  0.4184888  0.2617872  0.2281800
 [7]  0.2194518  0.1257092  0.1195882 -0.4065258

Largest  eigenvalues:
 [1] 61580201 57109972 53813061 53288774 52358517 50477069 49574754 49508185
 [9] 49391295 48785623

Smallest eigenvalues:
 [1]  0.29397676  0.28343614  0.28202910  0.27530875  0.20463956  0.07156716
 [7]  0.03669206 -0.02018551 -1.94313736 -4.95922472

Largest  eigenvalues:
 [1] 61308766 56327991 54178169 53081362 51476778 50313279 49459551 49330581
 [9] 48958272 48635424

Smallest eigenvalues:
 [1]  0.42860001  0.35267418  0.33539053  0.31460604  0.28888061  0.24218668
 [7]  0.17695307  0.02223382 -0.29773095 -0.57160497

Largest  eigenvalues:
 [1] 60003272 56476546 53764263 52636152 51935498 50304366 49011336 48979363
 [9] 48895585 48077438

Smallest eigenvalues:
 [1]  0.3558276  0.3517814  0.2753354  0.2611108  0.2215411  0.1735605
 [7]  0.1498920 -0.7989731 -1.9764232 -3.1533489

Largest  eigenvalues:
 [1] 60850880 57105435 53972151 53165966 52895460 51116548 49516853 49246506
 [9] 49049081 48262660

Smallest eigenvalues:
 [1]   0.25032698   0.24864823   0.19662907   0.19358242   0.06586161
 [6]  -0.08092775  -0.31459471  -0.64863961 -10.19658544 -68.90544984

Largest  eigenvalues:
 [1] 58459997 55730903 52918431 51715139 51444803 49714262 48728022 48423458
 [9] 47798431 47454382

Smallest eigenvalues:
 [1]  0.5358082  0.4961394  0.4092360  0.3545227  0.3436694  0.2927085
 [7]  0.2759035  0.2541941  0.1481678 -1.0055155

Largest  eigenvalues:
 [1] 60290689 56702836 53911717 52402961 52017677 50673730 49230352 49179069
 [9] 48700606 48346066

Smallest eigenvalues:
 [1]   0.4210492   0.4193421   0.3922454   0.3441325   0.3004120   0.2033589
 [7]  -0.0564633  -3.5679114  -9.9891876 -55.9477940

Largest  eigenvalues:
 [1] 59875544 57760215 54136097 52759751 52476478 50893122 49423083 49172527
 [9] 48923185 48335416

Smallest eigenvalues:
 [1]  0.46940503  0.39951203  0.37368832  0.36420294  0.25247354  0.22709284
 [7]  0.19153401  0.07257433  0.02402702 -0.04434930

Largest  eigenvalues:
 [1] 61783590 57900945 55129450 53820789 52453064 50777316 50100028 50010609
 [9] 49353870 48872391

Smallest eigenvalues:
 [1]  0.38379897  0.35492111  0.24568625  0.23418153  0.22972098  0.20332943
 [7]  0.13437010  0.02420657 -2.17283038 -2.51410862

Largest  eigenvalues:
 [1] 60868508 57347481 54551179 53414728 52588932 51099484 49954711 49569755
 [9] 49466249 48437955

Smallest eigenvalues:
 [1]  0.42714063  0.35157046  0.33711050  0.24169897  0.23614316  0.22021076
 [7]  0.10723145  0.03969452 -0.31057211 -1.59897258

Largest  eigenvalues:
 [1] 61887478 56805517 53898680 53891541 52036930 50448111 50104662 49358051
 [9] 49297896 48491635

Smallest eigenvalues:
 [1]    0.14256191    0.14250161    0.02342479   -0.24950722   -1.42897034
 [6]   -3.98634130   -5.55561035   -6.62603456   -6.63040944 -114.28439462

Largest  eigenvalues:
 [1] 59992263 56529620 53563024 52779672 52280943 50715776 49258468 49004822
 [9] 48907391 48203071

Smallest eigenvalues:
 [1]  0.4513500  0.3918543  0.3602837  0.3341270  0.3271343  0.3056630
 [7]  0.2714532  0.1672799  0.1055999 -0.6934877

Largest  eigenvalues:
 [1] 60622125 57237798 54466228 52697723 52267879 50774691 49212866 49169347
 [9] 49047962 48306048

Smallest eigenvalues:
 [1]  0.46959605  0.45872647  0.36557961  0.36470279  0.33003131  0.28049758
 [7]  0.27917951  0.13882972 -0.01067653 -0.03897265

Largest  eigenvalues:
 [1] 58850987 56475300 53658419 52354847 51338741 50582279 49110882 49008203
 [9] 48196325 47808108

Smallest eigenvalues:
 [1]  0.5144844  0.4536761  0.4371657  0.4112515  0.3374469  0.2929794
 [7]  0.2205514  0.1697489  0.1542738 -0.4354097

Largest  eigenvalues:
 [1] 60747911 57314365 54092350 52743931 52577360 50919821 49792884 49433942
 [9] 49057394 48808371

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	1.097739	0.5756892	41.5781	0.35	2.814556	1.640583

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

EDA ~ alt + n + body_temp + PM25

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- EDA_fd
covariates <- list(altitude = altitude_fd, 
                   noise = noise_fd,
                   temp_body = body_temperature_ENT_fd,
                   pollution = pollution25_fd)
path_plot <- 'figures/model_EDA_alt_noise_tempBody_PM25_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     noise = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     temp_body = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     pollution = list(nbetabasis = 80, norder = 4, lambda = 1e3))

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, HR = HR,
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 14.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 308 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	0.9471101	0.6771254	22.52582	0.425	5.772056	2.589453

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

EDA ~ alt + n + body_temp + PM1

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- EDA_fd
covariates <- list(altitude = altitude_fd, 
                   noise = noise_fd,
                   temp_body = body_temperature_ENT_fd,
                   pollution = pollution1_fd)
path_plot <- 'figures/model_EDA_alt_noise_tempBody_PM1_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     noise = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     temp_body = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     pollution = list(nbetabasis = 80, norder = 4, lambda = 1e3))

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, HR = HR,
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 14.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 322 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Smallest eigenvalues:
 [1]  0.14483019  0.13960402  0.12707429  0.09882543  0.09599995  0.06519062
 [7]  0.04430862  0.03099529 -3.92924016 -4.39570664

Largest  eigenvalues:
 [1] 48376187 45714509 42890947 42867486 41586334 40306422 39946535 39808216
 [9] 39037988 38887276

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	0.9455276	0.6887335	21.9582	0.555	5.737343	2.358661

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

EDA ~ noise + temp + body_temp

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- EDA_fd
covariates <- list(#altitude = altitude_fd, 
                   noise = noise_fd,
                   temp_body = body_temperature_ENT_fd,
                   temperature = temperature_fd)
path_plot <- 'figures/model_EDA_noise_temp_bodyTemp_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
                     #altitude = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     noise = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     temp_body = list(nbetabasis = 80, norder = 4, lambda = 1e3),
                     temperature = list(nbetabasis = 80, norder = 4, lambda = 1e3))

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, HR = HR,
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 23.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 182 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	0.9997611	0.5450801	14.49862	0.04	1.126926	1.18645

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

EDA ~ alt + noise + temp + body_temp

• First, we have to define some variables.
• Then, execute the cell below. It should compute everything :)

outcome <- EDA_fd
covariates <- list(altitude = altitude_fd, 
                   noise = noise_fd,
                   temp_body = body_temperature_ENT_fd,
                   temperature = temperature_fd)
path_plot <- 'figures/model_EDA_alt_noise_temp_bodyTemp_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 80, norder = 4, lambda = 1e5),
                     altitude = list(nbetabasis = 70, norder = 4, lambda = 1e3),
                     noise = list(nbetabasis = 70, norder = 4, lambda = 1e3),
                     temp_body = list(nbetabasis = 70, norder = 4, lambda = 1e3),
                     temperature = list(nbetabasis = 70, norder = 4, lambda = 1e3))

set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates, 
                            path_plot = path_plot, basis_params = basis_params)

outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
    assign(cov, model_1$covariates[[cov]])
}

############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)

############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic 
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome, 
                            covariates = covariates, path_plot = path_plot, HR = HR,
                            basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)

############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
            model_2$plots[[1]] / 
(model_2$plots[[2]] | model_2$plots[[3]]) 
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)

############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) 
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0

message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
    try({
        BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
        outcome_BS <- outcome[BS_sample]
        for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
        # define formula
        formula_BS <- paste0('outcome_BS ~ ')
        for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
        formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
        # fit the model
        model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
        # calculate and save betas
        for(j in 1:length(model_concurrent$betaestlist)) {
            beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
        i <- i + 1
        }, silent = TRUE)}

############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS, 
             n_beta = length(model_concurrent$betaestlist), 
             model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)

############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))

Final number of observations = 23.

Plotting the fitted curves  ...

Plotting the beta functions ...

Calculating the functional R^2 ...

Plotting the functional R^2 ...

Calculating the functional F-ratio test ...

[1] "Estimated Computing time = 232 seconds."

Plotting the results of the functional F-ratio test ...

DONE :-)

Calculating the bootstrap CI for beta functions ...

Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...

DONE :-)

model_2$df_res_metrics

A data.frame: 1 × 6

	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
95%	0.9835984	0.5460793	16.12738	0.17	1.579801	1.178132

Global envelope test

GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
    GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1, 
             nsim = nsim, model_concurrent = model_concurrent,
             beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
    GET_results[[j]] <- GET_res
}

options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)

save(GET_results, file = paste0(path_plot, '/GET_results.RData'))

Model comparison

Finally, we compare fitted functional models based on various criteria.

# Specify the models folders
models_path <- list.dirs(path = "figures/") |>
  (\(x) x[grepl("^figures/model_EDA.*_CENTERED$", x)])() |>
  sub("^figures/", "", x = _)

# Create a data frame where the characteristics will be stored
model_comparison <- data.frame(model = NA, N = NA, RMSE = NA, maxR2 = NA, integratedR2 = NA, 
                               pval = NA, qval = NA, Fobs = NA)

# Load all models 
for (model_path in models_path) {
    load(file = paste0("figures/", model_path, "/model.RData"), verbose = FALSE)
    model_comparison <- rbind(
        model_comparison, 
        c(substr(model_path, 7, nchar(model_path) - 9), 
          length(model_1$common_IDs), 
          unlist(as.vector(model_2$df_res_metrics))))
}

model_comparison <- model_comparison[-1, ] |> 
    mutate(N = as.numeric(N),
           RMSE = round(as.numeric(RMSE), 6),
           maxR2 = round(as.numeric(maxR2), 6),
           integratedR2 = as.numeric(integratedR2),
           pval = as.numeric(pval),
           qval = round(as.numeric(qval), 4),
           Fobs = round(as.numeric(Fobs), 4))
model_comparison[(order(model_comparison$RMSE)), ]

A data.frame: 28 × 8

	model	N	RMSE	maxR2	integratedR2	pval	qval	Fobs
	<chr>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
22	EDA_alt_noise_tempBody_PM1	14	0.945528	0.688733	21.958200	0.555	5.7373	2.3587
23	EDA_alt_noise_tempBody_PM25	14	0.947110	0.677125	22.525824	0.425	5.7721	2.5895
17	EDA_alt_noise_temp_acc	31	0.959756	0.533264	14.448738	0.090	1.1066	1.0144
21	EDA_alt_noise_temp_steps	31	0.967796	0.484247	13.279872	0.260	1.3471	0.9115
25	EDA_alt_noise_tempEntrant	19	0.971104	0.634487	14.239710	0.095	1.8896	1.6762
20	EDA_alt_noise_temp_speed	32	0.978453	0.498659	25.745133	0.765	1.3214	0.9233
24	EDA_alt_noise_tempEmpatica	32	0.980686	0.502600	11.136725	0.010	0.8105	0.9532
19	EDA_alt_noise_temp_bodyTemp	23	0.983598	0.546079	16.127379	0.170	1.5798	1.1781
12	EDA_alt_noise_speed_PM1	19	0.990957	0.582579	15.192438	0.215	2.7682	1.8955
13	EDA_alt_noise_speed_PM25	19	0.992560	0.574583	15.338634	0.190	2.6574	1.9415
29	EDA_noise_temp_bodyTemp	23	0.999761	0.545080	14.498624	0.040	1.1269	1.1864
11	EDA_alt_noise_speed	32	1.008945	0.399442	10.770685	0.765	1.2732	0.6518
5	EDA_alt_noise_acc_PM1	18	1.009266	0.649744	15.440150	0.245	3.0610	1.8601
6	EDA_alt_noise_acc_PM25	18	1.010421	0.660726	15.608628	0.200	2.8388	1.9379
18	EDA_alt_noise_temp_body	23	1.015597	0.456796	13.112231	0.285	1.3621	0.8815
26	EDA_alt_temp_body	28	1.017492	0.337989	6.511186	0.190	0.8153	0.5146
3	EDA_airpress_noise_temp	24	1.018808	0.412089	10.848122	0.540	1.3142	0.6740
8	EDA_alt_noise_pollution1	19	1.018820	0.547578	11.974803	0.415	1.9853	1.0370
4	EDA_alt_noise_acc	31	1.019642	0.441674	8.819600	0.235	0.9927	0.6200
9	EDA_alt_noise_pollution25	19	1.020716	0.555826	12.185977	0.410	2.0415	1.0578
10	EDA_alt_noise_Sex	31	1.021243	0.360871	8.206033	0.330	0.7591	0.4893
14	EDA_alt_noise_steps	31	1.023609	0.343626	7.898181	0.525	1.3688	0.6210
7	EDA_alt_noise	32	1.026654	0.356377	6.133042	0.265	0.6648	0.4472
27	EDA_alt_temp_pollution1	26	1.038146	0.546560	13.712147	0.065	1.4053	1.1640
28	EDA_alt_temp_pollution25	26	1.043578	0.512391	13.000250	0.095	1.3735	1.0466
2	EDA_airpress_noise	24	1.053468	0.337832	6.318836	0.790	1.1106	0.3901
16	EDA_alt_noise_steps_PM25	18	1.096776	0.575932	40.109877	0.480	2.6891	1.4899
15	EDA_alt_noise_steps_PM1	18	1.097739	0.575689	41.578101	0.350	2.8146	1.6406

write.csv(model_comparison[(order(model_comparison$RMSE)), ],
          file = "model_comparison_EDA_CENTERED.csv")